Deformation of a concrete matrix subject to a cyclic freeze–thaw process

Abstract

The cyclic freeze–thaw process has been recognized as one of the most primary factors leading to structural and function failure of concrete. Strain, which may have certain inherent advantages when compared to traditional test parameters such as real-time non-destructive monitoring, which is more accurate and continuous with little error caused by manual intervention, was used to characterize the deformation and deterioration of a concrete matrix under a cyclic freeze–thaw process in this study. With the cyclic freeze–thaw process, the strain hysteretic loop is raised upwards indicating that residual strain is generated in the concrete matrix. The residual strain generated proves that damage in the concrete matrix is continuously accumulated and an irreversible deterioration process. The variation of freeze characteristic temperature ΔT_f and the apparent frost heaving coefficient Δα_f defined in this study can be used to characterize the degree of freeze–thaw damage and the frost resistance of concrete, respectively. Through theoretical analysis, a numerical model, which can show the relationship between concrete freeze–thaw damage and residual strain has been deducted and verified, which indicates that residual strain can be used to characterize the frost resistance of concrete subjected to a cyclic freeze–thaw process such as traditional parameters. Moreover, the residual strain generated in 3.5 wt% NaCl solution is larger than in water, showing that chloride attack accelerates the freeze–thaw damage of concrete.

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1. Introduction

It is known that concrete is one type of porous solid comprised cement paste and aggregates. At normal atmospheric pressure, water freezes with 9 vol% expansion below 0 °C. Therefore, under cyclic freeze–thawing, the concrete matrix is widely accepted to generate hydrostatic pressure¹ and crystallization pressure,² which may be considered as a type of inner tensile stress. A number of microcracks may generate and propagate when the inner tensile stress exceeds the ultimate tensile strength of the concrete matrix.^3,4 When cyclic freeze–thawing is conducted in salt solution, the damage is more severe.^5,6 Freeze–thaw damage of concrete can be classified into two types, one being surface scaling⁷ and the mass loss used to characterize the degree of surface scaling of concrete. The other being internal micro-cracks and their propagation;⁵ the initiation and propagation of microcracks inevitably results in the deformation of the matrix. At present, the most frequently-used test parameter of internal damage is the relative dynamic elastic modulus. In recent years, strain, which is able to reflect the deformation of a concrete matrix has increasingly been monitored as a measure of internal damage^8,9 and has been shown to increase progressively with the progress of deterioration.

This study is an attempt to analyze the strain–temperature variation and residual strain of concrete with different water cement ratios under a cyclic freeze–thaw process or under freeze–thaw cycling coupled with chloride attack. The cooling phase was divided into an initial freezing phase and freezing phase, and the freezing phase was analyzed emphatically. Furthermore, the variation of the freeze characteristic temperature ΔT_f defined in this study was used to characterize the degree of freeze–thaw damage and the variation of the apparent frost heaving coefficient Δα_f was used to characterize the frost resistance of concrete. The test results of residual strain have been compared with traditional test parameters and a numerical model developed, which can show the relationship between concrete freeze–thaw damage and residual strain, and the ability of residual strain in characterizing concrete freeze–thawing damage.

2. Experimental

2.1 Materials

The binder materials were Portland cement (strength grade P.I 42.5, composition tested by S8 TIGER X-ray Fluorescence Spectrometry given in Table 1) with a specific surface area of 347 m³ kg⁻¹ and volume density of 3.10 g cm⁻³, river sand with a fineness modulus of 2.8 and silt content less than 1 wt%, crushed gravel with particle sizes of 5–10 mm and 10–20 mm in a ratio of 4 : 6, and triterpenoid-saponin air entraining agent (the allowed maximum dosage is 0.03 wt% of the cementitious material content).

Table 1 The chemical composition of cement wt%

SiO2	Al2O3	Fe2O3	CaO	MgO	SO3	NaO2eq.	Loss	f-CaO	Cl^−
21.57	4.45	2.76	63.90	1.88	2.57	0.57	1.51	0.60	0.008

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2.2 Preparation of the specimens

The mix proportions and the physical properties of the concrete samples are listed in Table 2. Only the water cement ratios are different in the mix proportions of specimens A, B1 and C, being 0.5, 0.6 and 0.65, respectively. The purpose to choose these W/C ratios was to obtain more obvious contrast results of strain. Based on the mix proportion of B1, the air entraining agent (AEA) was doped into the specimen B2 and B2-1, analyzing the effect of chloride attack on the freeze–thaw damage of concrete. AEA doping may bring amount evenly distributed stable and closed tiny air pores in the concrete matrix, which can relieve the expansion that is caused by frozen water, NaCl solution and the hydrostatic pressure produced.

