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An experimental study was conducted using a hydraulic servo machine to examine the compressive dynamic performance of rubber concrete under freeze-thaw cycles by considering 4 different numbers of freeze-thaw cycles and 8 different strain rates. The compressive stress-strain curves of rubber concrete under different loading conditions were obtained. By comparatively analyzing the mechanical characteristic parameters of the compressive stress-strain curves (i.e., peak stress, elastic modulus, and peak strain), the following conclusions were drawn: at the same loading strain rate, the compressive peak stress of rubber concrete is gradually decreased while the mass loss rate is gradually increased, as the number of freeze-thaw cycles increases. Compared to ordinary concrete, rubber concrete has a better frost resistance property. At the same number of freeze-thaw cycles, the compressive peak stress and elastic modulus of rubber concrete are gradually increased as the loading strain rate increases. The increase in the number of freeze-thaw cycles enlarges the increasing amplitude of the peak stress and elastic modulus under the action of loading strain rate. The compressive peak stress and elastic modulus dynamic increase factors of rubber concrete exhibit a linear relationship with the dimensionless logarithm of the loading strain rate. Meanwhile, a calculation model was proposed for the compressive peak stress dynamic increase factor of rubber concrete under the coupling effect of freeze-thaw cycles and loading strain rate, and the corresponding stress mechanism was discussed in detail. The research findings are of great significance to the application and development of antifreeze concrete in engineering practice.

As one of the most widely used construction materials, the durability of concrete has long been an important concern in the field of concrete research; particularly, freeze-thaw cycle is considered the main factor in the deterioration of concrete materials [

In order to improve the frost resistance property of concrete, a certain amount of air-entraining agent would usually be added to the concrete mixture. Relevant literature has reported that adding an appropriate amount of rubber particles into the concrete mixture can also effectively improve the frost resistance property of concrete, where rubber particles are equivalent to the solid air-entraining agent [

In this paper, an experimental study was carried out using a hydraulic servo machine to examine the compressive dynamic performance of concrete with a replacement rate of 10% rubber particles under the action of freeze-thaw cycles. A total of 4 different numbers of freeze-thaw cycles and 8 different loading strain rates were considered. Through the experiment, the compressive stress-strain curves of rubber concrete under different loading conditions were obtained and comparatively analyzed in terms of mechanical characteristic parameters (i.e., peak stress, elastic modulus, and peak strain). The results were used to examine the coupling effect of freeze-thaw cycles and strain rate on rubber concrete. The conclusions of this study will provide a theoretical basis for the research of antifreeze concrete and its applications in engineering practice.

In view of the purpose of this study, the strength of concrete without rubber particles was designed to be 30 MPa according to applicable concrete design specifications. Based on the conclusions of relevant literature [^{3} and 2580 kg/m^{3}, respectively. The fineness modulus of fine aggregate is 2.5, and the particle size of coarse aggregate ranges 4∼16 mm. The rubber particles used in this experiment have a particle size of 2∼5 mm, a fiber content of ≤0.1%, and an apparent density of 1270 kg/m^{3}. The tensile strength and breaking elongation of the rubber particles are >15 MPa and >500%, respectively.

Chemical composition of cement (mass fraction/%).

Ingredients | SiO_{2} | Al_{2}O_{3} | Fe_{2}O_{3} | CaO | MgO | SO_{3} | R_{2}O | Loss on ignition |
---|---|---|---|---|---|---|---|---|

Content | 21.08 | 5.47 | 3.96 | 62.28 | 1.73 | 2.63 | 0.50 | 1.61 |

Pour the weighed cement, fine aggregates, and rubber particles into the mixer. After thorough stirring, add coarse aggregates into the mixer. After thorough stirring again, pour the weighed water slowly into the mixer and stir the mixture evenly. Then, pour the rubber concrete mixture into the mold and place the mold on a vibrating table to vibrate until compact. Demolded one day later and place the specimen in a standard curing room (temperature 20 ± 2°C, humidity 95%) for 28 days before using it for the experiment. The slump of the rubber concrete mixture with a 10% rubber particle replacement rate is 23 mm, and the mass of the specimen is slightly lower than that of ordinary concrete.

