Temperature effects_maturity

 In the CEB-FIP Model Code 90, maturity is a concept used to predict the rate at which concrete gains strength based on temperature and time. Eq. (2.1-87) is used to calculate the maturity-adjusted time $$t_T$$​, which accounts for the effects of temperature on concrete's strength development.

\( S=\int d^{4} x\left(\frac{R}{2 \kappa}\right) \)

begin{eqation}S=\int d^{4} x\left(\frac{R}{2 \kappa}\right)end{equation}

Definition of Equation (2.1-87):

The maturity-adjusted time $$tTt_TtT​$$ is calculated as:

$$tT=∫t0texp⁡[QR(1T0−1T(τ))]dτt_T = \int_{t_0}^{t} \exp \left[ \frac{Q}{R} \left( \frac{1}{T_0} - \frac{1}{T(\tau)} \right) \right] d\tautT​=∫t0​t​exp[RQ​(T0​1​−T(τ)1​)]dτ$$

Where:

• tTt_TtT​ = maturity-adjusted time (in days)
• ttt = real elapsed time (in days)
• t0t_0t0​ = start time for the calculation (usually 0)
• QQQ = activation energy for hydration process, typically around 33,500 J/mol for ordinary Portland cement
• RRR = universal gas constant, approximately 8.314 J/mol·K
• T0T_0T0​ = reference temperature (293.15 K, which is 20°C)
• T(τ)T(\tau)T(τ) = concrete temperature at time τ\tauτ in Kelvin (K)
• τ\tauτ = time variable used for integration

Example Calculation:

Let’s assume the concrete is cured at a constant temperature of 30°C (303.15 K), and the elapsed time is 7 days.

Step 1: Convert the temperature to Kelvin

• The reference temperature T0T_0T0​ is 20°C (or 293.15 K).
• The concrete temperature T(τ)T(\tau)T(τ) is 30°C (or 303.15 K).

Step 2: Calculate the exponent

QR(1T0−1T(τ))=335008.314(1293.15−1303.15)\frac{Q}{R} \left( \frac{1}{T_0} - \frac{1}{T(\tau)} \right) = \frac{33500}{8.314} \left( \frac{1}{293.15} - \frac{1}{303.15} \right)RQ​(T0​1​−T(τ)1​)=8.31433500​(293.151​−303.151​)

1. First, calculate the inverse of the temperatures:

1293.15=0.00341 K−1,1303.15=0.00330 K−1\frac{1}{293.15} = 0.00341 \, \text{K}^{-1}, \quad \frac{1}{303.15} = 0.00330 \, \text{K}^{-1}293.151​=0.00341K−1,303.151​=0.00330K−1 0.00341−0.00330=0.00011 K−10.00341 - 0.00330 = 0.00011 \, \text{K}^{-1}0.00341−0.00330=0.00011K−1

1. Now, multiply by QR\frac{Q}{R}RQ​:

335008.314×0.00011=0.4432\frac{33500}{8.314} \times 0.00011 = 0.44328.31433500​×0.00011=0.4432

Step 3: Integrate over time

Since the temperature is constant, the integral simplifies to:

tT=∫07exp⁡(0.4432) dτ=7×exp⁡(0.4432)t_T = \int_{0}^{7} \exp(0.4432) \, d\tau = 7 \times \exp(0.4432)tT​=∫07​exp(0.4432)dτ=7×exp(0.4432) exp⁡(0.4432)=1.5578\exp(0.4432) = 1.5578exp(0.4432)=1.5578

So, the equivalent age tTt_TtT​ is:

tT=7×1.5578=10.9046 dayst_T = 7 \times 1.5578 = 10.9046 \, \text{days}tT​=7×1.5578=10.9046days

Conclusion:

For concrete cured at 30°C over 7 real days, the equivalent maturity-adjusted age tTt_TtT​ is approximately 10.9 days. This means that the concrete cured at 30°C gains strength equivalent to about 10.9 days of curing at 20°C.

This method helps account for the influence of temperature on the rate of strength development in concrete.