# Influence of Water Pressure on the Mechanical Properties of Concrete after Freeze-Thaw Attack under Dynamic Triaxial Compression State

Authors: Ruijun Wang; Yan Li; Yang Li; Fan Xu; Xiaotong Li; Tenghuan Fu
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

This study aims at determining the effect of water pressure on the mechanical properties of concrete subjected to freeze-thaw (F-T) 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 F-T 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 F-T 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 F-T 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 F-T 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 F-T times. With the increase in F-T cycles or water pressure, the strain sensitivity of the dynamic increase factor of ultimate compressive strength and peak strain decreased, respectively. After 100 F-T cycles, the dynamic compressive strength under all water pressure levels tended to increase as the strain rate increased, whereas the peak strain decreased gradually.


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## Body

## 1. Introduction

In the vast cold regions of the world, hydraulic concrete structures are subjected to freeze-thaw (F-T) cycles due to day and night replacement and seasonal changes. The performance of concrete after F-T deteriorates to varying degrees. Furthermore, these structures bear the impact of dynamic loads, such as vehicles, waves, and earthquakes, which seriously affect the long-term use and safe operation of concrete structures. The mechanical behaviour of concrete under dynamic load is different from that under static load [1, 2].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. [3] reported the effect of water pressure on the mechanical properties of concrete and established failure modes, which were affected by strain rate and water content. Yan and Lin [4] evaluated concrete dynamic strength and deformation properties under initial static stress and found that total deformation of concrete was greatly influenced by initial static loading history. Xiao et al. [5] reported that, when the strain rate reaches approximately 10−1·s−1, the compressive strength increased linearly as the strain rate increased. Furthermore, the strength increased more strongly at high strain rates [6]. Ahmad et al. [7] concluded that, compared with elastic modulus, compressive strength is more sensitive to strain rate. This view was also supported by [8]. Scholars have found that peak strain increases with strain rate [9–12]. Chen et al. [5, 13, 14] studied the tensile strength of cement-based materials and compared the strain rate sensitivity of concrete under tension and pressure. They found that dynamic tensile strength increased as strain rate increased, while the dynamic increase factor was less influenced by the water-cement ratio.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 fibre-reinforced concrete (SFRC), and ceramsite concrete. Several studies emphasised the mechanical behaviour of RAC under the effect of strain rate. Researchers [15–19] found that elastic modulus and peak stress increase as strain rate increases. Moreover, the strain rate sensitivity of elastic modulus and peak stress of RAC are more remarkable than those of RAC with carbonated RAC due to the Stefan effect [19]. Deng et al. [20] reported that the compressive strength of RAC under triaxial loading is much higher than that under uniaxial loading. The stress ratio and replacement rate of RCA affect strength and strain greatly. Wang and Xiao [10] investigated the influence of RCA replacement ratio and strain rate on the mechanical performance of confined recycled aggregate concrete (CRAC) and proposed a constitutive model for CRAC, which may be used for dynamic analysis of RAC. Some researchers conducted experiments to evaluate the mechanical behaviours of SFRC at a high strain rate. They concluded that dynamic compressive strength, critical strain, and energy absorption increased as strain rate and steel fibre content increased. Furthermore, the growth of strength and strain is less significant than that of energy absorption because increases in strength and strain are ultimately reflected in increases in energy absorption [21–24]. Chen et al. [25] tested the dynamic performance of ceramsite concrete with different numbers of F-T cycles and ceramsite volume fraction. They suggested that the increase in F-T cycles or the volume fraction of ceramsite is harmful to the compressive strength and damage degree of ceramsite concrete.Several studies on the dynamic uniaxial compressive performance of concrete after F-T cycles can be found in the literature. Wang et al. [26] studied the coupled influence of strain rate and F-T on the uniaxial dynamic compressive performance of fully graded concrete. Furthermore, they proposed a failure mechanism of fully graded concrete, considering the influence of F-T cycle number and strain rate. Yi et al. [27] conducted a uniaxial compressive experiment with different F-T cycles and loading rates to verify the rationality of the model of porous asphalt mixtures. Zhou et al. [28] tested five groups of sandstone dynamic mechanical behaviours under the effect of F-T cycles. They suggested that the void ratio rises and the structure of pores changes considerably as the number of F-T cycles increase. Dynamic peak stress and elastic modulus are reduced, but peak strain increases with the process of F-T cycles. Lu et al. [29] conducted a uniaxial compressive experiment on concrete specimens subjected to the combined effects of F-T cycles and fatigue loading. They found that concrete dynamic compressive strength increases with the increase in strain rate, and the strain rate effect of concrete becomes apparent after F-T cycles. Li et al. [30] conducted a test on the dynamic mechanical properties of sandstone samples exposed to F-T cycling and reported that, as F-T cycles increased, peak strain and apparent damage increase, but peak stress is reduced.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 [31–33]. Wang et al. [34] evaluated the coupled effects of water content and loading rate on the properties of concrete. They reported that a high water content of concrete corresponds to high sensitivity; this finding is consistent with that of [3]. However, few studies have been conducted on the dynamic performance change of concrete under triaxial compression stress after F-T cycles, hence proving the importance of this research.In this study, the dynamic mechanical properties of concrete subjected to F-T cycles under triaxial compressive loading were investigated. The strain rate, number of F-T 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 F-T cycles, and water pressure on ultimate compressive strength, peak strain, and dynamic increase factor were analysed systematically.


## 2. Materials and Methods

### 2.1. Materials and Mix Proportions

In this investigation, Chinese standard [35] P.O. 42.5R ordinary Portland cement supplied by the Shanxi Qinling cement plant in China was used. The chemical composition of the cement used for the test is listed in Table 1. Weihe River sand was used as fine aggregate, with a fineness modulus of 2.35. The coarse aggregate of natural river pebble with diameters of 5–20 and 20–30 mm was used, constituting half of the total coarse aggregate. Tap water, air-entraining agent, and polycarboxylic superplasticiser were used. The mix proportions of concrete are shown in Table 2.Table 1
Chemical composition of the cement.
Contents
Cement
SiO2 (%)
21.45
Al2O3 (%)
6.45
CaO (%)
61.5
Fe2O3 (%)
3.09
MgO (%)
1.21
K2O (%)
1.38
Na2O (%)
0.25
SO3 (%)
2.01
Loss on ignition (%)
4.05
Specific gravity (g/cm3)
3.15Table 2
Mix proportions of concrete mixtures (kg/m3).
Cement
Sand
Aggregate size (mm)
Water
Fly ash
Superplasticiser
Air-entraining agent
5–20
20–30
285
705
626.5
626.5
136
55
2.28
0.0855


### 2.2. Casting and Curing of Specimens

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 F-T cycles. Cylinder specimens with dimensions of Φ100 mm × 200 mm were used to assess the triaxial mechanical properties of concrete after F-T cycles at different strain rates. Three specimens were used in each test, and the average value was used for the test results.