Table 2 The mix proportion and physical properties of concrete^a

No.	Cement (kg m^−3)	W/C	Sand (kg m^−3)	Gravel (kg m^−3)	AEA (%)	Slump (mm)	Air content (%)	28 d compressive strength (MPa)	Freeze–thaw process
a The mix proportion of specimen B2-1 is the same as that of specimen B2 and only the freeze–thaw process was different, so the same test result for the physical properties was used.
A	330	0.5	733	1120	0	25	2.5	40.7	In water
B1	330	0.6	733	1120	0	60	2.8	34.2	In water
C	330	0.65	733	1120	0	75	3.2	30.1	In water
B2	330	0.6	733	1120	0.01	105	4.5	27.4	In water
B2-1	330	0.6	733	1120	0.01	105	4.5	27.4	In NaCl solution

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One group of each numbered concrete specimen with dimensions of 100 mm × 100 mm × 100 mm was employed to test the 28 d compressive strength. The other two groups of each numbered concrete specimen with dimensions of 100 mm × 100 mm × 400 mm were also employed. Of these two groups, one was used to test the mass loss and dynamic elastic modulus, and the other was used to continuously test the strain using a VWS-10 vibrational chord strain sensor (as shown in Fig. 1(a), its long cylindrical shape with both ends of the base makes it convenient to be fixed to the specimen).

Fig. 1 The appearance of the vibrational chord strain sensor and its location.

According to the mix proportions, the raw materials were water mixed within the time specified. After mixing, the fresh concrete was used to test the slump and air content and immediately placed into the moulds. The strain sensors were embedded in the center of the concrete specimens with dimensions of 100 mm × 100 mm × 400 mm, as shown in Fig. 1(b). The specimens were demolded after 24 h and then placed into a curing room at 20 ± 2 °C and ≥90% relative humidity. After 24 d of curing, the specimens were moved into vacuum water-saturation equipment and saturated in water or 3.5 wt% NaCl solution for 4 d.

2.3 Methods

2.3.1 Testing method for the compressive strength. The 28 d compressive strength of the concrete samples was tested according to GB/T 50081-2009. During the test, the concrete samples, with a compressive strength lower than C30, were evaluated at a loading speed of 0.3–0.5 MPa s⁻¹, while the concrete samples with a compressive strength higher than C30 were evaluated at a loading speed of 0.5–0.8 MPa s⁻¹. The average value of three replicates was taken as the representative value.

2.3.2 Testing parameters for the cyclic freeze–thaw process. The cyclic freeze–thaw process was carried out in accordance with the quick frost method in GB/T 50082-2009. The water saturated specimens were moved to the test chamber and placed in the rubber sleeves filled with water to a level of more than 2 cm. Fig. 2 shows the temperature profiles during the freeze–thaw cycles.

Fig. 2 The temperature profile for the freeze–thaw cycles.

Traditional parameters. The dynamic elastic modulus and mass loss of the specimens were tested every 25 cycles. The test is finished when the value of the relative dynamic elastic modulus was reduced to 5% or the value of the mass loss reached 5% or the number of freeze–thaw cycles reached 300.
Strain. The strain sensors were connected to a MCU-32 automatic strain data-logger. The data acquisition rate was set every 5 min. Then, the freeze–thaw cycles were started and strain variations were measured and recorded using the test system, which comprised a data-logger and computer. The strain ε was calculated using eqn (1).

ε = kΔF + bΔT = k(F − F₀) + (b − a)(T − T₀) (1)

where ε = the strain of the tested structure, k = testing sensitivity of the strain sensor, F = the real-time testing value of the strain sensor, F₀ = the testing reference value of the strain sensor, b = the temperature correction coefficient, a = the linear expansion coefficient of the tested structure, T = the real-time testing value of temperature and T₀ = the testing reference value of temperature.

