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8.3 ANFIBIOS, PECES Y REPTILES
In 1960, Copeland et al.[120] proposed that the Arrhenius equation could explain the effect of temperature on the early age rate of hydration. The Arrhenius equation can be written as follows:
Equation 2.12
where:
kT = rate constant, days-1 or hours-1
A = constant, days-1 or hours-1
Ea = apparent activation energy, J/mol,
R = universal gas constant, 8.314 J/mol K,
T = average temperature of the concrete during interval t, 0C
Later, Freiesleben Hansen and Pedersen[121] proposed a method that was developed based on the Arrhenius equation to calculate the equivalent age in the following equation:
Equation 2.13
where:
te = the equivalent age at the reference temperature, hours or days
Ea = apparent activation energy, J/mol,
R = universal gas constant, 8.314 J/mol K,
T = average temperature of the concrete during interval t, 0C Tr = reference temperature, 0C
Thus, the age conversion factor can be calculated using the following equation:
Equation 2.14
The age conversion factor is an exponential function and is expressed in terms of the absolute temperature, 0K. The equation above clearly shows that the age
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conversion factor with a certain temperature greatly influenced by the value of activation energy, which is used as shown in Figure 2.6.
Byfors[122] and Naik[123] proved that over a wide range of temperature, the maturity-strength relationships obtained from the Arrhenius equation, is more reasonable good than that of the Nurse-Saul function.
Figure 2.6:The influence of activation energy on the age conversion factor based on the Arrhenius equation (Equation 2.14)[106]
Figure 2.7 shows the effect of temperature on the age conversion factors of different maturity functions. It appears that there is a good agreement among all the maturity methods presented for the curing temperatures between 5 and 250C. However, the age conversion factor of all the maturity methods; are considerably different when the concrete is cured at elevated temperatures, i.e. higher than 250C. Furthermore, the value of activation energy that is used to calculate the age conversion factor, has a significant effect on the Arrhenius age conversion factor at temperatures that higher than 250C.
46 Temperature (0C) 0 10 20 30 40 50 60 A ge co nv er si on fa ctor 0 5 10 15 20 25 Nurse-Saul Arrhenius, Ea = 30 kJ/mol Weaver - Sadgrove Rastrup Arrhenius, Ea = 60 kJ/mol
Figure 2.7: Age conversion factors vs. temperature
The age conversion factors (β) that are calculated using both the Weaver- Sadgrove and Arrhenius functions are comparable, when the activation energy of 30 kJ/mol is applied to calculate the age conversion factor using the Arrhenius equation. However, using higher activation energy to determine the age conversion factor gives a huge difference in the value of the age conversion factor and the relationship between the age conversion factor and curing temperature becomes more nonlinear[101].
In 1962, Alexander and Taplin[124] investigated whether the strength gain of concrete followed the maturity rule when the concrete was cured at different temperatures. They found that at low maturities, concretes that were cured at a higher temperature had a higher strength than that of cured at lower temperature. Conversely, at later maturities, concrete cured at a high temperature results in lower strength. This implies that the strength-maturity curve for a specific curing temperature regime at a certain maturity crosses the respective curve for a higher
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temperature-curing regime. This is generally called as the “crossover effect”, which was introduced by Verbeck and Helmuth[125] in 1968, as is illustrated in Figure 2.8.
Figure 2.8: The effect of early-age curing temperature on the strength-maturity relationship[101].
Verbeck and Helmuth[125] added that there was a rapid strength development at early age. However, the products of the reactions did not have enough time to be
uniformly distributed within the pores of the hardening paste. As a result, ‘shells’
formed of low permeability surrounded the unhydrated cement grains. Un- uniformly distributed of the hydration products leads to more large pores, which reduces the strength of concrete. The shell obstructs continuous hydration of the unreacted cement at later ages. Therefore, the lower strength at later age of concrete cured at high temperature at early age is believed due to the unreacted cement cannot continue the process of hydration. It is caused water that needed for the hydration of cement cannot reach the unreacted cement as it is hindered by a low permeability shell[40].
The explanation that is given by Verbeck and Helmuth[125] clearly identify the effect of curing temperature at very early ages on the strength development of concrete, especially in the inner structure of concrete. The inner structure of concrete is very important to the strength development at later ages and the durability of the concrete.
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A few years later, Hudson and Steele[126, 127] continued investigating the relationships between strength, age and curing temperature. They proposed maturity method to estimate the 28-day strength of concrete based on the results of the tests at early age. Moreover, their results were later included in ASTM standard[128].