Keywords

1 Introduction

Recently, the bridge construction industry has been widely using high-strength and HPC mixes so as to meet the project requirements of increased span length and accelerated construction schedules. Those concrete mixes tend to use larger cement content to surge the strength at early ages. However, hydration of a higher amount of cement leads to a greater concrete temperature and a higher temperature difference between the concrete surface and the core. As a result, thermal tensile stresses will be higher hence growing the risk of cracking [1]. Accurate characterization of the cement hydration for concrete is vital to forecast the evolution of temperature, stress field, and thermal cracking potential of the concrete element so that necessary measures can be taken to minimize cracking risk and ensure its structural integrity and durability.

To capture the thermal behavior of concrete, input hydration parameters need to be determined. There have been theoretical/mathematical models for presenting the cement hydration progress such as adiabatic curve proposed by Tanabe et al. [2]. The limitations of those theoretical models are: (1) the heat generated by reacting cement is considered uniform throughout the concrete mass and (2) the role of supplementary cementitious materials is not taken into account. Therefore, hydration parameters determined from a laboratory or field test on an actual concrete mix are more accurate [3, 4].

In this study, the ATR for a HPC mix was measured using an adiabatic calorimeter developed at the University of Transport and Communications, Vietnam. The heat of hydration parameters [5] of the HPC mix were determined using the curve fitting method. A FE model of a bridge pier using HPC was developed using the ANSYS APDL codes. The heat of hydration parameters were then used as input parameters to the FE model in order to predict the temperature distribution in the bridge pier and footing. The temperature development of a pier using a normal concrete mix was also analyzed to compare with that of the HPC pier, then the hazard of cracking in concrete for the two cases would be discussed.

2 Experimental

2.1 ATR for HPC

Using the concept described by Gibbon et al. [6] and improved by Lin and Chen [4], an adiabatic calorimeter for measuring ATR of concrete was developed. The basic principle of adiabatic calorimetry is to keep the concrete sample temperature and the ambient temperature the same by minimizing the heat exchange. The adiabatic calorimeter, sketched in Fig. 1, automatically matches the water temperature with the concrete sample temperature in order to remain the hydration heat unchanged. There are 2 Resistance Temperature Detectors (RTD) sensors that continuously measure the concrete sample and the water temperatures at 10 Hz frequency. Two heaters will automatically turn on and off based on the difference between the water and the sample temperatures (0.1°C in this set up). The system, therefore, is very close to an adiabatic condition that can obtain ATR of the concrete sample.

Fig. 1
figure 1

Schematic diagram of adiabatic calorimeter [4]

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The HPC mix design is presented in Table 1 whereas Table 2 lists the chemical composition of cement. After mixing, the fresh concrete was placed in the container of the adiabatic chamber before the ATR would be obtained (Fig. 2). The measured ATR over time is plotted in Fig. 3. The initial concrete temperature was 22.2 °C. The rise in the sample adiabatic temperature was 54.5 °C at 72 h (the peak temperature was 76.7 °C).

Table 1 HPC mix design (kg/m3)
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Table 2 Cement chemical composition (%)
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Fig. 2
figure 2

Placing concrete specimen in adiabatic calorimeter

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Fig. 3
figure 3

Measured ATR

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Since the water-reducing and retarding admixture and fly ash were present in the HPC mix, the hydration reaction was delayed leading to the slow increase in the specimen temperature. After 16 h, the exothermic reaction began to accelerate. The hydration process took place very quickly within 16 and 35 h due to the low water to cement content ratio of the concrete mix [7]. The concrete temperature finally levelled off after 50 h. The ATR can be used as the input for thermal analysis of a concrete bridge structure.