2.3.3 Testing method for the pore structure. A hand cutter machine was used to cut the concrete specimen with dimensions of 100 mm × 100 mm × 100 mm to 20 mm thickness perpendicular to the molding surface. The samples were cleaned before one of the sawn faces was chosen to grind, polish, clean, brush fluorescent liquid, repolish and finally clean. After all the procedures, the samples were used for testing.

2.3.4 Testing method for the Cl⁻ migration height. The concrete specimen with a dimension of 100 mm × 100 mm × 100 mm was cut into two halves and vacuum dried. As shown in Fig. 3, the specimen was placed into the 10 wt% NaCl solution. Using a reagent color-developing method to test the Cl⁻ migration height every 1 h; the reagent was 0.1 mol L⁻¹ AgNO₃ solution. The test was finished until the color-developing height reached the top surface or the time reached 6 h. The experiment was repeated after 50 freeze–thaw cycles.

Fig. 3 Schematic of the specimen splitting side and its location.

3. Results and discussion

3.1 Generation of residual strain

It is found from Fig. 4 that the strain variation paths of the concrete matrix during the cooling phase and the heating phase of every freeze–thaw cycle are not overlapped, forming a hysteresis loop. The phenomenon is generally considered to be caused by “the ink bottle effect”.^8,10 There are a number of small-end and big-center pores similar to the ink bottle in concrete. The big pores freeze first during the cooling phase and the small pores thaw in advance during the heating phase. There is some ice captured due to them not being able to move out of “the ink bottles” during the heating phase, causing the values of strain tested at the same temperature during the cooling phase and the heating phase to be different, thereby generating the hysteretic loop. However, the value was not able to return to the beginning when the hysteresis loop was over, indicating that irreversible damage was generated during every freeze–thaw cycle in the concrete matrix.

Fig. 4 Strain variation of specimen A and B1 with temperature during the 1st cycle and the 25th cycle.

In addition, the hysteretic loops of specimen A and specimen B1 both move up after 25 cycles. The phenomenon could not be explained by “the ink bottle effect” and the most possible reason was that irreversible freeze–thaw damage was generated caused by the initiation and propagation of cracks in the concrete. In other words, residual strain was generated in the concrete matrix. In this study, the residual strain was defined as the difference value between the values of strain tested at the lowest temperature in different freeze–thaw cycle, using the value of strain at the lowest temperature in the first cycle as the initial value. After 25 cycles, the residual strain of specimen A and specimen B1 were 325 με and 449 με, respectively. The smaller the water cement ratio was, the less residual strain was generated.

3.2 Freeze characteristic temperature and apparent frost heaving coefficient

After observing Fig. 4(a) and (b), it was found that there was an obvious strain inflection point in the freezing phase of every hysteresis loop. Ref. 11 defines the corresponding temperature for the strain inflection point as the freeze characteristic temperature T_f, which is influenced not only by the ice crystal nucleation temperature of concrete, but also by the pore structure characteristic parameters, including total porosity and pore distribution. Because the pore sizes are different in concrete, the freezing points of the pore solution are different. T_f is considered to be the temperature when a large amount of the pore solution in concrete begins to freeze, rather than the exact freezing point of the pore solution. Therefore, the cooling phase was divided into to two stages, i.e., before and after T_f, named the initial freezing phase and freezing phase, respectively. The strain tested in these two stages both vary linearly. During the initial freezing phase, most of the pore solution is under supercooled conditions¹¹ and the motivation of strain variation lies in the migration and redistribution of the pore solution, as well as the freezing of a small amount of the pore solution, which causes expansive stress. The expansive stress was not enough to counteract the stress caused by cold contraction, so the strain decreases linearly slightly. During the freezing phase, a large amount of the pore solution in concrete freezes causing the constantly generated expansive stress to increase; therefore, the strain increases linearly with increasing temperature.

From the above, the linear part after T_f was used to characterize the deformation of the concrete matrix in which a large amount of the pore solution freezes, so we can conclude that to study the freezing phase was more meaningful. Ref. 9 defines the absolute value of the slope of the linear part as apparent frost heaving coefficient α_f, which characterizes the variation velocity of strain after a large amount of the pore solution in concrete freezes, as shown in eqn (2):

where Δε = the variation of strain in the freezing phase, ΔT = the variation of temperature in the freezing phase.

