Evaluation of early-age cracking risk in mass concrete footings under different placement conditions

This article presents the assessment of early-age cracking risk in a mass concrete footing which is cast under different construction conditions. A finite element (FE) model was developed for predicting temperature, thermal stress, and cracking potential in a concrete footing at early age. Different scenarios of concrete placement were considered to investigate the effect of construction stages on thermal cracking potential in the concrete. The analysis method in this study can help engineers optimize construction schedules to control temperature and reduce cracking risk in mass concrete structures.


Introduction
Concrete structures such as dams, bridge foundations, piers, and abutments are often classified as "mass concrete" (ACI, 2000), (ACI, 2005), (Do, 2014). When a larger volume of fresh concrete is poured, a larger amount of heat releases from the cement hydration process. The temperature at the inside portion of the concrete is increasing while that at the surface is quickly decreasing due to the exposure to the air. This creates a large temperature difference between the core and the outer surface of the concrete, leading to high tensile stresses that may exceed the concrete tensile strength, which will cause thermal cracks (ACI, 2005), (Tian et al., 2012), (Tía, 2013), (Do, 2014). As long as cracking occurs in the concrete, it begins to affect the regular service and durability of the structure (Maruyama and Lura, 2019). Therefore, it is necessary to analyze the temperature and the corresponding stress fields in mass concrete structures for controlling temperature and preventing crack initiation in the early-age concrete (Nguyen and Luu, 2019), (Nguyen and Bui, 2019) There are different measures to reduce the temperature difference and thermal tensile stress in mass concrete such as use of lower cement content, use of aggregates (Klemczak et al., 2017) with a low coefficient of thermal expansion, casting concrete at night or in the early morning (Do, 2019), use of ice water, use of liquid nitrogen, precooling of mix constituents, post cooling using embedded pipes (Hong et al., 2017), (Nguyen et al., 2019), and use of insulating formwork (Do, 2020), (Do et al., 2014a), (Do et al., 2013). Recently, laboratory (Zhao et al., 2019), (Do et al., 2019a) and field tests (Sargam et al., 2019) on early-age properties and thermal cracking of concrete have been also conducted to evaluate the cracking risk as well as the efficiencies of thermal control methods to control cracking in mass concrete. Each measure has both advantages and disadvantages depending on construction conditions. Among these measures, the control of concrete placement stages has not been widely used because of its costs. Hence, the aim of this study is to determine the temperature and thermal stress in a concrete footing cast in different placement conditions, thus suggesting the best scenario for reducing cracking risk in the structure.

Description of the mass concrete footing
In this study, an assumed 8-m×6-m×3-m concrete footing cast on soil is modeled. The modeled soil layer is assumed to have dimensions of 16-m×12-m×4-m. The concrete footing has two planes of symmetry, therefore only one-quarter of the footing is analyzed in order to reduce the computation time. The geometry and dimensions of the footing are shown in (Figure 1).
The ambient temperature can be simulated using the the (Equation 1) (Léger et al., 1993): where T env is the ambient temperature (°C), and t day is the time (days). The temperature of the foundation under the concrete block is considered 25°C and the initial concrete temperature is assumed to be 30°C. The concrete mix proportion is shown in (Table 1) (Tia et al., 2016), (Do, 2016). The adiabatic temperature rise for the concrete mix was tested and is shown in (Figure 2). The thermal and physical characteristics of the concrete and the soil foundation used in the analysis are presented in (Table 2).   The ambient temperature can be simulated using the the (Equation 1) (Léger et al., 1993):   4) (Cengel, 2014):

FE basis for solving heat transfer problem The governing equation of a 3D unsteady heat transfer problem is based on the principle of energy conservation and Fourier's law of heat conduction and expressed in (Equation
where t is the material temperature (°C), k x , k y , k z are the thermal conductivity coefficients of the material dependent on the temperature in the directions x, y and z, respectively, (W/m-°C), q v is the amount of heat released by internal sources (for example, exothermic heating) to a given moment in time (W/m 3 ), c is specific heat (J/kg-°C), ρ is the density concrete (kg/m 3 ), t is time (s).
Two types of heat transfer boundary conditions are often used to analyze heat problems, which are expressed by (Equation 5) and (Equation 6) (Cengel, 2014): where T p is the temperature of the surface or foundation (°C), q v is the heat generated per unit volume (J/m 3 ), h is the convective coefficient (W/m 2 -°C), T s is the temperature of concrete or foundation (°C), T f is the ambient temperature of the construction area (°C), l x , l y , and l z are the directional cosine of the surface according to the x, y and x axes, respectively.
The problem of heat transfer is solved using the following matrix equation (Equation 7), (Zienkiewicz and Taylor, 2000): In the problem of unstable heat transfer, it is necessary to analyze time into steps Δt as follows (Equation 8): ) is obtained by combining (Equation 7) and (Equation 8) and expressed as follows: where [K] is conductivity operator, [C] is capacity operator, and [Q] is heat load due to heat of hydration, Δt = Δt n -Δt n-1 is the time step.
Solving (Equation 9) gives temperature fields in the concrete block at different time steps. Thermal stress in the concrete is determined by (Equation 10) (Zienkiewicz and Taylor, 2000): where {σ} is the thermal stress vector, [D] is the elasticity matrix, [B] is the strain-displacement matrix, based on the element shape functions, {u} is the nodal displacement vector, {ε}= {ε x ε y ε z ε xy ε yz ε zx } is the strain vector, and {ε th } is the thermal strain vector. The determination of temperature field in a mass concrete structure is a complex problem because it depends not only on the shape of the structure but also on other factors such as the internal heat generation, construction conditions, and the ambient temperature. In recent years, numerical approaches such as finite difference and FE methods have been widely used to predict temperature and stress fields in mass concrete structures (Nguyen et al., 2019), (Trong et al., 2019), (Aniskin et al., 2018), (Do et al., 2020), (Do et al., 2020a), (Do, 2013). In this study, the Midas/Civil software (MIDAS, 2011) based on the FE method was used to model the early-age behavior of the concrete footing depicted in (Figure 1).

