## 4 Predictions for Compressive Strength Development of HVFA UhPC  
### Typical Compressive Strength Development  
Figure 7 shows typical compressive strength development (\(f_{c}^{\prime}(t)\)) normalized by 28-day compressive strength for UHPC mixture with _W/B_ of 0.16. In the same figure, predictions by empirical equations specified in _fib_ 2010 model [27] are also presented for comparisons. The compressive strength gains of UHPC cured under standard condition were significantly affected by R\({}_{f}\). With the increase in R\({}_{f}\), the strength gain rate (\(f_{c}^{\prime}(t)\)/\(f_{c}^{\prime}\)) at early ages tended to decrease whereas lower values for the rate were obtained at the long-term ages, showing a clear crossover behaviour. The rate at 3 days ranged between 0.79 and 0.82 for UHPC with R\({}_{f}\) = 0% and 0.39 and 0.48 for UHPC with R\({}_{f}\) = 70%. The corresponding values at 180 days ranged between 0.97 and 1.12 for the former mixtures and 1.16 and 1.35 for the latter mixtures. This pozzolanic effect is similar to the trends commonly observed in normal-strength concrete. On the other hand, \(f_{c}^{\prime}(t)/f_{c}^{\prime}\) obtained from the UHPC with the heat curing for 2 days exhibited a different phenomenon from the common trend. The strength gain rate of UHPC cured under heat curing condition was insignificantly affected by R\({}_{f}\). The rates at 3 days ranged between 0.92 and 0.99 for all the specimens. The corresponding values at 180 days ranged between 0.86 and 1.02. The compressive strength of UHPC with fly ash under heat curing mostly reached its 28-day strength at just 3 days. The initial heating curing plays an important role in the rate of hydration degree at early age of UHPC with fly ash whereas its effect becomes minimal at long-term age because the hydration reaction gradually reaches a stable state with age. It should be noted that heat curing was somewhat unfavorable for compressive strength development of UHPC with fly ash, indicating a slight lower 180-day compressive strength than 28-day strength. This can be caused by the rapid reaction and porous microstructure of the system. [PERSON] and [PERSON], cited by [28], revealed that a rapid hydration of cement from high curing temperatures will result in a high early strength because of more hydration products being formed. However, the rapid hydration does not allow the generated hydration products sufficient time available to diffuse properly away from the cement particles due to the low solubility and diffusivity of the hydration products. This leads to a high concentration of hydration products in a zone immediately surrounding the cement grain, and forms a relatively dense shell around the hydrating cement grains. As a consequence, this retards any subsequent hydration which makes a more porous structure and a reduction of long-term strengths. [PERSON] and [PERSON] [29] also suggested that the heat curing could induce a non-uniform precipitation of the hydration products within the  
Figure 6: The relation between the highest 28-day \(f_{c}^{\prime}\) of UHPC and fly ash (FA) content. hardened cement paste. Furthermore, [PERSON], cited by [30], reported that high temperatures would result in a coarser crystal structure compared to long, defect-free crystals formed at low temperatures. Besides, [PERSON] et al., cited by [30], found an increase of the macro porosity and a decrease of the meso and micro porosity without any change in total porosity for a temperature increase from 25 \({}^{\circ}\)C to 65 \({}^{\circ}\)C. This situation does not occur in normal temperature curing where there is adequate time for the hydration products to diffuse and precipitate uniformly throughout the interstitial space among the cement grains that keeps gaining strength with time. When cement is partially substituted by FA, the real volume of FA is higher than that of cement because the specific gravity of FA is smaller than that of cement.