Research on mechanical properties and pore structure evolution process of steam cured high strength concrete under freeze thaw cycles

Abstract

With the widespread use of high-strength concrete structures (HC), the impact of pore structure on their performance has become a current research focus. The mechanism by which different curing conditions and freeze-thaw cycles influence the evolution of pore structure remains unclear. Therefore, this study systematically investigated the frost resistance of high-strength concrete under different curing conditions, measured the mass loss rate, compressive strength, and relative dynamic elastic modulus of concrete under freeze-thaw cycles. Utilizing low-field nuclear magnetic resonance (NMR) technology, this study analyzed the evolution of pore structure in HC under freeze-thaw cycles. Additionally, the fractal dimension was used to evaluate the change of concrete internal pore structure, so as to reflect the influence of pore structure on the mechanical properties of concrete subjected to freeze-thaw cycles, and then evaluated the freeze-thaw damage of HC. The experimental results indicated that the steam curing regimes led to an increase in the porosity of HC, thereby influencing its frost resistance. Steam-cured high-strength concrete (SMHC) exhibited a higher degradation rate under freeze-thaw cycles, resulting in a greater level of deterioration compared to standard curing high-strength concrete (SDHC), even under the same number of freeze-thaw cycles.

Introduction

In recent years, with the rapid development of infrastructure and industrialized construction, high-strength concrete (HC) prefabricated components have been widely utilized. Steam curing, as an important curing method in the production of HC prefabricated components, plays an irreplaceable role in early strength enhancement, mold turnover rate, and construction efficiency^1–5. However, high temperature and high humidity curing conditions will cause thermal damage effects such as pore coarsening and brittleness increase in concrete, which will affect the frost resistance and durability of concrete^5–9. Additionally, concrete in cold regions is susceptible to freeze-thaw action, which induces the generation and development of micro-cracks in concrete, resulting in concrete surface collapse and bearing capacity decrease. Therefore, it is of great practical significance to study the frost resistance of HC under steam curing.

In the past few decades, numerous studies have been conducted on the evolution laws of mechanical deterioration^10,11and damage mechanisms^12–14of steam-cured concrete caused by freeze-thaw cycles. Shi et al¹⁵. found that the high-temperature and high-humidity gradient during steam curing is unfavorable for the development of the concrete’s microstructure, exerting adverse effects on its long-term performance. Based on acoustic emission technology, Chen et al^16,17. discussed the fracture form and crack development of steam-cured concrete in freeze-thaw environment, and established a damage constitutive model based on the basic theory of damage mechanics. Wang et al¹⁸. studied the microscopic characteristics of the internal paste of concrete at different curing temperatures, providing a theoretical basis for the research on its macroscopic performance and durability. Chen et al¹. studied the mechanical and frost resistance of concrete under different curing conditions, indicating that the compressive strength of conventionally cured concrete is higher than that of steam-cured concrete, and pore degradation is the main reason for the decrease in compressive strength of steam-cured concrete.However, the experiment is only for low-strength concrete and is not applicable to high-strength concrete. Therefore, it is necessary to further study the evolution law of dynamic mechanical properties of high strength concrete after freeze thaw.

The pore structure is the key factor affecting the mechanical properties and durability of concrete materials^19–21, especially in the freeze-thaw environment, and it will play a decisive role in its properties. Kashif et al^22,23. found that incorporation of 0.03% graphene oxide into cement composites can significantly improve mechanical properties and reduce microcracks. In this regard, many researchers have carried out a large number of experimental and theoretical studies to explore the changes of internal pores in concrete when subjected to freeze-thaw cycles. Zhang²⁴. investigated the dynamic evolution on the microstructural deterioration of unsaturated polyester resin modified concrete for bridge deck paving layer in the salt freeze-thaw environment, quantitatively characterizing the corresponding characteristics parameters utilizing mercury intrusion approach (MIP) and scanning electron microscope (SEM) method. The evolution of internal microstructure of hydraulic concrete subjected to freeze-thaw cycle was investigated by using the combination of X-ray computed tomography (X-ray CT) technology²⁵.However, each of the above methods of testing the internal pore structure in concrete has its own limitations. MIP is an invasive test that has irreversible damage to the pore structure, and the sample needs to be vacuum dried.The scope of aperture testing by SEM is limited.In addition, X-ray CT techniques to detect the pore structure of concrete materials usually takes a long time and is expensive.