The specifications of concrete freeze-thaw cyclic experiment highlight that the concrete specimens need to be saturated before proceeding with the experiment. In this study, all the specimens were saturated by sinking them into water. The specimens would be weighed repeatedly during this period until their masses became basically unchanged. That is, the saturation state was reached. Then, the concrete specimens were placed into a freeze-thaw cyclic machine for periodic freezing and thawing. After reaching the predetermined number of freeze-thaw cycles, the specimens would be taken out and smoothened with mortar to avoid the potential problem that the specimen cannot be fully axially stressed during the loading process. In this study, the number of freeze-thaw cycles was designed to be 0, 50, 100, and 150 (indexed as D-0, D-50, D-100, and D-150, respectively) [

Equipment for freeze-thaw cycle test and loading. (a) Equipment for freeze-thaw cycle test. (b) Loading equipment.

A material single-axis hydraulic servo machine was used to examine the compressive dynamic performance of rubber concrete under different numbers of freeze-thaw cycles. This machine is equipped with independent load sensors and deformation sensors. The ranges of load and displacement measurement and the precision of sensors are compliant with the experimental requirements. Referencing the sizes of specimens used in the existing literature, the specimen size in this study was determined to be 100 mm cube. In the present study, cube specimens were used to obtain the compressive stress-strain curve mainly due to the following reasons: (1) the “Standard for test methods of long-term performance and durability of ordinary concrete (GB/T 50082-2009)” recommends the use of 100 mm cube specimen as the standard test specimen. (2) The relevant literature [

To examine the dynamic performance of rubber concrete under different numbers of freeze-thaw cycles, the compressive dynamic loading was realized through loading strain rate. Each loading strain rate corresponds to a different magnitude of dynamic action. In this paper, 8 different loading strain rates were designed according to earthquake-magnitude dynamic actions. Specifically, the lowest compressive loading strain rate is 10^{−5}/s (static loading strain rate), while the highest compressive loading strain rate is 5 × 10^{−2}/s, as shown in Figure

Strain rate loading conditions.

The change of mass under the action of freeze-thaw cycles is one of the important indicators for the frost resistance property of concrete. By weighing the rubber concrete specimens after applying different numbers of freeze-thaw cycles, the mass loss rate of rubber concrete was obtained. As mentioned earlier, the number of freeze-thaw cycles was determined to be 0, 50, 100, and 150 in this study, and the corresponding mass loss rate is equal to 0%, 0.45%, 0.76%, and 1.30%, respectively, as shown in Figure

Number of freeze-thaw cycles and mass loss rate.

According to the qualitative relationship between the number of freeze-thaw cycles and the mass loss rate, it was proposed that the number of freeze-thaw cycles (

The effect of the number of freeze-thaw cycles on the mechanical properties of rubber concrete was analyzed based on the loading strain rate of 10^{−5}/s. The corresponding stress-strain curve is shown in Figure

The compressive stress-strain curve of ordinary concrete under static loading strain rate.

It can be seen from Figure

From the compressive stress-strain curve under the static loading strain rate, as shown in Figure

The effect of the number of freeze-thaw cycles on the peak stress of rubber concrete. (a) Peak stress. (b) Peak stress variation coefficient.

It can be seen from Figure

According to the dynamic compressive experiment plan under the action of different numbers of freeze-thaw cycles, the compressive stress-strain curves of rubber concrete under different loading conditions were obtained as shown in Figure

The compressive dynamic stress-strain curves of rubber concrete under the action of different numbers of freeze-thaw cycles. (a) D-0. (b) D-50. (c) D-100. (d) D-150.

According to Figure

Analysis of the effect of loading strain rate on the compressive peak stress of concrete is often based on the compressive peak stress dynamic increase factor (_{DIF-σ}), as shown in the following equation:_{d} is the compressive peak stress of concrete under the dynamic loading strain rate; _{s} is the compressive peak stress of concrete under the static loading strain rate.

The effect of loading strain on the compressive peak stress of rubber concrete was examined and analyzed based on the compressive peak stress values extracted from the stress-strain curves under different numbers of freeze-thaw cycles (Figure

The effect of strain rate on the peak compressive stress.

The effect of strain rate on the dynamic increase factor.