### 2.3. Apparatus and Testing Methods

In accordance with the Chinese standard GB/T 50082-2009 [36] (similar to ASTM C666/C666M-03), a rapid F-T cycle test was conducted by using an F-T apparatus. During the test, each F-T cycle was completed within 4 h, and the thawing time was more than one quarter of the freezing and thawing time. The minimum and maximum temperatures of the specimen center were controlled within (–18 ± 2) °C and (5 ± 2)°C, respectively. The cooling time from 3°C to −16°C was more than one-half of the freezing time, and the heating time from –16°C to 3°C was more than one-half of the thawing time. F-T cycles were repeated 100 times, and the specimens were evaluated every 25 cycles for the calculation of RDME.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 Figure1. The axial load capacity is 2000 kN for concrete materials, and its accuracy is 0.1%. The target values of water pressure and loading rate were set before loading. Then, the electromagnetic directional valve was opened to connect the pressurised water cylinder and the confining pressure channel. Afterwards, the pressure servo oil source was opened; the servo valve controlled the cylinder plunger forward, and the water pressure increased to the target value, which was detected by the pressure sensor. Once the deviation occurred, the servo valve controlled the pressure drive cylinder piston to swing back and forth to maintain the set value of the water pressure. The axial strain rate in the test was set at 1 × 10−5, 1 × 10−4, 2 × 10−4, 5 × 10−4, and 1 × 10−3·s−1.Figure 1
Test setup: (a) schematic of the system; (b) servohydraulic static and dynamic triaxial testing system.
(a)
(b)


## 2.1. Materials and Mix Proportions

In this investigation, Chinese standard [35] P.O. 42.5R ordinary Portland cement supplied by the Shanxi Qinling cement plant in China was used. The chemical composition of the cement used for the test is listed in Table 1. Weihe River sand was used as fine aggregate, with a fineness modulus of 2.35. The coarse aggregate of natural river pebble with diameters of 5–20 and 20–30 mm was used, constituting half of the total coarse aggregate. Tap water, air-entraining agent, and polycarboxylic superplasticiser were used. The mix proportions of concrete are shown in Table 2.Table 1
Chemical composition of the cement.
Contents
Cement
SiO2 (%)
21.45
Al2O3 (%)
6.45
CaO (%)
61.5
Fe2O3 (%)
3.09
MgO (%)
1.21
K2O (%)
1.38
Na2O (%)
0.25
SO3 (%)
2.01
Loss on ignition (%)
4.05
Specific gravity (g/cm3)
3.15Table 2
Mix proportions of concrete mixtures (kg/m3).
Cement
Sand
Aggregate size (mm)
Water
Fly ash
Superplasticiser
Air-entraining agent
5–20
20–30
285
705
626.5
626.5
136
55
2.28
0.0855


## 2.2. Casting and Curing of Specimens

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 F-T cycles. Cylinder specimens with dimensions of Φ100 mm × 200 mm were used to assess the triaxial mechanical properties of concrete after F-T cycles at different strain rates. Three specimens were used in each test, and the average value was used for the test results.


## 2.3. Apparatus and Testing Methods

In accordance with the Chinese standard GB/T 50082-2009 [36] (similar to ASTM C666/C666M-03), a rapid F-T cycle test was conducted by using an F-T apparatus. During the test, each F-T cycle was completed within 4 h, and the thawing time was more than one quarter of the freezing and thawing time. The minimum and maximum temperatures of the specimen center were controlled within (–18 ± 2) °C and (5 ± 2)°C, respectively. The cooling time from 3°C to −16°C was more than one-half of the freezing time, and the heating time from –16°C to 3°C was more than one-half of the thawing time. F-T cycles were repeated 100 times, and the specimens were evaluated every 25 cycles for the calculation of RDME.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 Figure1. The axial load capacity is 2000 kN for concrete materials, and its accuracy is 0.1%. The target values of water pressure and loading rate were set before loading. Then, the electromagnetic directional valve was opened to connect the pressurised water cylinder and the confining pressure channel. Afterwards, the pressure servo oil source was opened; the servo valve controlled the cylinder plunger forward, and the water pressure increased to the target value, which was detected by the pressure sensor. Once the deviation occurred, the servo valve controlled the pressure drive cylinder piston to swing back and forth to maintain the set value of the water pressure. The axial strain rate in the test was set at 1 × 10−5, 1 × 10−4, 2 × 10−4, 5 × 10−4, and 1 × 10−3·s−1.Figure 1
Test setup: (a) schematic of the system; (b) servohydraulic static and dynamic triaxial testing system.
(a)
(b)


## 3. Results and Discussion

### 3.1. Surface Scaling

The surface scaling of the concrete specimens after 0, 25, 50, 75, and 100 F-T cycles is shown in Figure2. Unlike the samples that did not undergo an F-T cycle, the local surface of the samples became rough and the cement mortar on the epidermis spalled off after 50 F-T cycles. After 75 and 100 F-T cycles, the rough surface and flaking area of the specimen were enlarged, and microholes appeared.Figure 2
Deterioration of concrete specimens after F-T cycles.


### 3.2. Mass Loss Rate

Figure3 illustrates the change in mass loss of the concrete after 100 F-T cycles. The mass loss rate of the concrete specimens generally showed a trend of initial decline followed by a gradual increase. The mass loss rates at 0, 25, 50, 75, and 100 F-T cycles were 0, −0.05%, 0.08%, 0.10% and 0.24%, respectively. After 0–25 F-T cycles, the loss rate of concrete mass showed a downward trend due to the microcracks inside the specimen after the F-T cycle. The concrete specimen absorbed water from the surrounding environment, and water turned into ice due to freezing. Pores expanded and resulted in additional pores because of frost heaving. Therefore, water was immersed in the pores, and the internal water content continuously increased. Simultaneously, the flaking of the mortar on the surface worsened with the increase in F-T cycles, resulting in the reduced quality of the specimen. Therefore, during the early stage of F-T cycles, the mortar peeled off less, and the increase in mass caused by water absorption dominated, thereby indicating that the overall quality of the specimen increased. After 25–50 F-T cycles, the spalling of mortar aggravated due to intensified F-T degradation. Given that the mass loss caused by the apparent spalling of cement mortar of the concrete specimen was greater than the water absorption of the internal crack, the mass loss rate of the specimen shows an upward trend. Under the effect of the F-T cycle, the water flowing into the concrete pores turned into ice, causing the volume of concrete to expand and the width of microcracks to increase. Moreover, with the formation of some new pores, the amount of water absorbed by the cracks in the specimen was equal to the amount dropped by mortar, and the mass loss rate after 50–75 F-T cycles was relatively flat. However, after 75–100 F-T cycles, the drop of particles on the surface of the specimen played a major role, and the mass loss rate continued to rise.Figure 3
Mass loss rate of concrete during F-T cycles.


