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Expansive Growth Processes

Within the microstructural model, hydration is represented as a three step cyclic process consisting of dissolution, diffusion, and reaction [7,12]. Material randomly dissolves from the cement surfaces in contact with water-filled pore space, diffuses within the capillary pore network, and reacts to form both C-S-H and CH. Once again, to reduce artificial edge effects, periodic boundaries are used during the "diffusion" process such that a species may exit one face (side) of the 3-D microstructure and enter the opposite face. After all material dissolved in one cycle has reacted, the next cycle is begun with a new dissolution. Correct volume stoichiometry is maintained explicitly based on data from Young and Hansen [14] by creating the correct number of "diffusing" C-S-H and CH species for each species of cement that dissolves. Solid C- S-H gel is allowed to form only on the surfaces of cement particles or on solid C-S-H formed earlier in the hydration. Conversely, CH forms by a nucleation and growth mechanism within the available pore space [7].

Pozzolanic reactions can be modelled by allowing the diffusing CH species to react at the silica fume particle surfaces to produce pozzolanic C-S-H according to [8]: On a volume basis, each unit volume of silica (fume) is capable of reacting with 2.08 volume units of CH to produce 4.6 volume units of pozzolanic C-S-H. Although reductions in the C/S ratio, from 1.7 to 1.4, have been observed in cements containing pozzolanic admixtures [15,16], to keep the model tractable, a constant C/S ratio of 1.7 has been used throughout for both primary C-S-H and pozzolanic C-S-H. Reaction stoichiometry is maintained volumetrically by counting the number of CH diffusing species that have reacted with the admixture particles, and then terminating the pozzolanic reaction when this number reaches 2.08 times the initial number of admixture volume units (pixels). Where experimental evidence (based on the amount of solid CH remaining at a given degree of hydration) in this study suggested that a lower pozzolanic reactivity should be assigned to the silica fume, the value of 2.08 was changed to a value of 1.33, to enable a meaningful comparison between simulation and experiment. This difference may imply that the density and/or stoichiometry of pozzolanic C-S-H are different from that of primary C-S-H, although no such distinction is made in the model.

Since the pozzolanic reaction is expansive (in terms of solids), volume stoichiometry is maintained by specifying a probability that two volume units of pozzolanic C-S-H are produced instead of one when a diffusing CH species encounters a reactive (pozzolanic) surface. Since each 2.08 volume units of CH should produce 3.6 volume units of pozzolanic C-S-H, in addition to the volume unit originally occupied by the silica fume, this probability of expansion is (3.6- 2.08)/2.08 = 0.73.