2.2 Degree of Hydration

The rate of hydration heat is a function of the hydrating concrete temperature and time. The higher the concrete temperature, the greater the rate of the exothermic reaction at an early age. The degree of hydration is proportional to the heat evolved as proposed by Van Breugel [8]:

$$\alpha (t) = \frac{H(t)}{{H_{u} }}$$
(1)

where: α(t) = degree of hydration, H(t) = total heat generated at time t (J/g), and Hu = ultimate heat at the end of hydration (J/g) which can be determined using Eqs. (2) and (3):

$$H_{u} = H_{c} p_{cem} + 461p_{slag} + 1800p_{FA} p_{FA - CaO}$$
(2)
$$\begin{aligned} H_{c} & = 500p_{{C_{3} S}} + 260p_{{C_{2} S}} + 866p_{{C_{3} A}} + 420p_{{C_{4} AF}} \\ & \quad + 624p_{{SO_{3} }} + 1186p_{FreeCa} + 850p_{MgO} \\ \end{aligned}$$
(3)

where pcem = ratio of cement to cementitious materials content, and Hc = total heat evolved from pure cement hydration (J/g).

A mathematical function for degree of hydration was proposed by Hansen and Pedersen [9] as follows:

$$\alpha (t_{e} ) = \alpha_{u} \exp \left[ { - \left( {\frac{{\tau_{s} }}{{t_{e} }}} \right)^{\beta } } \right]$$
(4)

where τ (h) and β = hydration parameters; te= equivalent age of concrete (h); \(\alpha_{u} = \frac{1.031w/c}{{0.194 + {\text{w}}/c}}\) is ultimate degree of hydration [7]; and w/c = water to cementitious material content ratio.

The equivalent age of concrete is computed using Eq. (5):

$$t_{e} = \int\limits_{0}^{t} {\exp \left[ { - \frac{{E_{a} }}{R}\left( {\frac{1}{{273 + T_{c} }} - \frac{1}{{273 + T_{r} }}} \right)} \right]} dt_{{}}$$
(5)

where Tr = reference temperature (20 °C or 23 °C); Ea= activation energy (J/mol); R = universal gas constant (8.314 J/mol/K); Tc = temperature of the concrete (°C); and Δti= ti-ti−1 is the time step used (h).

The activation energy represents “temperature sensitivity” of the exothermic reaction, and can be predicted as follows [5]:

$$\begin{aligned} E_{a} & = {\text{41,230}} + {\text{1,416,000}}\left( {p_{{C_{3} A}} + p_{{C_{4} AF}} } \right)p_{cem} p_{{SO_{3} }} p_{cem} - {\text{347,000}}p_{{Na_{2} O_{eq} }} \\ & - 19.8Blaine + {\text{29,600}}p_{{F{\text{A}}}} p_{{F{\text{A - CaO}}}} + {\text{16,200}}p_{slag} - {\text{51,600}}p_{SF} \\ \end{aligned}$$
(6)

where pFA = percentage of fly ash in the cementitious material; pFA-CaO = percentage of CaO in fly ash; pslag = percentage of slag in the cementitious material; pSF = percentage of silica fume in the cementitious material; Blaine = fineness of cement (m2/kg); pX = percentage of X component in the cement (cem = cement, C3A, C4AF, SO3) and pNa2Oeq = percentage of Na2Oeq in cement (0.658 × %K2O + %Na2O).

In this study, based on the chemical compositions of cement, the activation energy was determined to be Ea = 34,454 (J/mol), and αu = 0.642. The experimental degree of hydration versus equivalent age for the HPC mix is plotted in Fig. 4. The hydration parameters τ = 24.98 h and β = 1.842 were determined using the curve fitting method from the experiment and Eq. (4) (R2 = 0.9949).

Fig. 4
figure 4

Experimental and fitted degree of hydration curves

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In this study, based on the chemical compositions of cement, the activation energy was determined to be Ea = 34,454 (J/mol), and the ultimate degree of hydration αu = 0.642. The experimental degree of hydration versus equivalent age for the HPC mix is plotted in Fig. 4. The hydration parameters τ = 24.98 h and β = 1.842 were determined using the curve fitting method from the experiment and Eq. (4) (R2 = 0.9949).