### 3.3. RDME

As shown in Figure4, the RDME of concrete specimens tends to decrease with the increase in the number of F-T cycles. The value of initial dynamic elastic modulus was 42.07 GPa. The RDME of concrete specimens at 0, 25, 50, 75, and 100 F-T cycles was 100%, 99.46%, 98.67%, 97.69%, and 95.20%, respectively. The loss rate of RDME increased with the increase in F-T cycles due to the formation of frost heaving pressure caused by F-T cycles. Furthermore, the microstructure of concrete was affected, the degree of damage aggravated, the cracks multiplied, and density was reduced. During this process, water accelerated into the interior of the void, which aggravated the damage of specimens under the action of F-T cycles, resulting in increased damage of the internal structure of the concrete.Figure 4
RDME of concrete during F-T cycles.


### 3.4. Dynamic Mechanical Properties

#### 3.4.1. Ultimate Compressive Strength

Figure5 shows the relationship between the dynamic ultimate compressive strength and the number of F-T cycles under a constant water pressure of 5 MPa. Test results revealed that the ultimate compressive strength of concrete decreased with the increase in the number of F-T cycles at the same loading rate, and different trends occurred at various stages of the F-T cycles. The gradient of the ultimate compressive strength of concrete at 0–50 F-T cycles is smaller than that at 50–100 F-T cycles. This result may have occurred because during the early F-T cycles, the fine particles inside the concrete were squeezed and compactness increased, thereby making it difficult for water to enter the pores. This condition limited the expansion of the pores. These results agreed with those suggested by Li et al. [30] that, during the F-T cycles, mineral particles are compacted and the cohesive forces between them are gradually strengthened, which can availably offset part of the frost heave force, thus limiting pore expansion. Therefore, the internal damage of the concrete was weakened, and the influence of the F-T cycle on ultimate compressive strength was reduced. At 50–100 F-T cycles, the pore structure inside the concrete changed greatly as the degree of F-T deterioration increased. The width of some small pores increased and evolved into microcracks, and the pores that connected with each other caused the rapid decrease in the ultimate compressive strength of the concrete under dynamic loading.Figure 5
Dynamic ultimate compressive strength of concrete during F-T cycles.The relationship between ultimate compressive strength of concrete and strain rate at a water pressure of 5 MPa is shown in Figure6. Concrete is a material with high strain rate sensitivity. With the same number of F-T cycles, the ultimate compressive strength of concrete increased with the increase in strain rate. This view is also supported by [26, 29].Figure 6
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 [37–39], a microcrack process area is believed to be present before flaw expands. The speed of crackle growth also determines the size of the process area, as proposed by [40]. Therefore, at a high strain rate, the propagation velocity of flaw becomes faster, and the process area becomes larger. Thus, crack expansion requires more energy, while concrete has insufficient time to store energy at a higher strain rate. The extra energy can be released by only increasing the stress, which finally manifests as an increase in strength.On the other hand, free water viscosity affects concrete. Kaplan et al. [41] believed that, when a specimen is subjected to compression stress, the pores and channels perpendicular to the loading direction in the concrete tend to close, allowing free water to flow inside the specimen. The presence of viscosity and liquid-phase pressure gradients causes pore water pressure to increase at a high loading rate, which delays the occurrence of excessive cracks in the solid phase and eventually increases compressive strength. Through experimental observations and theoretical assumptions, Rossi et al. [8, 42–44] indicated that the mechanical properties of concrete under high strain rate could be explained by the Stefan effect and material cracking process interaction. Moreover, for the cone-type concrete failure mode, lateral deformation was restricted to viscous stress. Thus, the damage of specimens decreased. The effect of damping caused by the viscous stress could also slow down the expansion of microcracks for the concrete failure mode of slant shear. Finally, the strength of concrete increased [3].Viscous fluid exists between two flat parallel plates with a distance ofh. When two parallel plates are separated or closed at a certain speed, their motion will be affected by the viscous resistance generated by the viscous fluid. This phenomenon is called the Stefan effect. Moreover, a great velocity corresponds to a great reaction force, as shown in Figure 7. Pores and cracks of varying sizes in concrete contain free water. At this point, cement matrix and water can be regarded as a microdisc system, and pore water will generate viscous resistance under dynamic loading, as shown in Figure 8. This condition is an important factor that affects the strain rate sensitivity of concrete [8]. From this perspective, more free water will immerse into the pores after the F-T cycles. As the strain rate increases, the number of viscously resistant microelements increases, and the influence of free water on viscous resistance becomes greater. Therefore, the damage to the concrete is lessened and concrete exhibits a higher ultimate compressive strength value, which agrees with Li et al. [19], who reported that the strength increase in RAC samples is greater than that of CRAC due to higher viscous resistance.Figure 7
Stefan effect.Figure 8
Stefan effect of concrete pore water.


#### 3.4.2. Peak Strain

Similarly, the relationship between the peak strain and the number of F-T cycles under a water pressure of 5 MPa is shown in Figure9. At the same strain rate, the peak strain of concrete tended to increase gradually as the number of F-T cycles increased, because during the F-T cycles, the water in the pores would freeze and swell. Under the repeated action of the frost heaving force, the pores gradually increased, the concrete volume increased, and the compactness gradually decreased. However, in the compression test, the concrete first underwent the compaction process after the F-T cycles. Therefore, the peak strain of the concrete, as well as its ductility, increased.Figure 9
Peak strain of concrete during F-T cycles.Figure10 illustrates the relationship between peak strain and strain rate under a water pressure of 5 MPa. With the same number of F-T cycles, the peak strain of the concrete tended to decrease with the increase in strain rate. According to the theory of minimum energy consumption, the destruction of a system is always operated with the minimum energy consumption per unit time. A previous research showed that cracks mostly expand from interfacial zones between aggregates and mortars, and few cracks directly passing through weak aggregates due to the strengths of a mortar matrix and interfacial transition zone are lower than the strength of a natural coarse aggregate [16, 19]. Fracture pattern depends on aggregate shape and other factors, such as aggregate properties and matrix-aggregate interface. Therefore, at a relatively low strain rate, the crack had enough time to select a fracture path, that is, the crack started at the weak surface between the aggregate and the mortar and then expanded and passed through the mortar along the weak surface. At a relatively high strain rate, the crack became more dispersed. The crack had insufficient time to select the weakest failure interface but expanded along the path with the fastest energy release immediately. It would break directly through the aggregate, resulting in the failure path becoming shorter, thereby decreasing the deformation of the concrete.Figure 10
Peak strain of concrete at different strain rates.


