Induction Period Modelling

One of the amazing properties of cement-based materials (both portland cements and pure tricalcium silicate) is the induction period they exhibit when mixed with water. After a short burst of hydration, the material undergoes a dormant period where very little reaction occurs. Then the reactions accelerate and the material sets and strengthens into the hardened concrete. While several mechanisms have been proposed for this induction period, the hypothesis gaining favor recently is that the induction period is controlled by the nucleation and growth of the C-S-H phase [18]. To implement this process in the CEMHYD3D model, the early-time dissolution probabilities for all of the cement clinker phases (C₃S, C₂S, C₃A, and C₄AF) are made to be proportional to the square of the amount of C-S-H that has formed. As the C-S-H volume fraction increases, the calculated dissolution probabilities can not exceed the base dissolution probabilities (set in the array disbase in the program disrealnew).

To demonstrate that making the early dissolution probabilities proportional to some function of the C-S-H which has formed is a viable approach, a study was conducted using pure tricalcium silicate (C₃S) paste. Isothermal calorimetry measurements were made for w/c=0.4 C₃S pastes at three different temperatures (20 ºC, 30 ºC, and 40 ºC). For the hydration of C₃S, an activation energy of 33 kJ/mol was assumed. The measured heat release data was converted to degree of hydration assuming a heat of reaction of 517 J/g for C₃S [15]. In this case, the dissolution probabilities were made to be linearly proportional to the amount of C-S-H which has formed. As shown in Fig. 11, the agreement between the experimental measurements and model predictions is reasonable (particularly considering the signal/noise ratio present with the small calorimetry samples), suggesting that modelling the induction period by making initial dissolution probabilities proportional to the amount of formed C-S-H may be a reasonable approach. For cement, as opposed to pure C₃S, as will be illustrated in the Example Applications section, a better agreement to early time heat release data is obtained by using a parabolic instead of a linear proportionality between dissolution rates and amount of formed C-S-H.

  

Figure 11: Experimental (solid lines) and model predicted (dashed lines) hydration rates as a function of hydration temperature for a C₃S paste with w/c=0.4.