This study aims at determining the effect of water pressure on the mechanical properties of concrete subjected to freezethaw (FT) attack under the dynamic triaxial compression state. Two specimens were used: (1) a 100 mm × 100 mm × 400 mm prism for testing the loss of mass and relative dynamic modulus of elasticity (RDME) after FT cycles and (2) cylinders with a diameter of 100 mm and a height of 200 mm for testing the dynamic mechanical properties of concrete. Strain rates ranged from 10^{−5}·s^{−1} to 10^{−3}·s^{−1}, and FT cycles ranged from 0 to 100. Three levels of water pressure (0, 5, and 10 MPa) were applied to concrete. Results showed that as the number of FT cycles increased, the mass loss rate of the concrete specimen initially decreased and then increased, but the RDME decreased. Under 5 MPa of water pressure and at the same strain rate, the ultimate compressive strength decreased, whereas the peak strain increased with the increase in the number of FT cycles. This result is contrary to the variation law of ultimate compressive strength and peak strain with the increase in strain rate under the same number of FT times. With the increase in FT cycles or water pressure, the strain sensitivity of the dynamic increase factor of ultimate compressive strength and peak strain decreased, respectively. After 100 FT cycles, the dynamic compressive strength under all water pressure levels tended to increase as the strain rate increased, whereas the peak strain decreased gradually.
In the vast cold regions of the world, hydraulic concrete structures are subjected to freezethaw (FT) cycles due to day and night replacement and seasonal changes. The performance of concrete after FT deteriorates to varying degrees. Furthermore, these structures bear the impact of dynamic loads, such as vehicles, waves, and earthquakes, which seriously affect the longterm use and safe operation of concrete structures. The mechanical behaviour of concrete under dynamic load is different from that under static load [
Numerous studies have been conducted to investigate the effect of strain rate on concrete characteristics, such as compressive strength, peak strain, elastic modulus, and flexural and tensile strength. Wang et al. [
Aside from focusing on conventional concrete, substantial research has also been conducted on the dynamic mechanical properties of other types of concrete, such as recycled aggregate concrete (RAC), steel fibrereinforced concrete (SFRC), and ceramsite concrete. Several studies emphasised the mechanical behaviour of RAC under the effect of strain rate. Researchers [
Several studies on the dynamic uniaxial compressive performance of concrete after FT cycles can be found in the literature. Wang et al. [
Studies on the dynamic performance of concrete under multiaxial compression have also been conducted. Under multiaxial stress loading, compressive strength in dynamic state is higher than that in static state [
In this study, the dynamic mechanical properties of concrete subjected to FT cycles under triaxial compressive loading were investigated. The strain rate, number of FT cycles, and water pressure level ranged from 10^{−5}·s^{−1} to 10^{−3}·s^{−1}, 0 to 100, and 0 to 10 MPa, respectively. The microstructure was measured via scanning electron microscopy (SEM). The effects of strain rate, number of FT cycles, and water pressure on ultimate compressive strength, peak strain, and dynamic increase factor were analysed systematically.
In this investigation, Chinese standard [
Chemical composition of the cement.
Contents  Cement 

SiO_{2} (%)  21.45 
Al_{2}O_{3} (%)  6.45 
CaO (%)  61.5 
Fe_{2}O_{3} (%)  3.09 
MgO (%)  1.21 
K_{2}O (%)  1.38 
Na_{2}O (%)  0.25 
SO_{3} (%)  2.01 
Loss on ignition (%)  4.05 
Specific gravity (g/cm^{3})  3.15 
Mix proportions of concrete mixtures (kg/m^{3}).
Cement  Sand  Aggregate size (mm)  Water  Fly ash  Superplasticiser  Airentraining agent  

5–20  20–30  
285  705  626.5  626.5  136  55  2.28  0.0855 
Concrete specimens were cast in steel moulds with dimensions of 100 mm × 100 mm × 400 mm and Φ100 mm × 200 mm. The specimens were removed from the moulds after 24 h of casting and cured for 28 days under standard conditions (relative humidity was higher than 95%, and temperature was 20 ± 2°C). Prism specimens with dimensions of 100 mm × 100 mm × 400 mm were used to measure the loss of mass and relative dynamic modulus of elasticity (RDME) after FT cycles. Cylinder specimens with dimensions of Φ100 mm × 200 mm were used to assess the triaxial mechanical properties of concrete after FT cycles at different strain rates. Three specimens were used in each test, and the average value was used for the test results.