#### 3.4.3. Dynamic Increase Factor (DIF)

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 F-T cycles is shown in Figure11. As the strain rate increased, the DIF of the ultimate compressive strength of each number of F-T cycle increased. However, the increase rate varied under different F-T cycles. The relationship between strength increment and strain rate was established by the following fitting test data:(1)fcfcs=1+αlgε˙cε˙cs,where fc is the ultimate compressive strength in dynamic loading, fcs is the ultimate compressive strength in quasistatic loading, ε˙c is the current strain rate (ε˙c = 1 × 10−4, 2 × 10−4, 5 × 10−4, and 1 × 10−3·s−1 in this study), ε˙cs is the quasistatic strain rate (ε˙cs = 1 × 10−5·s−1), and α is a parameter.Figure 11
Relationship of compressive strength increase factor versus relative strain rate.As the number of F-T cycles increased, the slope of the fitting curve gradually decreased; that is, the increase in the number of F-T cycles reduced the rate sensitivity of the ultimate compressive strength of the concrete, because as the number of F-T 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 F-T cycle was lower than those at 50 and 100 F-T cycles. The wedge effect can be ignored. Thus, the slope of 0 F-T cycle was higher than those of 50 and 100 cycles. Concrete rate sensitivity decreased as the number of F-T cycles increased.The relationship between the DIF of peak strain and strain rate under different numbers of F-T cycles is shown in Figure12. With the increase in strain rate, the DIF of peak strain decreased in each cycle. However, the magnitude of reduction in the fitted curves was not the same. To analyse the relationship between peak strain increment and strain rate, the relationship between peak strain and strain rate was established by fitting test data, as shown below:(2)εpεusp=1+βlgε˙cε˙cs,where εp is the peak strain in dynamic loading, εusp is the peak strain in quasistatic loading, ε˙c is the current strain rate (ε˙c = 1 × 10−4, 2 × 10−4, 5 × 10−4, and 1 × 10−3·s−1 in this study), ε˙cs is the quasistatic strain rate (ε˙cs = 1 × 10−5·s−1), and β is a parameter.Figure 12
Relationship of peak strain increase factor versus relative strain rate.Figure12 shows that, under the same number of F-T cycles, the peak strain growth rates were all less than 1 as the strain rate increased, that is, the peak strain gradually decreased. Moreover, the variation curve of specimens with more F-T cycles was relatively gentle, which means that the increase in F-T cycles weakens the sensitivity of the peak strain rate of concrete. The reason is that, with the increase in the strain rate, the internal microcrack of concrete cannot be fully compressed due to the short time of load action, and the crack will expand in a manner that consumes less energy, that is, directly passing through the aggregate, to cause damage. These results are consistent with those of Wang et al. [45, 46], who demonstrated that cracks propagate by cutting through aggregates and aggregates are fractured into many small pieces with the increase of strain rate. More cracks passed through the aggregate rather than bypass the expansion and compression closure of the aggregate. Eventually, the peak strain decreased gradually with a growth rate of less than 1. However, many intricate and different sizes of internal cracks exist in concrete with more severe F-T deterioration. The crack that originally broke through the aggregate changed the damage mode and increased the length of the damage path. Thus, the decrease in peak strain was small.


### 3.5. Influence of Water Pressure on Dynamic Mechanical Properties

Each test was repeated three times, and the average ultimate strength of concrete subjected to 100 F-T cycles under triaxial compression at different strain rates and standard deviationδ are shown in Table 3. The concrete’s ultimate strength under uniaxial compressive loading was lower than that under triaxial compressive loading due to the constraint effect of triaxial compression. This condition can explain why the further expansion of the crack was limited by the water pressure. This finding is close to the results of [34, 47–49], which also stated that the grading of aggregates may be one of the factors that influence the value of ultimate strength [47]. The strength of concrete decreased as water pressure increased at a strain rate of 10−5·s−1 [3], which is contrary to the findings of this study. This phenomenon may be primarily due to the different concrete conditions before the triaxial test. In this study, specimens were cured in water, whereas in [3], concretes were placed in a natural environment for 1200 days. Researchers [50, 51] noted that water will flow to the crackle tip and destroy the capillary structure of the dry concrete matrix under the action of water pressure. However, only a small amount of water will immerse into the water-cured concrete because of water-filled pores, thereby resulting in slower crack propagation and little or even negligible damage to the matrix.Table 3
Average ultimate strength of concrete under biaxial compression loading (MPa).
Water pressure
Strain rate
1 × 10−5·s−1
±δ
1 × 10−4·s−1
±δ
2 × 10−4·s−1
±δ
5 × 10−4·s−1
±δ
1 × 10−3·s−1
±δ
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
0.20Figure13 shows the relationship between the compressive strengths of concrete and water pressure, where σl is the water pressure and fus is the ultimate compressive strength in quasistatic loading. The dynamic strength of concrete tended to increase with the increase in strain rate. When the constant lateral pressure was in the lower range (0–5 MPa), the dynamic ultimate compressive strength of concrete had a remarkable tendency to increase with the increase in strain rate. However, when the water pressure was higher (5–10 MPa), the increase in dynamic ultimate compressive strength of concrete became muted with the increase in strain rate. In addition, some researchers [33] believe that when the confining pressure exceeds a certain value and this value is the uniaxial compressive strength of concrete, the compressive strength of concrete no longer considers the effect of strain rate.Figure 13
Relationship of ultimate compressive strength versus water pressure at different strain rates.Figure14 shows the effect of water pressure on the relationship between DIF and strain rate. The DIF of dynamic compressive strength and peak strain trend is shown at different strain rates. Figure 14(a) illustrates the relationship between the DIF of dynamic compressive strength of concrete and the strain rate under different water pressures. At the same strain rate, the slope of the fitted line decreased gradually with the increase in water pressure after 100 F-T cycles. This result indicates that the presence of water pressure reduced the sensitivity of concrete strength. This finding is consistent with the view that the effect of strain rate decreases as water pressure increases [2, 33], but it diverges from the data by [3, 34]. Concrete in these papers [2, 3, 33, 34] was not exposed to F-T cycles. Moreover, under 5 and 10 MPa of water pressure, the increment speed was nearly the same, because the water content of concrete under 5 MPa is equal to that under 10 MPa. As previous research [3] indicated, water is important in the improvement of concrete strength under the same strength of concrete skeleton at the same strain rate. Figure 14(b) also reveals that the peak strain of specimens increased with the increase in water pressure. This result can be due to the fact that, when water pressure was applied, the concrete specimens were restrained by lateral pressure, and the appearance and expansion of internal cracks were delayed. The compressive strength and deformation capacity of concrete improved, and the deformation property changed from brittleness to ductility. Consequently, the DIF of strength and peak strain of concrete under conventional triaxial stress state was strongly dependent on the value of water pressure.Figure 14
Effect of water pressure on the relationship between MDIF and strain rate: (a) DIF of dynamic compressive strength; (b) DIF of peak strain.
(a)
(b)


### 3.6. Microstructure Characterisation

The damage of concrete exposed to the combined effect of F-T 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 F-T cycles and strain rate on the concrete dynamic compressive strength at a water pressure of 5 MPa; the micrographs of concrete are shown in Figure15. Figures 15(a)–15(c) demonstrate that at the strain rate of 1 × 10−4·s−1, a relatively tight and dense structure and only one microcrack inside the concrete specimens exist without the effect of F-T cycles, which can be explained by shrinkage deformation of cement paste during hydration reaction [52, 53]. However, different degrees of F-T damage occurred after being subjected to 50 and 100 F-T cycles. The length, width, and number of microcracks increased. Microcracks connected to each other can be easily seen in Figure 15(c), which is good evidence that at the same strain rate, and the value of ultimate compressive strength decreased with the increase in F-T cycles.Figure 15
SEM images (magnification 1000×) of the specimen after F-T 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)
(b)
(c)
(d)A comparison of Figures15(c) and 15(d) reveals that, under the same number of F-T cycles (100), the width of microcracks with a strain rate of 1 × 10−3·s−1 was smaller than that with a strain rate of 1 × 10−4·s−1, because the speed of microcrack propagation increased with the increase in strain rate, and microcracks did not have enough time to expand fully. This view is consistent with the results indicating that the ultimate compressive strength at the strain rate of 1 × 10−3·s−1 is higher than at 1 × 10−4·s−1 after 100 F-T cycles under a water pressure of 5 MPa.