Table 3 shows the T_f, ΔT_f, α_f and Δα_f values of the concrete specimens derived from Fig. 4(a) and (b). It is obvious that the T_f values for specimen B1 in which the water cement ratio was higher in the 1st cycle and the 25th cycle are both higher than those of specimen A. The water cement ratio largely influences the pore structure of the concrete specimen. The higher the water cement ratio, the larger pores content and while the freezing points of the larger pores are higher, the T_f values of specimen B1 are higher. In addition, the T_f values of specimen A and specimen B1 both increase after 25 cycles, because cyclic freeze–thawing causes an increase in the number of pores and larger pores in the concrete sample. The ΔT_f value of specimen B1 was higher, indicating that the larger pores content of specimen B1 increases more quickly than that of specimen A; in other words, the degree of damage in specimen B1 was higher during the freeze–thaw cycles. Therefore, ΔT_f can be used to characterize the degree of damage in concrete in which the water cement ratios are different and subjected to freeze–thaw cycles.

Table 3 The apparent frost heaving coefficient and freeze characteristic temperature of the concrete samples^a

Calculated values	Specimen A, W/B = 0.5		Specimen B1, W/B = 0.6
	1st cycle	25th cycle	1st cycle	25th cycle
a ΔTf = the variation of the freeze characteristic temperature and Δαf = the variation of the apparent frost heaving coefficient.
Tf (°C)	−6.39	−6.13	−6.27	−5.91
ΔTf = Tf25 − Tf1 (°C)	0.26		0.36
αf (10^−6 per °C)	12.9	15.13	13.62	16.76
Δαf = |αf25 − αf1| (10^−6 per °C)	2.23		3.14

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The α_f values of specimen B1 in the 1st cycle and the 25th cycle are also higher than those of specimen A. In other words, the strain variation velocity of specimen B1 was higher with increasing temperature. Strain can be used to characterize the deformation capacity of the concrete matrix. The higher the deformation rate of the matrix, the looser the matrix, and the poorer the frost resistance of concrete is. After 25 cycles, the α_f values of specimen A and specimen B1 increase 2.23 × 10⁻⁶ per °C and 3.14 × 10⁻⁶ per °C, respectively, indicating that the higher the water cement ratio, the higher the Δα_f value of concrete. In other words, the more quickly the strain variation increases with temperature, the looser the concrete matrix is, the higher the freeze–thaw damage degree is and the poorer the frost resistance of concrete is. Therefore, Δα_f can be used to characterize the frost resistance of concrete in which the water cement ratios are different and subjected to freeze–thaw cycles.

3.3 Residual strain and traditional parameters

3.3.1 Residual strain. It was found from Fig. 5 that after the same number of freeze–thaw cycles, the higher the water cement ratio of the specimen, the higher the value of residual strain, indicating that the higher the water cement ratio of the specimen, the higher the deformation of the matrix occurs during cyclic freeze–thawing. Taking 50 freeze–thaw cycles for example, the residual strain values for specimen A, B1 and C were 575 με, 630 με and 807 με, respectively. It was also observed in Fig. 6 that after 50 freeze–thaw cycles, the surface of specimen A had almost no damage, while some coarse aggregates of specimen B1 were exposed on the surface.

Fig. 5 Residual strain of concrete with different W/B under freeze–thaw cycles.

Fig. 6 The damage in specimen A and B1 with different W/C ratios after 50 freeze–thaw cycles.

3.3.2 Traditional parameters. It is found from Fig. 7 and 8 that after the same number of freeze–thaw cycles, the higher the water cement ratio of specimen is, the more quickly the mass loss increases and the more quickly the relative dynamic elastic modulus decreases. After 50 freeze–thaw cycles, the mass losses were −0.26%, 0.74% and 4.11% for specimen A, B1 and C, and the relative dynamic elastic modulus decreases to 94.3%, 88.7% and 61.5%, respectively. Specimen C in which the water cement ratio was at its maximum was completely destroyed after 50 cycles, while specimens B1 and C were destroyed after 100 and 175 cycles.

Fig. 7 The mass loss of concrete with different W/B ratios under freeze–thaw cycling.