It can be seen from Figures ^{−5}/s. It is increased to 24.46 MPa at the loading strain rate of 10^{−2}/s, suggesting an increase of 30.73% relative to the static loading condition. When the number of freeze-thaw cycles is 50, 100, and 150, the compressive peak stress of rubber concrete is equal to 16.64 MPa, 13.36 MPa, and 11.07 MPa, respectively, at the loading strain rate of 10^{−5}/s and is increased to 22.57 MPa, 19.04 MPa, and 16.47 MPa, respectively, at the loading strain rate of 10^{−2}/s, suggesting an increase of 35.62%, 42.56%, and 48.80%, respectively, relative to the static loading condition. The literature [^{−5}/s to 10^{−2}/s and found that the peak stress of ordinary concrete was generally increased by 30%∼40%. Meanwhile, the effect of loading strain rate on the compressive peak stress of rubber concrete was slightly weaker than that of ordinary concrete. Such conclusions are consistent with the findings obtained by the literature [

For the mathematical analysis of the effect of loading strain rate on the compressive peak stress of concrete, the expression form as shown in equation (^{−5}/s∼10^{−1}/s) [_{1} and _{1} are undetermined parameters of the mathematical model.

Parameter _{1} is the compressive peak stress dynamic increase factor under the static strain rate, which is generally taken as 1. According to the dynamic compressive peak stress of rubber concrete under the action of different numbers of freeze-thaw cycles in this study, mathematical regression analysis was performed by applying equation (

It can be seen from equations (_{1} in equation (_{1} is gradually increased as the number of freeze-thaw cycles increases, suggesting a changing trend consistent with the finding of qualitative analysis. In order to propose the relationship between the compressive peak stress dynamic increase factor of rubber concrete and the loading strain rate under the action of freeze-thaw cycles, a linear relationship equation was established between parameter _{1} and the number of freeze-thaw cycles (

The relationship between the number of freeze-thaw cycles _{1}.

In order to examine the coupling effect of freeze-thaw cycles and loading strain rate on the compressive peak stress dynamic increase factor of rubber concrete, equation (_{1} was taken a value of 1 according to its specific meaning. Thus, the following equation was obtained:

Elastic modulus is one of the important parameters in the analysis of concrete mechanical properties. In general, the elastic modulus of concrete under different loading conditions can be calculated using the following equation based on the compressive stress-strain curve._{0.1} and _{0.1} refer to 10% of the compressive peak stress and peak strain of concrete, respectively; _{0.5} and _{0.5} refer to 50% of the compressive peak stress and peak strain of concrete, respectively.

Based on the compressive stress-strain curves of rubber concrete under the action of different numbers of freeze-thaw cycles and loading strain rates, equation (

The effect of strain rate on the elastic modulus.

The effect of strain rate on the elastic modulus dynamic increase factor.

It can be seen from Figures ^{3} MPa, 6.67 × 10^{3} MPa, 4.16 × 10^{3} MPa, and 2.40 × 10^{3} MPa, respectively. When the loading strain rate is 5 × 10^{−2}/s, the corresponding elastic modulus of rubber concrete is increased to 11.56 × 10^{3} MPa, 10.01 × 10^{3} MPa, 6.55 × 10^{3} MPa, and 3.96 × 10^{3} MPa, respectively. Thus, under the action of loading strain rate, the elastic modulus of rubber concrete is increased by 30.70%, 54.58%, 63.11%, and 68.03%, respectively. Based on the overall trend analysis, it can be seen that the elastic modulus of rubber concrete is gradually increased under the action of loading strain rate as the number of freeze-thaw cycles increases.

According to the dynamic elastic modulus of rubber concrete under different numbers of freeze-thaw cycles, equation (

From Figure _{DIF-E} under different numbers of freeze-thaw cycles. By comparatively analyzing the undetermined parameter _{2} in equation (

The peak strain values were extracted from the compressive stress-strain curves of rubber concrete under different loading conditions. The effect of loading strain rate on the peak strain of rubber concrete under different numbers of freeze-thaw cycles was analyzed based on the relative value of peak strain _{d}/_{s}, as shown in Figures

The effect of strain rate on the ultimate strain.

The effect of strain rate on the ultimate strain variation coefficient.

It can be seen from Figures ^{−5}/s and 5 × 10^{−2}/s. Affected by the loading strain rate, the changing amplitude of peak stress is 0%∼10.65%, −10.19%∼0.60%, −9.60%∼0%, and −4.48%∼4.25%, respectively. The analysis above implies that the loading strain rate has a discrete effect on the peak strain of rubber concrete. In the existing literature, the conclusions on the effect of loading strain rate on peak strain can be summarized as follows: (1) the peak strain is gradually increased as the loading strain rate increases; (2) the peak strain is gradually decreased as the loading strain increase; (3) there is no clear trend in the peak strain as the loading strain rate increases. The finding of this study is consistent with the third conclusion, which is mainly attributed to the coupling effect of the randomness, discreteness, and rate dependence of concrete materials [

The split-tensile section of the rubber concrete with a 10% rubber replacement rate and the compressive failure mode of the rubber concrete under the static strain rate without going through freeze-thaw cycles is shown in Figure

10% rubber concrete with 0 freeze-thaw cycles. (a) Specimen section. (b) Static compressive failure mode.