## 3.1. Surface Scaling

The surface scaling of the concrete specimens after 0, 25, 50, 75, and 100 F-T cycles is shown in Figure2. Unlike the samples that did not undergo an F-T cycle, the local surface of the samples became rough and the cement mortar on the epidermis spalled off after 50 F-T cycles. After 75 and 100 F-T cycles, the rough surface and flaking area of the specimen were enlarged, and microholes appeared.Figure 2
Deterioration of concrete specimens after F-T cycles.


## 3.2. Mass Loss Rate

Figure3 illustrates the change in mass loss of the concrete after 100 F-T cycles. The mass loss rate of the concrete specimens generally showed a trend of initial decline followed by a gradual increase. The mass loss rates at 0, 25, 50, 75, and 100 F-T cycles were 0, −0.05%, 0.08%, 0.10% and 0.24%, respectively. After 0–25 F-T cycles, the loss rate of concrete mass showed a downward trend due to the microcracks inside the specimen after the F-T cycle. The concrete specimen absorbed water from the surrounding environment, and water turned into ice due to freezing. Pores expanded and resulted in additional pores because of frost heaving. Therefore, water was immersed in the pores, and the internal water content continuously increased. Simultaneously, the flaking of the mortar on the surface worsened with the increase in F-T cycles, resulting in the reduced quality of the specimen. Therefore, during the early stage of F-T cycles, the mortar peeled off less, and the increase in mass caused by water absorption dominated, thereby indicating that the overall quality of the specimen increased. After 25–50 F-T cycles, the spalling of mortar aggravated due to intensified F-T degradation. Given that the mass loss caused by the apparent spalling of cement mortar of the concrete specimen was greater than the water absorption of the internal crack, the mass loss rate of the specimen shows an upward trend. Under the effect of the F-T cycle, the water flowing into the concrete pores turned into ice, causing the volume of concrete to expand and the width of microcracks to increase. Moreover, with the formation of some new pores, the amount of water absorbed by the cracks in the specimen was equal to the amount dropped by mortar, and the mass loss rate after 50–75 F-T cycles was relatively flat. However, after 75–100 F-T cycles, the drop of particles on the surface of the specimen played a major role, and the mass loss rate continued to rise.Figure 3
Mass loss rate of concrete during F-T cycles.


## 3.3. RDME

As shown in Figure4, the RDME of concrete specimens tends to decrease with the increase in the number of F-T cycles. The value of initial dynamic elastic modulus was 42.07 GPa. The RDME of concrete specimens at 0, 25, 50, 75, and 100 F-T cycles was 100%, 99.46%, 98.67%, 97.69%, and 95.20%, respectively. The loss rate of RDME increased with the increase in F-T cycles due to the formation of frost heaving pressure caused by F-T cycles. Furthermore, the microstructure of concrete was affected, the degree of damage aggravated, the cracks multiplied, and density was reduced. During this process, water accelerated into the interior of the void, which aggravated the damage of specimens under the action of F-T cycles, resulting in increased damage of the internal structure of the concrete.Figure 4
RDME of concrete during F-T cycles.


## 3.4. Dynamic Mechanical Properties

### 3.4.1. Ultimate Compressive Strength

Figure5 shows the relationship between the dynamic ultimate compressive strength and the number of F-T cycles under a constant water pressure of 5 MPa. Test results revealed that the ultimate compressive strength of concrete decreased with the increase in the number of F-T cycles at the same loading rate, and different trends occurred at various stages of the F-T cycles. The gradient of the ultimate compressive strength of concrete at 0–50 F-T cycles is smaller than that at 50–100 F-T cycles. This result may have occurred because during the early F-T cycles, the fine particles inside the concrete were squeezed and compactness increased, thereby making it difficult for water to enter the pores. This condition limited the expansion of the pores. These results agreed with those suggested by Li et al. [30] that, during the F-T cycles, mineral particles are compacted and the cohesive forces between them are gradually strengthened, which can availably offset part of the frost heave force, thus limiting pore expansion. Therefore, the internal damage of the concrete was weakened, and the influence of the F-T cycle on ultimate compressive strength was reduced. At 50–100 F-T cycles, the pore structure inside the concrete changed greatly as the degree of F-T deterioration increased. The width of some small pores increased and evolved into microcracks, and the pores that connected with each other caused the rapid decrease in the ultimate compressive strength of the concrete under dynamic loading.Figure 5
Dynamic ultimate compressive strength of concrete during F-T cycles.The relationship between ultimate compressive strength of concrete and strain rate at a water pressure of 5 MPa is shown in Figure6. Concrete is a material with high strain rate sensitivity. With the same number of F-T cycles, the ultimate compressive strength of concrete increased with the increase in strain rate. This view is also supported by [26, 29].Figure 6
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 [37–39], a microcrack process area is believed to be present before flaw expands. The speed of crackle growth also determines the size of the process area, as proposed by [40]. Therefore, at a high strain rate, the propagation velocity of flaw becomes faster, and the process area becomes larger. Thus, crack expansion requires more energy, while concrete has insufficient time to store energy at a higher strain rate. The extra energy can be released by only increasing the stress, which finally manifests as an increase in strength.On the other hand, free water viscosity affects concrete. Kaplan et al. [41] believed that, when a specimen is subjected to compression stress, the pores and channels perpendicular to the loading direction in the concrete tend to close, allowing free water to flow inside the specimen. The presence of viscosity and liquid-phase pressure gradients causes pore water pressure to increase at a high loading rate, which delays the occurrence of excessive cracks in the solid phase and eventually increases compressive strength. Through experimental observations and theoretical assumptions, Rossi et al. [8, 42–44] indicated that the mechanical properties of concrete under high strain rate could be explained by the Stefan effect and material cracking process interaction. Moreover, for the cone-type concrete failure mode, lateral deformation was restricted to viscous stress. Thus, the damage of specimens decreased. The effect of damping caused by the viscous stress could also slow down the expansion of microcracks for the concrete failure mode of slant shear. Finally, the strength of concrete increased [3].Viscous fluid exists between two flat parallel plates with a distance ofh. When two parallel plates are separated or closed at a certain speed, their motion will be affected by the viscous resistance generated by the viscous fluid. This phenomenon is called the Stefan effect. Moreover, a great velocity corresponds to a great reaction force, as shown in Figure 7. Pores and cracks of varying sizes in concrete contain free water. At this point, cement matrix and water can be regarded as a microdisc system, and pore water will generate viscous resistance under dynamic loading, as shown in Figure 8. This condition is an important factor that affects the strain rate sensitivity of concrete [8]. From this perspective, more free water will immerse into the pores after the F-T cycles. As the strain rate increases, the number of viscously resistant microelements increases, and the influence of free water on viscous resistance becomes greater. Therefore, the damage to the concrete is lessened and concrete exhibits a higher ultimate compressive strength value, which agrees with Li et al. [19], who reported that the strength increase in RAC samples is greater than that of CRAC due to higher viscous resistance.Figure 7
Stefan effect.Figure 8
Stefan effect of concrete pore water.


