1. Introduction
Concrete is considered one of the most important materials in construction. Therefore, it is vital to explore the impact of engineering environments on concrete behavior. Factors affecting the concrete strength are temperature, water/cement (W/C) ratio, coarse/fine aggregate ratio, relative humidity, concrete age, and concrete curing [
1]. Since concrete gains strength through a hydration process between cement and water curing, the temperature has a significant effect on the compressive behavior of concrete. The faster reaction is obtained at a higher temperature and subsequently higher strength. Whereas, that faster rate of hydration causes a reduction in the final strength of concrete because the physical form of the hardened cement paste is less well-structured and more porous at high temperatures [
2].
Most of the mechanical properties of hardened concrete are also related to its compressive strength [
3]. The uniaxial compression tests are commonly used to determine the strength and deformation properties of concrete. The standardized method for determining compressive strength is regulated in ASTM C387 [
4]. Specimens are tested up to failure under the effect of uniaxial compression load. The compressive strength of concrete is calculated by dividing the recorded maximum load by the cross-sectional area [
5].
Previous studies were performed on the compressive behavior of concrete at different temperatures. The compressive strength of concrete with the same moisture content decreased as the heating temperature increased [
6,
7]. The concrete curing temperatures below 5 °C or over 100 °C led to a reduction of almost 20% in the concrete strength [
8]. The optimal mechanical performance of concrete was obtained when there was less difference between the ambient temperature and concrete temperature [
9]. The setting time was affected by temperature [
2]. The low-temperature setting time was as much as 195% of the setting time at 23 °C (73 °F). Whereas, the setting time was 68% at high temperatures. The strength of concrete had significant influences on the stress–strain responses both at room and elevated temperatures [
10,
11,
12,
13]. Because of the decrease in the compressive strength of concrete at high temperatures, the slope of the stress–strain curve decreased indicating reductions in the stiffness of concrete [
10]. The strain corresponding to the peak strength increased as the temperature increased [
11,
12]. The rate of the strength development of concrete was affected by the W/C ratio as well as the cement type and temperature [
14,
15]. The mechanical properties of air-entrained concrete at elevated temperatures were studied [
16]. The air entrainment had an adverse effect on the compressive strength of concrete at elevated temperatures.
The mechanical properties of concrete can be predicted through fitting analyses of constitutive models. Hognestad et al. developed the first polynomial constitutive model for concrete, which was also one of the earliest constitutive models [
17]. This model was a dimensionless full curve equation that was unified for the ascending and descending parts of the stress–strain curve. The formulation of this model provided a reference for the constitutive models developed later. To improve the accuracy of the fitting results and meet the needs of engineering, a dimensionless piecewise constitutive model was developed in which the ascending segment was a parabola and the descending segment was a straight line [
18]. To precisely fit the constitutive curve of concrete under compression, the ascending curve was appropriate to be fitted by a polynomial equation and the descending curve was fitted by a rational fraction equation [
19,
20]. Relationships were proposed to capture the changes in the mechanical properties of concrete resulting from temperature [
12,
13,
21]. These properties included the compressive and tensile strength, compressive strain at peak stress, and initial modulus of elasticity of concrete [
21].
Good amounts of data exist on the effect of temperature on the mechanical properties and stress–strain relationships of concrete. However, there are limited data for this effect on concrete at different ages. Therefore, concrete cylinders were prepared, cured, and stored under different temperature conditions to be tested under compression at different ages. The stress–strain curve, mode of failure, compressive strength, ultimate strain, and modulus of elasticity of concrete were evaluated at ages between 7 and 90 days. The experimental results were used to propose constitutive models to predict the mechanical properties of concrete under the effect of temperature. Moreover, previous constitutive models for the stress–strain relationships of concrete at normal temperatures were examined to capture these relationships under the effect of temperature.
4. Previous Constitutive Models for the Stress–Strain Relationships
Previous constitutive models were proposed to trace the compressive stress–strain relationship of concrete at normal temperatures. The constitutive models proposed by Shah et al. [
40] and Kent and park [
41] were examined in this study to represent the compressive stress–strain relationship of concrete under the effect of temperature (see
Table 8). The newly affected mechanical properties of concrete (compressive strength, ultimate strain, and modulus of elasticity) due to temperature were used in these models.
Where fc is the stress value at any strain εc, fc′ and εco are the maximum stress and the corresponding ultimate strain obtained from the proposed models (Equations (1) and (2)), respectively. The parameters A and K are used to determine the shape of the curve in the ascending and descending parts, respectively. The modulus of elasticity (Ec) of concrete is obtained based on the proposed model for concrete under the effect of temperature (Equation (3)). ε50u is the strain corresponding to 50% of the maximum concrete strength.
Figure 16 and
Figure 17 provide comparisons between the previous constitutive models after considering the temperature effect and the experimental results. The previous models presented analytical results which had good agreements with the experimental results. These models reflected the affected compression stress–strain relationships due to temperature by using the mechanical properties of concrete predicted by the proposed models. Therefore, it can be concluded that the previous constitutive models for stress–strain relationships of concrete at normal temperatures can be used to capture these relationships under the effect of temperature by using the compressive strength, ultimate strain, and modulus of elasticity that were affected by temperature.
5. Conclusions
In this study, an overview of the temperature effect on concrete is experimentally provided. Concrete cylinders were prepared, cured, and stored under different temperature conditions to be tested under compression. The stress–strain curve, mode of failure, compressive strength, ultimate strain, and modulus of elasticity of concrete were evaluated at ages between 7 and 90 days. The experimental results were used to validate previous constitutive models and to develop new models to predict the mechanical properties of concrete under the effect of temperature.
The previous constitutive models for stress–strain relationships of concrete at normal temperatures can be used to capture these relationships under the effect of temperature by using the compressive strength, ultimate strain, and modulus of elasticity affected by temperature and developed in this study.
The effect of temperature on the modulus of elasticity of concrete can be considered in the ACI 318-14 equation by using the compressive strength affected by temperature.
The increasing rate of slopes of the linear portions of the stress–strain relationships of concrete decreased through the concrete age as the temperature increased. This behavior indicated a reduction in the stiffness of concrete. However, dramatic reductions were monitored in the case of freezing.
The exposure to different temperature conditions altered the mode of failure of the tested specimens. A well-formed cone without vertical splitting was the mode of failure observed for the concrete cylinders at 21 °C and 40 °C. Columnar vertical cracking was the mode of failure observed at a temperature of 121 °C. Side fractures at the top or bottom of the concrete cylinders were the mode of failure noticed for the specimens at the highest temperature (260 °C).
Based on the experimental data and the newly proposed model, concrete lost 10–20% of its original compressive strength when heated to 100 °C and 30–40% at 260 °C.
The compressive strength of the frozen specimens remained at low levels over their ages. No significant strength was earned as the concrete aged. Keeping the concrete cylinders frozen at an early age could be very harmful and caused more damage to the concrete strength. Therefore, it is particularly important to protect concrete from freezing at an early age if possible, to complete the hydration process and gain most of the strength.
Most of the compressive strength was gained at the early age of concrete due to the exposure to elevated temperature. However, reductions in the strength occurred at later ages.
The specimens exposed to the moderate temperature of 21 °C achieved only 75% of their 28-day compressive strength at the early age of concrete and further strength was achieved as the concrete age increased.