In terms of concrete pore detection, low-field nuclear magnetic resonance (NMR) technology has been widely used as a non-destructive testing method^26,27.The method is based on water as the medium and has many advantages such as non-destructive, non-invasive, fast testing speed, and accurate results, which has become a very powerful way to monitor the internal micro-structural changes. Zhou et al²⁸. used low-field NMR technology and mercury intrusion porosimetry to compare the effects of different liquids on the permeability of cement-based materials. Shen et al²⁹. studied the impact of freeze-thaw cycles on the microscopic debonding at the sandstone-concrete interface using NMR technology. Hou et al³⁰. conducted a characteristic analysis of the pore structure of recycled concrete based on NMR technology. Li et al³¹. investigated the influence of pore size distribution on concrete cracking with different AEA content and curing age using NMR. Gajewicz et al³². studied the temporal evolution of the pore-size-distribution in mature cement pastes. MMR was used to characterize the pore structure characteristics of carbon nanotubes modified reactive powder concrete composites³³. The complete deterioration of mortar specimens was observed via NMR in detail to determine the relationship between freeze-thaw damage and pore structure deterioration³⁴. However, the relationship between the pore characteristic obtained from NMR and the mechanical properties of concrete is less studied.

Therefore, the freeze-thaw cycle tests for HC under different curing systems were carried out in this study. Based on NMR technology, the variation law of mechanical and frost resistance of HC was explored, and the dynamic variation characteristics of pore structure under different working conditions were analyzed. Combined with fractal theory, the relationship between pore volume fractal dimension and frost resistance of SMHC and SDHC was established. The study systematically investigated the changing patterns of freeze-thaw durability for SMHC, aiming to provide technical support for the healthy service of SMHC prefabricated components in freeze-thaw environments.

This study aims to analyze the variation of pore structure of SMHC and SDHC subjected to freeze thaw cycles, investigating the impact of the microstructure on their macroscopic response (such as compressive strength, mass loss rate, relative dynamic elastic modulus). Section 2 introduces experimental materials, curing system and test methods. Section 3 describes the results obtained, including mechanical properties, frost resistance and pore characteristics (pore amounts, pore-size distribution, porosity). Section 4 depicts the correlation between internal microstructure and macro behavior under freeze-thaw cycles. Lastly, Section. 5 presents the study’s conclusions.

Experiments

Materials and mix proportions

In this study, ordinary Portland cement ( P·O42.5 ) with density of 3150 kg/m³ produced by Hami Hongyi Building Materials Co., Ltd. was used, and the chemical composition of cement is shown in Table 1. The silica fume was non-densified silica fume sourced from Gansu Sanyuan Silica Materials Co., Ltd. The fly ash was Class II fly ash produced by DaNan Lake Power Plant, Hami City. The mineral powder utilized was of S75 grade from Renhe Mining Co., Ltd., Hami City. The coarse aggregate was 5–20 mm continuous graded gravel. Fine aggregate was medium sand in zone II. The polycarboxylate superplasticizer with water reduction rate of 38% was utilized to improve the workability of concrete and achieve the expected slump requirements. The mixing water was sourced from the municipal water supply in the Hami region. The mix proportions of HC are listed in Table 2.

Table 1.

Chemical composition of cement (%).

SiO2	Al2O3	Fe2O3	CaO	MgO	SO3	Loss on ignition
24.3	4.8	3.8	55.3	4.2	2.2	2.4

Table 2.

Mix proportions of HC (kg/m³).

Cement	Silica fume	Fly ash	mineral powder	Coarse aggregate	Fine aggregate	Water	Water reducing agent	w/b
305	62	80	140	987.48	658.32	152.5	14.7	0.26

Curing system

Standard curing system

The curing regimes were implemented in accordance with the provisions specified in Chinese Standard GB/T 50,081 − 2019³⁵. After molding, the specimens were left to stand for 24 h at a temperature of 20 °C ± 5 °C and a relative humidity of more than 50%. Subsequently, the molds were removed, and the specimens were immediately placed in a standard curing room with a temperature of 20 °C ± 2 °C and a relative humidity greater than 95% for curing.

Steam curing system

Figure 1illustrates the schematic diagram of curing system. The steam curing refers to Reference³⁵. Steam curing process encompasses four stages: standing, heating, constant temperature, and cooling. During the standing stage, the temperature and time were set as 20 °C ± 5 °C and 3 h, respectively. In the heating stage, the heating rate and final temperature were 20 °C/h and 45 °C, respectively. The constant temperature stage involved a temperature of 45 °C and a duration of 12 h. In the cooling stage, the cooling rate and final temperature were 20 °C/h and 20 °C, respectively. Considering issues such as the coarsening of pores in steam-cured concrete and the lower degree of hydration involvement of fly ash and mineral powder³⁶, the specimens were subsequently placed in a standard curing room and cured for 56 days before testing its pore structure and strength after freeze-thaw cycles.

Figure 1.

Schematic diagram of steaming system.