Compared with the split-tensile section and compressive failure mode of ordinary concrete, the failure section of rubber concrete appears to be relatively uneven and shows an obvious concave-convex failure mode. For the static compressive failure mode, the integrity of rubber concrete after compressive failure is higher than that of ordinary concrete, while the number of cracks, size, and brittleness characteristics of rubber concrete is all lower than that of ordinary concrete. The main reason for this is that the interface between the mortar and coarse aggregates is modified by the effect of rubber particles. To a certain extent, rubber particles inhibit the development of cracks and the rapid destruction of the specimen.

In the present study, the static and dynamic mechanical properties of rubber concrete with a 10% rubber replacement rate were examined under freeze-thaw cycles. The experimental results show that, compared with the freeze-thaw mechanical properties of ordinary concrete as reported in the literature, rubber particles exhibit a significant improvement effect on the mechanical properties of concrete under freeze-thaw cycles. The possible mechanism is that the rubber particles distributed in the concrete have strong deformability and provide a good buffer effect for the expansion of ice, which can inhibit the development and extension of cracks under freeze-thaw cycles to a certain extent. Meanwhile, rubber particles have a rough surface and can easily carry a part of the air component. Thus, they can exert a certain air-entraining effect, thereby improving the antifreezing property of concrete. The existing literature [

The failure of concrete is mainly a kind of instability state driven by energy, which is directly related to the internal damage evolution of the material and the energy consumption of plastic friction. The higher the strain rate, the faster the initial damage develops, and the greater the fracture energy is required by the concrete. Thus, the concrete shows a significant strain rate effect. With the increase in the number of freeze-thaw cycles, the microcracks and pores of rubber concrete gradually develop and expand, and its deformability is gradually improved. As a result, the initial internal damage of rubber concrete gradually increases with the increase in the number of freeze-thaw cycles. Eventually, with the increase of strain rate, the internal damage evolution and energy consumption of rubber concrete under a large number of freeze-thaw cycles are relatively large, so that as the number of freeze-thaw cycles increases, the strain rate effect of rubber concrete shows a gradually increasing trend.

From the experimental study on the compressive dynamic performance of rubber concrete under the action of different numbers of freeze-thaw cycles and loading strain rates, the compressive stress-strain curves of rubber concrete were obtained. By analyzing the mechanical characteristic parameters of rubber concrete (i.e., peak stress, elastic modulus, and peak strain) under different loading conditions, the following conclusions were drawn.

The development trend of the compressive stress-strain curve of rubber concrete is not affected by the number of freeze-thaw cycles and loading strain rate. As the number of freeze-thaw cycles increases, the plastic deformation ability of the compressive stress-strain curve is gradually strengthened. At the same loading strain rate, the compressive peak stress and elastic modulus of rubber concrete are gradually decreased while the peak strain is gradually increased as the number of freeze-thaw cycles increases. Compared to ordinary concrete, rubber concrete has a better frost resistance property.

For the same number of freeze-thaw cycles, the compressive peak stress and elastic modulus of rubber concrete are gradually increased as the loading strain rate increases, while the effect of loading strain rate on the peak strain is relatively discrete. As the number of freeze-thaw cycles increases, the compressive peak stress and elastic modulus dynamic increase factors of rubber concrete are gradually increased under the action of loading strain rate.

The compressive peak stress and elastic modulus dynamic increase factors of rubber concrete have a linear relationship with the dimensionless logarithm of the loading strain rate. Based on the coupling effect of freeze-thaw cycles and strain rate, a model equation for calculating the compressive peak stress dynamic increase factor was proposed. Meanwhile, the stress mechanism of rubber concrete under the coupling effect of freeze-thaw cycles and strain rate was discussed and analyzed.

The nature of the data is the experimental data of the compressive dynamic performance of rubber concrete under freeze-thaw cycles. The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that they have no conflicts of interest.

The research was supported by the National Natural Science Foundation of China (Grant no. 51969026) and Nalengelehe Water Conservancy Project Construction Management Bureau (Programme: Study on the Real Working Behavior and Long-Term Deformation Mechanism of the Ultra-Deep and Fully Enclosed Combined Anti-Seepage System in the Nalingelehe at High Altitude).