In accordance with the Chinese standard GB/T 500822009 [
The testing instrument used in this test was a servohydraulic, static, and dynamic triaxial testing system in the hydraulic laboratory of Xi’an University of Technology, as shown in Figure
Test setup: (a) schematic of the system; (b) servohydraulic static and dynamic triaxial testing system.
The surface scaling of the concrete specimens after 0, 25, 50, 75, and 100 FT cycles is shown in Figure
Deterioration of concrete specimens after FT cycles.
Figure
Mass loss rate of concrete during FT cycles.
As shown in Figure
RDME of concrete during FT cycles.
Figure
Dynamic ultimate compressive strength of concrete during FT cycles.
The relationship between ultimate compressive strength of concrete and strain rate at a water pressure of 5 MPa is shown in Figure
Dynamic ultimate compressive strength of concrete at different strain rates.
Griffith theory and the principle of subcritical crackle expansion can be applied to explain these trends. On the one hand, according to Griffith theory, when the flaw size of brittle material is larger than the critical size, fracture will occur. Subcritical cracks have enough time to expand at lower strain rates, and then failure occurs under a lower load. When the strain rate is higher, the subcritical crackles have less time for extension. At this time, the material structure can withstand a relatively larger load before the occurrence of failure. Furthermore, on the basis of knowledge of fracture mechanics [
On the other hand, free water viscosity affects concrete. Kaplan et al. [
Viscous fluid exists between two flat parallel plates with a distance of
Stefan effect.
Stefan effect of concrete pore water.
Similarly, the relationship between the peak strain and the number of FT cycles under a water pressure of 5 MPa is shown in Figure
Peak strain of concrete during FT cycles.
Figure
Peak strain of concrete at different strain rates.
The DIF of ultimate compressive strength or peak strain is defined as the ratio of ultimate compressive strength or peak strain at each strain rate to ultimate compressive strength or peak strain at a strain rate of 1 × 10^{−5}·s^{−1}.
The relationship between DIF of ultimate compressive strength and strain rate under different numbers of FT cycles is shown in Figure
Relationship of compressive strength increase factor versus relative strain rate.
As the number of FT cycles increased, the slope of the fitting curve gradually decreased; that is, the increase in the number of FT cycles reduced the rate sensitivity of the ultimate compressive strength of the concrete, because as the number of FT cycles increased, the capillary microcracks inside the concrete gradually developed, and the amount of water absorbed from the surrounding environment increased. On the one hand, the presence of water in concrete, with the increase in strain rate, enhanced water viscous action and increased the sensitivity of concrete accordingly. On the other hand, under the repeated action of frost heaving force, the internal pores of concrete further increased, and the wedging effect of water enhanced. Thus, the slope of the fitting curve grew slowly. At the same time, the crack expanded further due to concrete damage during the test loading stage, and the water in the concrete spread around the crack under the action of the pressing force to form a water wedge effect. However, the water content of concrete at 0 FT cycle was lower than those at 50 and 100 FT cycles. The wedge effect can be ignored. Thus, the slope of 0 FT cycle was higher than those of 50 and 100 cycles. Concrete rate sensitivity decreased as the number of FT cycles increased.
The relationship between the DIF of peak strain and strain rate under different numbers of FT cycles is shown in Figure
Relationship of peak strain increase factor versus relative strain rate.
Figure
Each test was repeated three times, and the average ultimate strength of concrete subjected to 100 FT cycles under triaxial compression at different strain rates and standard deviation
Average ultimate strength of concrete under biaxial compression loading (MPa).