Fig. 8 The relative dynamic elastic modulus of concrete with different W/B ratios under freeze–thaw cycling.

The test results reflected by residual strain and traditional parameters are consistent, indicating that residual strain can be used to characterize the frost resistance of concrete subjected to freeze–thaw cycling-like traditional parameters.

3.3.3 Parameters of the pore structure. The variation of the pore structure, including the air content, the average bubble diameter, the specific surface area of bubble and the bubble distance coefficient of specimen A and B1 before and after 50 freeze–thaw cycles are listed in Table 4.

Table 4 The pore structure parameters of concrete specimens before and after freeze–thaw cycling

No.	Number of cycles and increment	Air content (%)	Average bubble diameter (μm)	Specific surface area of bubble (μm^2 μm^−3)	Bubble distance coefficient (μm)
A	0 cycles	1.952	242.673	0.0251	508.147
	50 cycles	2.564	249.388	0.0244	491.098
	Increment (%)	31.352	2.767	−2.789	−3.355
B1	0 cycles	2.284	248.333	0.0246	482.674
	50 cycles	3.197	258.702	0.0236	461.538
	Increment (%)	39.974	4.175	−4.065	−4.379

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Table 4 shows that after 50 freeze–thaw cycles, the air content and bubble diameter increased, while the specific surface area of the bubble and the bubble distance coefficient decreased. The results were attributed to the appearance and extension of the internal microcracks of the concrete sample, which result in an increase in the degree of connectivity and the number of air pores that are connected with the cracks after certain freeze–thaw cycles. Because of this, freezing and expansion occurs and the percentage of air pore volume increases due to the effect of hydrostatic pressure and osmotic pressure, which finally results in the change of all the structural parameters of the concrete sample. The pore distance coefficient is a parameter, which reflects the average length of the pore solution. The decrease in the pore distance coefficient with an increase in the number of freeze–thaw cycles can be used to reflect the increase in the degree of damage in the inner part of the concrete sample and is consistent with the residual strain.

3.3.4 Cl⁻ migration height. As shown in Fig. 9, when the steeping time is same, the water cement ratio in the concrete specimen and the Cl⁻ migration height are higher. This is because that the higher the water cement ratio, the greater the larger pores content and the looser the matrix, the Cl⁻ migrates up more easily.

Fig. 9 The Cl⁻ migration height of concrete with different W/B ratios before cyclic freeze–thawing.

The Cl⁻ migration height of every specimen was higher after 50 freeze–thaw cycles than before within the same steeping time (Fig. 10). Taking 1 h steeping time for example, the Cl⁻ migration heights of specimen A, B1 and C were 17 mm, 24 mm and 36 mm before cyclic freeze–thawing and 52 mm, 64 mm and 100 mm after 50 freeze–thaw cycles. This further proves that the internal damage in concrete occurs after cyclic freeze–thawing, meaning the initiation and propagation of microcracks leading to the connectivity between the cracks and air voids. The irreversible residual strain was generated in this way.

Fig. 10 The Cl⁻ migration height of concrete with different W/B ratios after 50 freeze–thaw cycles.

3.4 Establishing a concrete damage numerical model based on residual strain

3.4.1 Theoretical analysis of the residual strain variation. It is known from the freeze–thaw damage mechanism of concrete that the whole freeze–thaw damage process of concrete needs to undergo three specific stages, obviously reflecting on the residual strain variation, as shown in Fig. 11.

Fig. 11 Schematic of the three stages of residual strain variation.

Accelerated growth period: freeze–thaw cycles just begin, so the microcracks and air voids in concrete do not have a large degree of connectivity. “The ink bottle effect”,^8,10 which indicates that the large pores freeze first during the cooling phase and the small pores thaw in advance during the heating phase, makes most of the pore solution and ice in concrete unable to migrate freely. The freeze induced tensile stress leads to the generation of the new microcracks, the propagation of the original microcrack tip and increasing water saturation. The repeated and irreversible damage process leads to increasing deformation of the concrete matrix, that is to say, the residual strain increases rapidly. In short, the main driving force of the generated irreversible deformation derives from the freezing and expansion of the pore solution in the concrete matrix.

