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Prediction of Adiabatic Heat Signature

Recently, the 3-D cement hydration and microstructural development model has been modified to include the capability to predict the adiabatic temperature rise for a concrete, i.e. the temperature vs. time curve which would be obtained for a concrete maintained under adiabatic (no heat lost to the surrounding environment) conditions. As hydration occurs, the cumulative heat generated by the hydration reactions is tabulated and the heat capacity of the concrete updated. Based on these two values, the incremental temperature rise from one cycle of dissolution to the next can be calculated as:

 

where T is the incremental change in temperature from cycle (i-1) to cycle i, Cp(i) is the value of the heat capacity for the concrete at cycle i, and H(i) is the cumulative heat generated by the hydration reactions through cycle i. In addition, the equivalent real time which elapses during this cycle of hydration is estimated using principles based on the maturity method [2,21] and a user-supplied calibration factor relating cycles to equivalent time at a temperature of 25oC.

Previously [1,2], the following conversion between cycles and time has been employed to calibrate model results to experimental data:

 

where to is a user-supplied induction time for the cement of interest. The differential time elapsing between cycles (i-1) and i can be determined by substitution into equation 5 and subsequent subtraction to obtain:

 

This increment in time would correspond to a constant temperature of reaction (typically 25oC). To adjust this value for the changing temperature under adiabatic curing conditions, the maturity method is adapted [2]. The variation in reaction rate, k, with temperature can be described by an Arrhenius type relationship [21]:

 

where Ea is an apparent activation energy, R is the universal gas constant (8.314 J/(mole K)), and T is absolute temperature in K. An equivalent time, te, at any temperature of interest, Ti, relative to a base reference temperature, Tr, can be calculated as:

 

where kT is the rate constant at the experimental temperature of interest and kr is the rate constant at the reference temperature. Finally, by combining equations 6 and 8, one obtains:

 

Figure 7 shows an example comparison between experimental and model predicted temperature rise, based on executing the program disreal3d with the input datafile provided in Appendix D.1. The agreement between model and experiment is quite good, particularly for times less than 30 hours, but it should be kept in mind that the user has had to supply an induction time, initial temperature, activation energy, and cycle-time conversion factor as input parameters to the program.

  


Figure 7: Experimentally measured and model predicted (solid line) adiabatic temperature rise for an ordinary portland cement concrete containing 72% aggregates on a mass basis.



Next: Acknowledgements Up: Example Applications Previous: Percolation Threshold of

Dale P Bentz
Fri Feb 21 08:44:14 EST 1997