Abstract
Conventional test method to measure the ATR of concrete needs a sample of larger than 50 L volume.Delicate control for the adiabatic condition requires a heavy insulation and closed-loop circuit to match the chamber temperature with the sample's temperature.Practically,the equipment to measure the ATR has been rarely applied.Semi-adiabatic condition is sometimes used to replace the original equipment.The measurement of ATR of concrete is cumbersome.It is impossible to evaluate the thermal shrinkage of all possible mix proportions in field.The heat of cement hydration can be predicted using a chemical model.The proportion of each compound in Portland cement determines the final heat output achieved by their full hydration.The degree of hydration controls the rate of heat evolution of a given Portland cement compound.
Heat production rate of cement hydration,Q(t;T)is measured using by adiabatic temperature rise test.The rate of heat production is following Eq.(1)[1].
where t,T,Q,f,k are hydration time,temperature,heat production,heat development function of chemical reaction,rate constant of cement hydration,respectively.If degree of hydration is defined with the heat production,its development is given by Eq.(2).[2,3]
where Qu is the limiting heat production at infinite age.The development function is the same with Bernhardt empirical formula[2],which was previously adopted for the maturity method[4].Note that a conventional definition for the degree of hydration ranges from 0 to 1,which isα=Q/Qn.Considering the dormant period t0 and integrating the above equations gives a closed form of heat production,Eq.(3).[4]
Fitting the model function with isothermal microcalorimetry data gives Qu,t0(T)and k(T).The total heat production Qu is constant regardless of the reaction temperature.The dormant period t0 may be a function of T,but we just need t0 at initial temperature(20℃)of ATR prediction.The total heat production Qu is constant at all temperature and it obviously depends on the mix proportion.The reaction rate adopts Arrhenius equation,Eq.(4).[5]
where k,T,A,Ea,R are rate of constant,absolute temperature in Kelvin,pre-exponential factor,activation energy for hydration and universal gas constant,respectively.
Specific heat capacity is a function of a linear or exponential decay with the degree of hydration,where specific heat of portland cement and water are 0.75 J/(g·K)and 4.18 J/(g·K),respectively.Adiabatic temperature rise equation is hard to get a closed form.Considering the thermal expansion of the sample is following Eq.(5).
where εV=αΔT,κ(α)is thermal coef ficient.Some of concrete hydration heat energy is consumed by the volumetric thermal expansion energy.
Adiabatic temperature rise equation considering thermal expansion is Eq.(6).ATR is calculated by integrating the Q(t,T)with increasing T,where Q(t=0,T)=Q(t,T0).Full hydration cannot be achieved in a sealed curing condition.The achievable degree of hydration is different for cement paste and concrete.
where c andαare concrete specific heat function of hydration rate[6-8]and hydration rate.[9]Isothermal microcalorimetry analysis was conducted for cement pasting proportioned by the water-tocement cement ratio of 0.45 to 0.55 for calculating the ATR using by Eq.(6).The predicted ATR is the verified by adiabatic temperature rise test using a conventional equipment for same mix proportion of isothermal microcalorimetry analysis.
Concrete mix proportions are shown in Table 1.C=370 kg with W/C=0.40,0.45,0.55;C=350,370,400,440 kg with W/C=0.45.ATR test sample consisted of 50 L steel drum with a 400 mm diameter and 400 mm height.
Table 1 shows mix proportion and their hydration temperature values(Q),correction hydration temperature(Q')values at equal origin temperature(20℃)and compressive strength.Based on the hydration modelling formula,Q'is corrected to the initial temperature correction for hydration test results was corrected by the weighted average.The effects of the initial temperature are small.The effects are minimal considering the error in hydration experimentation and the error in regression for the exponential function model.Using the results of the experiment,a model formula for the final insulation temperature rise is proposed as Q=0.147C where Q,C are final hydration temperature and cement content,respectively.
Table 1 Concrete mix proportion and end temp
Figure 1 (a)Isothermal microcalorimetry analysis,(b)Integration of Fig.1(a)for each initial temperature
The regression lines in Figure 1 are predicted using by Eq.(3).Final hydration energy has no relationship with starting temperature.Final hydration temperature for W/C=0.45 and C=370 kg is 55.7℃.Comparing the predicted ATR with the experimental ATR,the result is shown in Figure 2.
Figure 2 ATR with C=370 kg,W/C=0.45
The pre-prediction gives a higher heat production than ATR measurement.Energy dissipation due to the thermal expansion was marginal approximately 0.01%of the total heat production.Sealed conditions for cement paste and concrete was assumably different considering the water content in a unit volume of sample.
In general degree of concrete hydration vary according to the W/C ratio and type of sample[10].Different between predicted temperature and experiment temperature shown in Figure 3 is the difference of degree of hydration of cement paste and mortar.In Figure 3,reduction quantity is strongly related to hydration content[11].
Figure 3 degree of hydration of cement paste and mortar considering proportion of W/C
ATR measurement has high cost,but the isothermal microcalorimetry analysis is very low cost.All the parameters required for predicting the ATR can be obtained through the isothermal microcalorimetry analysis.The predicted hydration temperature is very similar to ATR results.