3 FE Model for Thermal Analysis of Bridge Pier

Numerical methods can be effectively used in solving the problem of heat evolution and transfer in hydrating concrete [10,11,12,13,14,15]. Following those approaches, a FE model was developed using the ANSYS Mechanical APDL codes. The structure consists of a concrete pier placed on a footing, and 1/4 of the entire structure was to be considered (Fig. 5). The concrete and the soil were modeled using an 8-node solid element (SOLID278) with a single degree of freedom at each node (temperature). The pier’s dimensions are 2.0 m × 5.0 m × 6.0 m and the footing’s dimensions are 12.5 m × 8.0 m × 2.5 m.

Fig. 5
figure 5

FE model for one-quarter pier

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The initial and external temperatures for the model boundary conditions were assumed to be 23 and 27 °C, respectively. The surface convection coefficient for the pier was assumed to be 29,288 J/h-m2 − °C [14].

The heat conduction equation in space is expressed by Eq. (7). The thermal analysis type is “transient” which considers changes of temperature and boundary conditions over time.

$$\uprho{\text{c}}_{\text{p}} \frac{{\partial {\text{T}}}}{{\partial {\text{t}}}} = \frac{\partial }{{\partial {\text{x}}}}\left( {{\text{k}}\frac{{\partial {\text{T}}}}{{\partial {\text{x}}}}} \right) + \frac{\partial }{{\partial {\text{y}}}}\left( {{\text{k}}\frac{{\partial {\text{T}}}}{{\partial {\text{y}}}}} \right) + \frac{\partial }{{\partial {\text{z}}}}\left( {{\text{k}}\frac{{\partial {\text{T}}}}{{\partial {\text{z}}}}} \right) + {\text{q}}$$
(7)

where q = rate of heat generation per unit volume (J/h-m3), ρ = concrete density (kg/m3), cp = specific heat of concrete (J/kg- °C), k = thermal conductivity (J/h-m − °C), T = temperature (°C), and t = time (h).

In this study, a normal concrete mix properties were also adopted [16] in order to compare with the HPC mix. The material properties of the normal concrete and HPC mixes are listed in Table 3.

Table 3 Concrete Material Properties Used in Thermal Analysis
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3.1 Discussion of Analysis Results

The predicted temperature distribution contours are presented in Fig. 6. The highest temperature was found to occur in the center of the model and decreased as it got closer to the surfaces of the pier. The pier center, top and corner temperatures are predicted and plotted in Fig. 7a. The temperature differences between the center and other points in the pier are presented in Fig. 7b. It is noted that the maximum temperature difference (between the center and the corner) peaked at 43.7 °C after 72 h that exceeds the maximum limit of 20 °C suggested by ACI [17].

Fig. 6
figure 6

Temperature distribution contours in HPC pier

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Fig. 7
figure 7

Temperatures a and temperature differences b in the pier using HPC mix

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The temperatures and temperature differences in the pier using the normal concrete mix are also shown in Fig. 8. As can be seen, the maximum temperature difference peaked at 34.0 °C in this case. From the comparison between the predicted results of the HPC and normal concrete, the pier using the HPC mix show a higher temperature difference than the normal one, thus it might have a higher thermal cracking risk. However, because the HPC has a higher tensile strength than the normal one does, the pier should be designed with smaller dimensions in order to reduce thermal cracking potential.

Fig. 8
figure 8

Temperatures a and temperature differences b in the pier using normal mix

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4 Conclusions and Recommendations

The paper presents the ATR for a HPC mix measured from an adiabatic calorimeter. The highest temperature rise in the sample was 54.5°C. Through the measured ATR, hydration parameters (τ = 24.98 h and β = 1.842) were determined from the curve fitting method.

The FE model developed in ANSYS is capable to predict temperature evolution in a bridge pier. The maximum temperature difference between the core and the corner of the pier using HPC mix peaked at 43.7°C thus suggesting very high risk of early-age thermal cracking. However it further needs to conduct strength tests on the HPC mix and then perform a stress analysis on the bridge pier to fully evaluate the thermal cracking risk in the concrete.