Test method

Freeze-thaw test

The freeze-thaw cycling tests were conducted using the CLD-3 automatic low-temperature freeze-thaw testing machine, following the slow freezing method outlined in “Standard test methods for long-term performance and durability of ordinary concrete, GB/T50082-2009 (China)³⁷. Thirteen groups of specimens were used for steam curing and another thirteen for standard curing, and each group contained three specimens with dimensions of 100 mm×100 mm×100 mm. The specimens with a curing age of 56 days were immersed in water at (20 ± 2) ℃ for 4 days. The freezing time is calculated when the temperature in the freeze-thaw box drops to -18 ℃. The temperature in the freeze-thaw box is maintained at (-20~-18) ℃ during freezing. The freezing time of the specimen in each freeze-thaw cycle is not less than 4 h. After freezing, immediately put into water with temperature of (18 ~ 20) ℃, so that the specimen into the melting state, melting time is not less than 4 hours. The completion of melting is regarded as the end of the freeze-thaw cycle, and the next freeze-thaw cycle is entered. Mass and elastic modulus were tested after every 25 cycles, compressive strength was tested after every 50 cycles, and pore structure was tested after every 100 cycles. The specimens were categorized based on the curing method and the count of freeze-thaw cycles, denoted as SDHC-x and SMHC-x, where SDHC and SMHC represent standard curing and steam curing, respectively, with x representing the specific number of freeze-thaw cycles.

Pore structure test

The pore structure test used the MesoMR23060H-I nuclear magnetic resonance imaging analyzer developed by Suzhou Newman Analytical Instrument Co., Ltd, as illustrated in Fig. 2. The magnetic field strength of the test system was 0.5 T, and the operating frequency of the test coil was 23 MHz. Thirteen groups of samples were prepared, and each group contained three samples with dimensions of 40 mm × 40 mm × 40 mm. Before the test, the sample was placed in a vacuum saturation device for 24 h to full saturation.The test parameters of Carr-Purcell-Meiboom-Gill pulse sequence(CPMG) are shown in the Table 3.

Figure 2.

Low field nuclear magnetic resonance system.

Table 3.

Low field NMR test parameters.

NS	TE/ms	NECH	TW/ms
16	0.20	18,000	3000

For low frequency magnetic fields, the total relaxation mechanism is dominated by surface relaxation, and the relaxation time can reflect the distribution of pore sizes inside the concrete, where the smaller the size of the pores, the shorter the relaxation time of water. In this experiment, the T₂ relaxation time was obtained from the CPMG echo sequence by the Laplacian numerical inversion.The pore size distribution can be calculated by surface relaxation time T₂distribution function using the expression given below in Eq. (1)³¹.

1

Where, is the surface relaxation strength/surface relaxation rate (m/ms), S is pore surface area(m²), V is the pore volume (m³) and r is the mean pore radius (m).

The surface relaxation rate is mainly related to the surface relaxation time, as shown in Eq. (2).

2

Where λis the thickness of a single layer of water film (water film thickness = 0.3nm³⁸); T_2s is the surface relaxation time (ms);

When the water content of the cement-based material specimen gradually decreases to the point where only a single layer of water molecular film is adsorbed on the surface of the hole wall, the initial relaxation time at this time is equal to the surface relaxation time T_2s, which can be substituted into Eq. (2) to determine the surface relaxation rate that is very critical for the low-field NMR pore measurement.

Compressive strength test

The TSY-3000 type automatic pressure testing machine was selected for the compressive strength test instrument. The loading speed was 1 MPa/s according to the Test Method Standard for Physical and Mechanical Properties of Concrete (GB/T50081-2019)³⁵. There were three samples with dimensions of 100 mm×100 mm×100 mm in each group, a total of thirteen groups in this test.

Results and discussion

Freeze resistance durability of HC

Exterior surface of HC before and after freeze-thaw cycling

Figure 3illustrates the exterior surface characteristics of HC before and after freeze-thaw cycling. Before freeze-thaw cycling, both SDHC and SMHC exhibited visible pores on the concrete surface, with some edges and corners of the specimens appearing dulled. Additionally, there was slight mortar detachment on the surface, and the exterior surface of SMHC was coarser compared with SDHC. Under the influence of freeze-thaw cycling, specimens of SDHC experienced damage after 550 cycles with compressive strength decreased by more than 25%³⁷, resulting in the appearance of microcracks on the surface. For SMHC specimens, damage occurred after 475 cycles of freeze-thaw cycling, with surface mortar detachment, rough and uneven concrete exterior, though no localized extensive defects were observed. There were minor cracks extending from the left edges and corners towards the interior of the concrete. High temperature and moist steam-cured process would give rise to great differences between surface and inner concrete due to temperature-stress difference, heat-mass transfer and non-uniform of hydration of cementitious, which is the reason why cracks appeared earlier in SMHC than in SDHC.The plane porosity on the surfaces of SDHC and SMHC concrete was measured at 6.31% and 9.94%, respectively. From the apparent morphology after freeze-thaw cycling, SDHC exhibited stronger freeze-thaw resistance than SMHC.