Slow growth period: with the progress of cyclic freeze–thawing, the degree of connectivity in concrete gradually increases, which makes the number of isolated microcracks with “ink bottle” shapes decrease. Most of the pore solution and ice in the loose concrete can migrate freely during the freeze–thaw cycles. On the other hand, because of the accumulated damage caused by the accelerated growth period, the microcracks in concrete start to connect and their connectivity can relieve the effect of the freeze induced tensile stress, i.e., the residual strain increases slowly. The main driving force of the deformation may be the moisture migration in concrete during this period. This stage shares a large proportion of the whole process and it is the most stable segment.

Aggravated destroy period: the connectivity of the microcracks in concrete increases, leading to a large amount of the external solution to easily enter into the looser concrete to generate a more destructive freeze induced tensile stress. The concrete matrix is too loose to undergo freeze induced tensile stress and the solution migration acting force, so the concrete matrix collapses in an instant, causing a sharp deformation. Consequently, the strain sensor breaks away from the concrete matrix. This stage occurs almost suddenly, sharing little proportion of the whole process, so it may be ignored.

Therefore, the first stage and second stage of residual strain variation can be used to characterize the freeze–thaw damage in concrete. The maximum residual strain value of the second stage can be used as the critical destroy value ε_rm, which can be directly obtained experimentally.

3.4.2 Unlimited growth model. The residual strain was generated continually during the freeze–thaw cycles, so the growth of residual strain can be regarded as being consecutive. In general, for a residual strain continuous function, the growth rate of residual strain can be regarded as constant, i.e., the growth of residual strain is in direct proportion to the generated residual strain in unit number of cyclic freeze–thawing.

The residual strain is ε_r(N) after N freeze–thaw cycles and ε_r(N) is a continuously differentiable function. Recording the residual strain generated when the first freeze–thaw cycle reaches the lowest temperature as the initial residual strain ε_r0, a set number of freeze–thaw cycles at the moment is 0 and growth rate of residual strain as λ, and λ is the proportionality coefficient of the increase in ε_r(N) and ε_r(N) with unit time. According to the fundamental assumption that λ is a constant value, the increase in residual strain from N to N + ΔN is:

ε_r(N + ΔN) − ε_r(N) = λε_r(N)ΔN (3)

Namely:

Taking the integral of the abovementioned equation, then it can be acquired that:

ε_r(N) = ε_r0 e^λN (5)

This indicates that the residual strain presents infinite growth according to exponential laws (λ > 0). However, under physical conditions and according to previous analysis, the damage in concrete is staged. It can be known by only reserving the first two stages that the variation velocity of residual strain will increase and then decrease, which is actually in accordance with the blocking model.

3.4.3 Blocking model. As the variation velocity of residual strain increases and then decreases, it can be assumed that the variation velocity of residual strain, as shown in Fig. 12 is in accordance with a normal distribution, variation velocity of residual strain when ε_r(N) = ε_rm is 0 and the growth velocity function λ(ε_r) of residual strain can be expressed as:

Fig. 12 The hypothesis of the residual strain variation velocity.

Substituting the abovementioned equation into eqn (4), it can be acquired that:

Taking the integral of the abovementioned equation it can be acquired that:

Setting the damage degree variable of concrete after N times of freeze–thaw cycles as ρ, the closer the ρ value is to 1, namely, the closer the ε_r(N) is to damage critical point ε_rm, and the closer the concrete will be to complete damage, then:

As the frost-heaving force generated within concrete in freeze–thawing process is actually not a constant cyclic strain, the variation velocity of the residual strain is not in accordance with the normal distribution as much, as shown in Fig. 12, and k_ε is introduced to correct the specific strain value. In addition, by processing the abovementioned freeze–thaw cycle, the residual strain variation is divided into three stages. This study takes the maximum value of residual strain in the second stage as the concrete damage point; however, it is rather hard to accurately quantify this value, i.e., taking the damage value of the damage degree variable as 1 is not entirely accurate. Therefore, k_ρ was introduced to conduct a correction and it can be acquired that:

The final damage model is shown in eqn (10) and this model establishes the relationship between the damage degree variable ρ and the number of rapid freeze–thaw cycles. In the equation, for each concrete with a fixed mix proportion, ε_rm/ε_r0 is a fixed value, which can be acquired experimentally, while k_ε, k_ρ and λ can be acquired by fitting the experimental results.

