2. CEMHYD3D Modeling

The influence of limestone filler on cement hydration was modeled using a modified version of CEMHYD3D V. 2.0 [10, 11]. Both the chemical reactivity and the "fine filler" effects of the limestone were considered. Based on experimental observations in the literature [2, 6-9], the formation of a monocarboaluminate [AFmc− (CaO)₃(Al₂O3)· CaCO₃·11H₂O] phase in preference to a monosulfoaluminate [AFm− (CaO)₃(Al₂O₃)·CaSO₄· 12H₂O] phase was added by modifying the CEMHYD3D computer codes to include the following reaction:

This reaction favors the production of AFmc (and ettringite) over that of the conventional Afm phase in the presence of calcium carbonate. In the CEMHYD3D model, this reaction becomes active only when the initial calcium sulfate is depleted and the previously formed ettringite begins to convert to the Afm phase by reaction with more of the cement clinker aluminate phases. This is in general agreement with experimental observations [6, 7]. While other reaction paths could be written for the formation of AFmc in a cement-based system, the above scheme was chosen for its simplicity in implementation in the CEMHYD3D codes and the fact that it does yield the desired effect: the formation of the AFmc phase at the expense of the AFm phase. The calcium carbonate generally has a rather low reactivity (because of its low solubility), and in typical simulations using the updated CEMHYD3D codes, for a 20 % by mass fraction substitution of ground limestone for cement, only about 5 % of the limestone present reacts during the first ≈180 d of hydration.

Numerous researchers have noted an acceleration of the hydration of cement due to the addition of fine limestone or other fine particles [3, 12-14]. Apparently, the surfaces of the individual filler particles provide sites for the nucleation cement hydration products such as the calcium silicate hydrate gel (C-S-H) ²  that is the dominant hydration product in most hydrated portland cements. Thus, the first modification to CEMHYD3D to incorporate this effect has been to allow the precipitation of both C-S-H and calcium hydroxide (CH) hydration products on the surfaces of the limestone particles.

In Version 2.0 of the CEMHYD3D model [11], the "induction" period of cement hydration has been modeled by making the initial dissolution probabilities of all four of the major cement clinker phases (C₃S, C₂S, C₃A, and C₄AF) proportional to the volume of C-S-H that has formed (an autoacceleratory type of behavior [15]). The best fit to available experimental degree of hydration data for ordinary portland cements is obtained when these initial dissolution probabilities are proportional to the normalized volume of C-S-H (the volume of C-S-H formed divided by the volume of the initial cement present) raised to the second power [11]. To model the "fine filler" effect in pastes with limestone substitutions for cement, the early time dissolution probabilities in CEMHYD3D have been further modified to be also proportional to the ratio of the initial total (cement clinker and limestone) surface area divided by the initial cement clinker surface area, once again raised to the second power. Modeling the influence of the substituted filler in this manner implies that hydration during the induction period is "accelerated" (or the length of the induction period is decreased) when a thinner C-S-H layer is formed over a larger surface area. It could also imply that less time is needed for the calcium (and hydroxide) ions to build up to some critical concentration in solution when the initial C-S-H is "dispersed" over a larger surface area than that provided by the initial cement particles. While neither of these mechanisms were included directly in the CEMHYD3D model, making the initial dissolution rates proportional to the ratio of the surface areas as described above would be consistent with either of them, and would provide a simple approach for obtaining the desired effects. One could also consider a proportionality based on filler and cement clinker volumes, instead of surface areas. However, utilizing surface areas has the advantage that the fineness of the substituted filler, as well as its overall volume fraction, can influence the hydration.