### 3.4.2. Peak Strain

Similarly, the relationship between the peak strain and the number of F-T cycles under a water pressure of 5 MPa is shown in Figure9. At the same strain rate, the peak strain of concrete tended to increase gradually as the number of F-T cycles increased, because during the F-T cycles, the water in the pores would freeze and swell. Under the repeated action of the frost heaving force, the pores gradually increased, the concrete volume increased, and the compactness gradually decreased. However, in the compression test, the concrete first underwent the compaction process after the F-T cycles. Therefore, the peak strain of the concrete, as well as its ductility, increased.Figure 9
Peak strain of concrete during F-T cycles.Figure10 illustrates the relationship between peak strain and strain rate under a water pressure of 5 MPa. With the same number of F-T cycles, the peak strain of the concrete tended to decrease with the increase in strain rate. According to the theory of minimum energy consumption, the destruction of a system is always operated with the minimum energy consumption per unit time. A previous research showed that cracks mostly expand from interfacial zones between aggregates and mortars, and few cracks directly passing through weak aggregates due to the strengths of a mortar matrix and interfacial transition zone are lower than the strength of a natural coarse aggregate [16, 19]. Fracture pattern depends on aggregate shape and other factors, such as aggregate properties and matrix-aggregate interface. Therefore, at a relatively low strain rate, the crack had enough time to select a fracture path, that is, the crack started at the weak surface between the aggregate and the mortar and then expanded and passed through the mortar along the weak surface. At a relatively high strain rate, the crack became more dispersed. The crack had insufficient time to select the weakest failure interface but expanded along the path with the fastest energy release immediately. It would break directly through the aggregate, resulting in the failure path becoming shorter, thereby decreasing the deformation of the concrete.Figure 10
Peak strain of concrete at different strain rates.


### 3.4.3. Dynamic Increase Factor (DIF)

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 F-T cycles is shown in Figure11. As the strain rate increased, the DIF of the ultimate compressive strength of each number of F-T cycle increased. However, the increase rate varied under different F-T cycles. The relationship between strength increment and strain rate was established by the following fitting test data:(1)fcfcs=1+αlgε˙cε˙cs,where fc is the ultimate compressive strength in dynamic loading, fcs is the ultimate compressive strength in quasistatic loading, ε˙c is the current strain rate (ε˙c = 1 × 10−4, 2 × 10−4, 5 × 10−4, and 1 × 10−3·s−1 in this study), ε˙cs is the quasistatic strain rate (ε˙cs = 1 × 10−5·s−1), and α is a parameter.Figure 11
Relationship of compressive strength increase factor versus relative strain rate.As the number of F-T cycles increased, the slope of the fitting curve gradually decreased; that is, the increase in the number of F-T cycles reduced the rate sensitivity of the ultimate compressive strength of the concrete, because as the number of F-T 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 F-T cycle was lower than those at 50 and 100 F-T cycles. The wedge effect can be ignored. Thus, the slope of 0 F-T cycle was higher than those of 50 and 100 cycles. Concrete rate sensitivity decreased as the number of F-T cycles increased.The relationship between the DIF of peak strain and strain rate under different numbers of F-T cycles is shown in Figure12. With the increase in strain rate, the DIF of peak strain decreased in each cycle. However, the magnitude of reduction in the fitted curves was not the same. To analyse the relationship between peak strain increment and strain rate, the relationship between peak strain and strain rate was established by fitting test data, as shown below:(2)εpεusp=1+βlgε˙cε˙cs,where εp is the peak strain in dynamic loading, εusp is the peak strain in quasistatic loading, ε˙c is the current strain rate (ε˙c = 1 × 10−4, 2 × 10−4, 5 × 10−4, and 1 × 10−3·s−1 in this study), ε˙cs is the quasistatic strain rate (ε˙cs = 1 × 10−5·s−1), and β is a parameter.Figure 12
Relationship of peak strain increase factor versus relative strain rate.Figure12 shows that, under the same number of F-T cycles, the peak strain growth rates were all less than 1 as the strain rate increased, that is, the peak strain gradually decreased. Moreover, the variation curve of specimens with more F-T cycles was relatively gentle, which means that the increase in F-T cycles weakens the sensitivity of the peak strain rate of concrete. The reason is that, with the increase in the strain rate, the internal microcrack of concrete cannot be fully compressed due to the short time of load action, and the crack will expand in a manner that consumes less energy, that is, directly passing through the aggregate, to cause damage. These results are consistent with those of Wang et al. [45, 46], who demonstrated that cracks propagate by cutting through aggregates and aggregates are fractured into many small pieces with the increase of strain rate. More cracks passed through the aggregate rather than bypass the expansion and compression closure of the aggregate. Eventually, the peak strain decreased gradually with a growth rate of less than 1. However, many intricate and different sizes of internal cracks exist in concrete with more severe F-T deterioration. The crack that originally broke through the aggregate changed the damage mode and increased the length of the damage path. Thus, the decrease in peak strain was small.