Crack index for evaluation of early-age cracking risk
The prediction of crack formation in an early-age concrete structure plays an important role in minimizing the cracking risk and/or controlling crack growth. Criteria for evaluating early-age thermal cracking in concrete vary from country to country (Do et al, 2020b). In the United States, the ACI guidelines for assessing thermal cracking are not specified except for a recommended limiting value for the temperature difference between the core and the outer surface of the concrete. In other countries such as Korea and Japan, "crack index" is preferably used as a measure for assessing early-age cracking potential in the concrete. Crack index is determined by (Equation 11) (Kim, 2010), (Japan Concrete Institute, 2017): where I ct is the crack index, f t (t) is the maximum tensile stress (MPa), and f sp (t) is the splitting tensile strength of the concrete (MPa).
Revista Ingeniería de Construcción Vol 36 Nº1 Diciembre de 2021 www.ricuc.cl The tendency of cracking can be evaluated using "crack index" based on engineering experience as introduced in (Table 3) and (Figure 4), (Kim, 2010).

Analysis Results and Discussion
The 3-D FE model was created using the Midas/Civil software. The element used in the thermal analysis is a 3-D eight-node thermal solid element, which has one degree of freedom -temperature -at each node. The concrete and foundation in the stress analysis are modeled with a 3-D eight-node structural solid element, which is coupled with the 3-D thermal solid element. The temperature distribution obtained from the thermal analysis is then served as "thermal loading" in the stress calculation. The FE model geometry is depicted in (Figure 5).

Criteria Crack index
No cracking I ct ≥ 1.5 To minimize cracking 1.2 ≤ I ct ≤ 1.5 To minimize harmful cracking 0.7 ≤ I ct ≤ 1.2 Table 3. Thermal crack index (I ct ) The ( Figure 6) shows the maximum temperature development at the center of the concrete footing under different construction cases. The maximum temperature decreases as the thickness of each lift decreases during the cement hydration. The maximum temperature value and time of occurrence are listed in (Table 3). The maximum temperatures at the concrete center are 75. 52°C,72.24°C,and 66.74°C in Cases 1,2,and 3,respectively. It may be noted that in Case 3, the maximum temperature and temperature difference are the smallest compared to Cases 1 and 2. After reaching the peak temperature, it begins to cool down. As predicted, the maximum temperature in the concrete will take a long time to decrease to a stable temperature. The crack index calculated at the surface is also listed in (Table 4). The ( Figure 4) and (Table 4) together show that the probabilities of cracking in the concrete footing are 81%, 50%, and 20%, in Cases 1, 2 and 3, respectively. It can be included that thermal cracking in the concrete in Case 3 is not likely to occur at early ages, thus suggesting the proposed method of concrete pouring is effective. In other hand, other measures should still be taken in Cases 1 and 2 for controlling early-age cracking in the concrete.

Conclusions
• The 3-D FE model created in this study has identified the temperature and thermal stress fields in the concrete footing at early ages in different construction scenarios. The results show that the construction schedules significantly affect the temperature development and thermal cracking risk in the concrete.
• When the concrete is cast with a maximum volume of 8-m×6-m×3-m in three lifts (as investigated in this study), thermal cracking will be not likely to occur. Thus, dividing large volume of mass concrete into reasonably smaller lifts can help minimize cracking risk in the concrete.
• For future work, the numerically predicted results (temperature field and crack index) should be compared with experimental results. As long as the research results have been verified, they can be used in the sustainable design and construction of mass concrete structures.
• The developed model can be used to perform thermal and stress analyses, and assess the risk of thermal cracking of other essential concrete members. The research methodology can help engineers/contractors optimize the construction stages and reduce the project schedule.