3.4.4 Verification of the damage numerical model. The freeze–thaw numerical model was used to fit the variation curves of specimen A and B1 damage degrees with processing of the freeze–thaw cycles, as shown in Fig. 13. It can be observed that the fitting correlation coefficient R² of the concrete damage degree curves by the freeze–thaw damage numerical model under the effect of freeze–thaw cycling is above 0.95 with a good fitting degree. It can be observed by establishing the relationship between the degree of damage and residual strain that the residual strain can accurately characterize the freeze–thaw damage in concrete, namely, certifying that the residual strain can really be a test index for concrete freeze–thaw damage.

Fig. 13 The damage degree variable curve fitting of specimens A and B1 under freeze–thaw cycling.

3.5 Deformation of concrete subjected to freeze–thaw cycling and chloride attack

The residual strain variations in specimens with the same mix proportion under freeze–thaw cycling and freeze–thaw cycling coupled with chloride attack are shown in Fig. 14. It was found that after the same number of freeze–thaw cycles except before 25 cycles, the residual strain values of specimen B2-1 are all higher than those of specimen B2. Taking 50 freeze–thaw cycles for example, the residual strain values of specimen B2-1 and B2 were 45 με and 30 με, respectively.

Fig. 14 Residual strain of concrete with same mix proportion under freeze–thaw cycles and freeze–thaw cycles coupled with chloride attack.

The residual strain values of specimen B2 tested during the first 25 cycles are higher. While with the process of freeze–thaw cycling, the residual strain values of specimen B2-1 are all higher than those of specimen B2 and the increasing rate was also larger. The possible reason for this finding was that the frost resistance of the concrete specimen was better in the earlier period of the freeze–thaw cycling process. The freezing point of the NaCl solution is lower than water; therefore, the duration of frost stress decreases and the residual strain values of specimen B2-1 decreases. With the process of freeze–thaw cycling, the cracks in concrete are constantly generated and propagate. The NaCl solution in the cracks may accelerate the scaling of the cracks walls, accelerating the surface scaling of concrete. Coupled with the synergy action of frost pressure, osmotic pressure and crystal pressure, this causes the higher and higher internal damage and residual strain values of specimen B2-1.

From the abovementioned findings, freeze–thaw cycling and chloride attack interact and influence each other, exacerbating the damage in concrete. On the one hand, using NaCl solution may bring the influence of osmotic pressure and possible crystal pressure at the lower temperature, exacerbating the damage in concrete subjected to freeze–thaw cycling. On the other hand, cyclic freeze–thawing causes the continued initiation and propagation of cracks in concrete, providing the channels for Cl⁻ migration, accelerating the chloride attack.

4. Conclusions

(1) With the freeze–thaw cycling process, the strain hysteretic loop is raised upwards indicating that residual strain was generated in the concrete matrix. The residual strain generated proves that the damage in the concrete matrix was continuously accumulated and an irreversible deterioration process. This process was directly related to the continued initiation and propagation of cracks in the matrix during the freeze–thaw cycling process.

(2) The freeze characteristic temperature T_f was considered to be the temperature when a large amount of the pore solution in concrete begins to freeze, rather than the exact freezing point of the pore solution. The apparent frost heaving coefficient α_f was used to characterize the variation velocity of strain after a large amount of the pore solution in the concrete sample froze. The variation of the freeze characteristic temperature ΔT_f defined in this study was used to characterize the degree of freeze–thaw damage and the variation of the apparent frost heaving coefficient Δα_f was used to characterize the frost resistance of concrete.

(3) The test results of the freeze–thaw damage reflected by the residual strain and traditional parameters were consistent and theoretical analysis was used to deduct a numerical model, which showed the relationship between the degree of freeze–thaw damage and residual strain, and accurate verification of this model indicates that the residual strain could be used to characterize the frost resistance of concrete subjected to freeze–thaw cycling-like traditional parameters.

Acknowledgements

Support from the National High-tech Research and Development Program of China (863 Program, Grant No. 2015AA034701), the Natural Science Foundation of Shandong Province, China (Grant No. ZR2014EL007) and the Open Project of State Key Laboratory of Silicate Materials for Architectures (Wuhan University of Technology, China) (Grant No. SYSJJ2016-10) are greatly acknowledged.

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