## 3.4.1. Ultimate Compressive Strength

Figure5 shows the relationship between the dynamic ultimate compressive strength and the number of F-T cycles under a constant water pressure of 5 MPa. Test results revealed that the ultimate compressive strength of concrete decreased with the increase in the number of F-T cycles at the same loading rate, and different trends occurred at various stages of the F-T cycles. The gradient of the ultimate compressive strength of concrete at 0–50 F-T cycles is smaller than that at 50–100 F-T cycles. This result may have occurred because during the early F-T cycles, the fine particles inside the concrete were squeezed and compactness increased, thereby making it difficult for water to enter the pores. This condition limited the expansion of the pores. These results agreed with those suggested by Li et al. [30] that, during the F-T cycles, mineral particles are compacted and the cohesive forces between them are gradually strengthened, which can availably offset part of the frost heave force, thus limiting pore expansion. Therefore, the internal damage of the concrete was weakened, and the influence of the F-T cycle on ultimate compressive strength was reduced. At 50–100 F-T cycles, the pore structure inside the concrete changed greatly as the degree of F-T deterioration increased. The width of some small pores increased and evolved into microcracks, and the pores that connected with each other caused the rapid decrease in the ultimate compressive strength of the concrete under dynamic loading.Figure 5
Dynamic ultimate compressive strength of concrete during F-T cycles.The relationship between ultimate compressive strength of concrete and strain rate at a water pressure of 5 MPa is shown in Figure6. Concrete is a material with high strain rate sensitivity. With the same number of F-T cycles, the ultimate compressive strength of concrete increased with the increase in strain rate. This view is also supported by [26, 29].Figure 6
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 [37–39], a microcrack process area is believed to be present before flaw expands. The speed of crackle growth also determines the size of the process area, as proposed by [40]. Therefore, at a high strain rate, the propagation velocity of flaw becomes faster, and the process area becomes larger. Thus, crack expansion requires more energy, while concrete has insufficient time to store energy at a higher strain rate. The extra energy can be released by only increasing the stress, which finally manifests as an increase in strength.On the other hand, free water viscosity affects concrete. Kaplan et al. [41] believed that, when a specimen is subjected to compression stress, the pores and channels perpendicular to the loading direction in the concrete tend to close, allowing free water to flow inside the specimen. The presence of viscosity and liquid-phase pressure gradients causes pore water pressure to increase at a high loading rate, which delays the occurrence of excessive cracks in the solid phase and eventually increases compressive strength. Through experimental observations and theoretical assumptions, Rossi et al. [8, 42–44] indicated that the mechanical properties of concrete under high strain rate could be explained by the Stefan effect and material cracking process interaction. Moreover, for the cone-type concrete failure mode, lateral deformation was restricted to viscous stress. Thus, the damage of specimens decreased. The effect of damping caused by the viscous stress could also slow down the expansion of microcracks for the concrete failure mode of slant shear. Finally, the strength of concrete increased [3].Viscous fluid exists between two flat parallel plates with a distance ofh. When two parallel plates are separated or closed at a certain speed, their motion will be affected by the viscous resistance generated by the viscous fluid. This phenomenon is called the Stefan effect. Moreover, a great velocity corresponds to a great reaction force, as shown in Figure 7. Pores and cracks of varying sizes in concrete contain free water. At this point, cement matrix and water can be regarded as a microdisc system, and pore water will generate viscous resistance under dynamic loading, as shown in Figure 8. This condition is an important factor that affects the strain rate sensitivity of concrete [8]. From this perspective, more free water will immerse into the pores after the F-T cycles. As the strain rate increases, the number of viscously resistant microelements increases, and the influence of free water on viscous resistance becomes greater. Therefore, the damage to the concrete is lessened and concrete exhibits a higher ultimate compressive strength value, which agrees with Li et al. [19], who reported that the strength increase in RAC samples is greater than that of CRAC due to higher viscous resistance.Figure 7
Stefan effect.Figure 8
Stefan effect of concrete pore water.


## 3.4.2. Peak Strain

Similarly, the relationship between the peak strain and the number of F-T cycles under a water pressure of 5 MPa is shown in Figure9. At the same strain rate, the peak strain of concrete tended to increase gradually as the number of F-T cycles increased, because during the F-T cycles, the water in the pores would freeze and swell. Under the repeated action of the frost heaving force, the pores gradually increased, the concrete volume increased, and the compactness gradually decreased. However, in the compression test, the concrete first underwent the compaction process after the F-T cycles. Therefore, the peak strain of the concrete, as well as its ductility, increased.Figure 9
Peak strain of concrete during F-T cycles.Figure10 illustrates the relationship between peak strain and strain rate under a water pressure of 5 MPa. With the same number of F-T cycles, the peak strain of the concrete tended to decrease with the increase in strain rate. According to the theory of minimum energy consumption, the destruction of a system is always operated with the minimum energy consumption per unit time. A previous research showed that cracks mostly expand from interfacial zones between aggregates and mortars, and few cracks directly passing through weak aggregates due to the strengths of a mortar matrix and interfacial transition zone are lower than the strength of a natural coarse aggregate [16, 19]. Fracture pattern depends on aggregate shape and other factors, such as aggregate properties and matrix-aggregate interface. Therefore, at a relatively low strain rate, the crack had enough time to select a fracture path, that is, the crack started at the weak surface between the aggregate and the mortar and then expanded and passed through the mortar along the weak surface. At a relatively high strain rate, the crack became more dispersed. The crack had insufficient time to select the weakest failure interface but expanded along the path with the fastest energy release immediately. It would break directly through the aggregate, resulting in the failure path becoming shorter, thereby decreasing the deformation of the concrete.Figure 10
Peak strain of concrete at different strain rates.


## 3.4.3. Dynamic Increase Factor (DIF)

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 F-T cycles is shown in Figure11. As the strain rate increased, the DIF of the ultimate compressive strength of each number of F-T cycle increased. However, the increase rate varied under different F-T cycles. The relationship between strength increment and strain rate was established by the following fitting test data:(1)fcfcs=1+αlgε˙cε˙cs,where fc is the ultimate compressive strength in dynamic loading, fcs is the ultimate compressive strength in quasistatic loading, ε˙c is the current strain rate (ε˙c = 1 × 10−4, 2 × 10−4, 5 × 10−4, and 1 × 10−3·s−1 in this study), ε˙cs is the quasistatic strain rate (ε˙cs = 1 × 10−5·s−1), and α is a parameter.Figure 11
Relationship of compressive strength increase factor versus relative strain rate.As the number of F-T cycles increased, the slope of the fitting curve gradually decreased; that is, the increase in the number of F-T cycles reduced the rate sensitivity of the ultimate compressive strength of the concrete, because as the number of F-T 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 F-T cycle was lower than those at 50 and 100 F-T cycles. The wedge effect can be ignored. Thus, the slope of 0 F-T cycle was higher than those of 50 and 100 cycles. Concrete rate sensitivity decreased as the number of F-T cycles increased.The relationship between the DIF of peak strain and strain rate under different numbers of F-T cycles is shown in Figure12. With the increase in strain rate, the DIF of peak strain decreased in each cycle. However, the magnitude of reduction in the fitted curves was not the same. To analyse the relationship between peak strain increment and strain rate, the relationship between peak strain and strain rate was established by fitting test data, as shown below:(2)εpεusp=1+βlgε˙cε˙cs,where εp is the peak strain in dynamic loading, εusp is the peak strain in quasistatic loading, ε˙c is the current strain rate (ε˙c = 1 × 10−4, 2 × 10−4, 5 × 10−4, and 1 × 10−3·s−1 in this study), ε˙cs is the quasistatic strain rate (ε˙cs = 1 × 10−5·s−1), and β is a parameter.Figure 12
Relationship of peak strain increase factor versus relative strain rate.Figure12 shows that, under the same number of F-T cycles, the peak strain growth rates were all less than 1 as the strain rate increased, that is, the peak strain gradually decreased. Moreover, the variation curve of specimens with more F-T cycles was relatively gentle, which means that the increase in F-T cycles weakens the sensitivity of the peak strain rate of concrete. The reason is that, with the increase in the strain rate, the internal microcrack of concrete cannot be fully compressed due to the short time of load action, and the crack will expand in a manner that consumes less energy, that is, directly passing through the aggregate, to cause damage. These results are consistent with those of Wang et al. [45, 46], who demonstrated that cracks propagate by cutting through aggregates and aggregates are fractured into many small pieces with the increase of strain rate. More cracks passed through the aggregate rather than bypass the expansion and compression closure of the aggregate. Eventually, the peak strain decreased gradually with a growth rate of less than 1. However, many intricate and different sizes of internal cracks exist in concrete with more severe F-T deterioration. The crack that originally broke through the aggregate changed the damage mode and increased the length of the damage path. Thus, the decrease in peak strain was small.