Water pressure  Strain rate  

1 × 10^{−5}·s^{−1}  ± 
1 × 10^{−4}·s^{−1}  ± 
2 × 10^{−4}·s^{−1}  ± 
5 × 10^{−4}·s^{−1}  ± 
1 × 10^{−3}·s^{−1}  ± 

0  20.98  0.09  24.43  0.02  26.01  0.08  27.55  0.10  29.22  0.16 
5  59.42  0.10  61.27  0.13  62.83  0.06  65.03  0.11  66.57  0.11 
10  69.64  0.06  71.53  0.11  73.26  0.14  75.09  0.13  76.59  0.20 
Figure
Relationship of ultimate compressive strength versus water pressure at different strain rates.
Figure
Effect of water pressure on the relationship between MDIF and strain rate: (a) DIF of dynamic compressive strength; (b) DIF of peak strain.
The damage of concrete exposed to the combined effect of FT cycles and strain rate under triaxial compression is a complex process that comprises physical and chemical aspects. Evaluation of the microstructure of damaged concrete is a common method to reveal the cause of failure. In this study, SEM was used to understand the coupled effect of FT cycles and strain rate on the concrete dynamic compressive strength at a water pressure of 5 MPa; the micrographs of concrete are shown in Figure
SEM images (magnification 1000×) of the specimen after FT cycles and triaxial compression: (a) 0 cycle and strain rate of 1 × 10^{−4}·s^{−1}; (b) 50 cycles and strain rate of 1 × 10^{−4}·s^{−1}; (c) 100 cycles and strain rate of 1 × 10^{−4}·s^{−1}; (d) 100 cycles and strain rate of 1 × 10^{−3}·s^{−1}.
A comparison of Figures
In this study, dynamic compressive experiments for concrete subjected to different numbers of FT cycles (0, 50, and 100) and under various water pressure levels (0, 5, and 10 MPa) were conducted at different strain rates (1 × 10^{−5}, 1 × 10^{−4}, 2 × 10^{−4}, 5 × 10^{−4}, and 1 × 10^{−3}·s^{−1}). The following conclusions can be drawn from the test results:
As the number of FT cycles increases, the mass of concrete specimen initially increases and then decreases, whereas the relative dynamic elastic modulus of concrete tends to decrease.
With the increment of FT cycles at the same strain rate and a water pressure of 5 MPa, the dynamic ultimate compressive strength of concrete decreases, but the peak strain of concrete tends to increase. The decrease in compressive strength is due to the dramatic change in pore structure under the action of FT cycles. However, the corresponding ductility increases as the porosity of concrete increases, thereby improving peak strain.
With the same number of FT cycles under a water pressure of 5 MPa, the dynamic ultimate compressive strength of concrete increases with the increase in strain rate, whereas the peak strain of the concrete tends to decrease.
The strain rate sensitivity of the DIF of ultimate compressive strength and peak strain decreases with the increase in FT cycles. The same results apply to the influence of water pressure on the strain rate sensitivity of the DIF of ultimate compressive strength and peak strain. A formula that describes the relationship between the DIF of compressive strength and peak strain and strain rate under different numbers of FT cycles is proposed based on the experimental results. The calculated results are in good agreement with the experimental data using this equation.
After 100 FT cycles, with the increase in strain rate, the dynamic compressive strength under every water pressure level tends to increase, and its value under triaxial compressive loading is higher than that under uniaxial compressive loading. However, peak strain decreases gently, especially with a smaller variation under 10 MPa water pressure.
The SEM images of concrete at the same strain rate after FT action reveals more microcracks and less compacted microstructures, which coincide with the results of ultimate compressive strength. Moreover, cracks in concrete structures are relatively narrower under a high strain rate.
For future work, more FT cycles and a higher strain rate range may be tested to understand the precise research of strength and deformation under dynamic loading. Moreover, other elements, such as mineral admixture, watercement ratio, and specimen size, affect the dynamic mechanical properties of concrete under triaxial compression. Therefore, additional experiments are needed.
The data used to support the findings of this study are available upon request from the corresponding author.
The authors declare no conflicts of interest regarding the publication of this paper.
This study was financially supported by the National Natural Science Foundation of China (51679197).