## 3.5. Influence of Water Pressure on Dynamic Mechanical Properties

Each test was repeated three times, and the average ultimate strength of concrete subjected to 100 F-T cycles under triaxial compression at different strain rates and standard deviationδ are shown in Table 3. The concrete’s ultimate strength under uniaxial compressive loading was lower than that under triaxial compressive loading due to the constraint effect of triaxial compression. This condition can explain why the further expansion of the crack was limited by the water pressure. This finding is close to the results of [34, 47–49], which also stated that the grading of aggregates may be one of the factors that influence the value of ultimate strength [47]. The strength of concrete decreased as water pressure increased at a strain rate of 10−5·s−1 [3], which is contrary to the findings of this study. This phenomenon may be primarily due to the different concrete conditions before the triaxial test. In this study, specimens were cured in water, whereas in [3], concretes were placed in a natural environment for 1200 days. Researchers [50, 51] noted that water will flow to the crackle tip and destroy the capillary structure of the dry concrete matrix under the action of water pressure. However, only a small amount of water will immerse into the water-cured concrete because of water-filled pores, thereby resulting in slower crack propagation and little or even negligible damage to the matrix.Table 3
Average ultimate strength of concrete under biaxial compression loading (MPa).
Water pressure
Strain rate
1 × 10−5·s−1
±δ
1 × 10−4·s−1
±δ
2 × 10−4·s−1
±δ
5 × 10−4·s−1
±δ
1 × 10−3·s−1
±δ
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
0.20Figure13 shows the relationship between the compressive strengths of concrete and water pressure, where σl is the water pressure and fus is the ultimate compressive strength in quasistatic loading. The dynamic strength of concrete tended to increase with the increase in strain rate. When the constant lateral pressure was in the lower range (0–5 MPa), the dynamic ultimate compressive strength of concrete had a remarkable tendency to increase with the increase in strain rate. However, when the water pressure was higher (5–10 MPa), the increase in dynamic ultimate compressive strength of concrete became muted with the increase in strain rate. In addition, some researchers [33] believe that when the confining pressure exceeds a certain value and this value is the uniaxial compressive strength of concrete, the compressive strength of concrete no longer considers the effect of strain rate.Figure 13
Relationship of ultimate compressive strength versus water pressure at different strain rates.Figure14 shows the effect of water pressure on the relationship between DIF and strain rate. The DIF of dynamic compressive strength and peak strain trend is shown at different strain rates. Figure 14(a) illustrates the relationship between the DIF of dynamic compressive strength of concrete and the strain rate under different water pressures. At the same strain rate, the slope of the fitted line decreased gradually with the increase in water pressure after 100 F-T cycles. This result indicates that the presence of water pressure reduced the sensitivity of concrete strength. This finding is consistent with the view that the effect of strain rate decreases as water pressure increases [2, 33], but it diverges from the data by [3, 34]. Concrete in these papers [2, 3, 33, 34] was not exposed to F-T cycles. Moreover, under 5 and 10 MPa of water pressure, the increment speed was nearly the same, because the water content of concrete under 5 MPa is equal to that under 10 MPa. As previous research [3] indicated, water is important in the improvement of concrete strength under the same strength of concrete skeleton at the same strain rate. Figure 14(b) also reveals that the peak strain of specimens increased with the increase in water pressure. This result can be due to the fact that, when water pressure was applied, the concrete specimens were restrained by lateral pressure, and the appearance and expansion of internal cracks were delayed. The compressive strength and deformation capacity of concrete improved, and the deformation property changed from brittleness to ductility. Consequently, the DIF of strength and peak strain of concrete under conventional triaxial stress state was strongly dependent on the value of water pressure.Figure 14
Effect of water pressure on the relationship between MDIF and strain rate: (a) DIF of dynamic compressive strength; (b) DIF of peak strain.
(a)
(b)


## 3.6. Microstructure Characterisation

The damage of concrete exposed to the combined effect of F-T 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 F-T cycles and strain rate on the concrete dynamic compressive strength at a water pressure of 5 MPa; the micrographs of concrete are shown in Figure15. Figures 15(a)–15(c) demonstrate that at the strain rate of 1 × 10−4·s−1, a relatively tight and dense structure and only one microcrack inside the concrete specimens exist without the effect of F-T cycles, which can be explained by shrinkage deformation of cement paste during hydration reaction [52, 53]. However, different degrees of F-T damage occurred after being subjected to 50 and 100 F-T cycles. The length, width, and number of microcracks increased. Microcracks connected to each other can be easily seen in Figure 15(c), which is good evidence that at the same strain rate, and the value of ultimate compressive strength decreased with the increase in F-T cycles.Figure 15
SEM images (magnification 1000×) of the specimen after F-T 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)
(b)
(c)
(d)A comparison of Figures15(c) and 15(d) reveals that, under the same number of F-T cycles (100), the width of microcracks with a strain rate of 1 × 10−3·s−1 was smaller than that with a strain rate of 1 × 10−4·s−1, because the speed of microcrack propagation increased with the increase in strain rate, and microcracks did not have enough time to expand fully. This view is consistent with the results indicating that the ultimate compressive strength at the strain rate of 1 × 10−3·s−1 is higher than at 1 × 10−4·s−1 after 100 F-T cycles under a water pressure of 5 MPa.


## 4. Conclusions

In this study, dynamic compressive experiments for concrete subjected to different numbers of F-T 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:(1)
As the number of F-T cycles increases, the mass of concrete specimen initially increases and then decreases, whereas the relative dynamic elastic modulus of concrete tends to decrease.(2)
With the increment of F-T 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 F-T cycles. However, the corresponding ductility increases as the porosity of concrete increases, thereby improving peak strain.(3)
With the same number of F-T 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.(4)
The strain rate sensitivity of the DIF of ultimate compressive strength and peak strain decreases with the increase in F-T 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 F-T cycles is proposed based on the experimental results. The calculated results are in good agreement with the experimental data using this equation.(5)
After 100 F-T 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.(6)
The SEM images of concrete at the same strain rate after F-T 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 F-T 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, water-cement ratio, and specimen size, affect the dynamic mechanical properties of concrete under triaxial compression. Therefore, additional experiments are needed.



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