Figure 3.

Comparison of SDHC and SMHC surface before and after freeze- thaw cycles. (a) The surface changes of SDHC before freeze-thaw cycles, (b) The surface changes of SMHC before freeze-thaw cycles, (c) The surface changes of SDHC after freeze-thaw cycles, (d) The surface changes of SMHC after freeze-thaw cycles.

Compressive strength

Figure 4illustrates the compressive strength of SDHC and SMHC following freeze-thaw cycles. As depicted, the compressive strength of SDHC and SMHC gradually decreased with an increasing number of freeze-thaw cycles, with SMHC exhibiting a larger reduction. Following 550 freeze-thaw cycles, the compressive strength of SDHC decreased by 31.37%, while the SMHC decreased by 27.7% after 475 freeze-thaw cycles, both exceed the standard-specified threshold of 25%³⁷, indicating that the structure has been damaged. This implies that SMHC is more susceptible to freeze-thaw damage, with a higher rate of compressive strength loss.

Figure 4.

The variation law of compressive strength of HC under freeze-thaw cycles.

It was worth noting that when the freeze-thaw cycles reached approximately 350 times, the compressive strength of SDHC and SMHC began to decrease rapidly until it was destroyed. The compressive strength loss rate of SDHC during 0-350 freeze-thaw cycles was 6.65%, and the loss rate was 26.47% during 350–550 freeze-thaw cycles. The loss rate of compressive strength in the last 200 freeze-thaw cycles was 3.98 times than that of the first 350 freeze-thaw cycles, SMHC also exhibited a similar pattern. This suggests that HC under freeze-thaw cycling experienced a threshold effect, and once this threshold (around 350 cycles) was surpassed, a rapid and significant reduction in compressive strength occurred within a short time.

Mass loss rate

Mass loss rate is the basic index to judge the freeze-thaw damage of concrete. The variation of the mass loss rate of SDHC and SMHC with the number of freeze-thaw cycles was shown in Fig. 5. When the number of freeze-thaw cycles increased from 0 to 50, the mass loss rates of SDHC and SMHC were − 0.13% and − 0.16%, respectively. This indicates that in the early stages of freeze-thaw cycling, the mass of both HC slightly increased, primarily due to capillary water absorption within the concrete during the melting phase^39–41. The mass loss rates of SDHC and SMHC after freeze-thaw damage were 0.50% and 0.43% respectively. The main reason for this phenomenon is that the volume of pore water in concrete dilates when it freezes, resulting in crystallization pressure that acts on the pore or capillary wall. In addition, cold water may migrate in the pores during the freezing process of concrete, resulting in hydraulic pore pressure and cryosuction pressure. These three kinds of pressures appear in the freezing process and disappear in the thawing process, which will cause fatigue damage to the porous skeleton⁴², and the internal damage will gradually accumulate with the increase of freeze-thaw cycles. When the freeze-thaw cycles damage accumulates to a certain extent, mortar detachment occurred on the concrete surface, resulting in an increase in the mass loss rate⁴³. Only a minor scaling of surface mortar occurred without widespread defects, so the mass loss rate of SDHC and SMHC were much lower than the standard value of 5% when the freeze-thaw damage occurred³⁷.As a result, the mass loss rates did not exhibit significant changes. Therefore, utilizing mass loss rates to evaluate the freeze-thaw resistance of HC has certain limitations.

Figure 5.

Mass loss rate of HC under freeze-thaw cycles.

Relative dynamic elastic modulus

The relative dynamic elastic modulus is also one of the indexes to evaluate the frost resistance of concrete. The variation of relative dynamic elastic modulus of SDHC and SMHC under different freeze-thaw cycles was shown in Fig. 6. The relative dynamic elastic modulus of SDHC and SMHC decreased with an increasing number of freeze-thaw cycles. For the initial 350 cycles, both concrete exhibited minimal damages, and the damage progression was slow. Beyond 350 cycles, the relative dynamic elastic modulus of SMHC began to significantly decrease, and the rate of reduction became noticeably faster.

Figure 6.

Relative dynamic elastic modulus of HC under freeze-thaw cycles.

Analysis of the relationship between relative dynamic elastic modulus and compressive strength

Due to the small changes in mass loss rate before and after freeze-thaw cycles, this section only considers the relationship between relative dynamic elastic modulus and compressive strength of HC. Based on the above analyses it was decided to use Eq. (3) to fit the relationship between the two factors, and the fitting results are shown in Fig. 7.

3

Figure 7.

Relationship between compressive strength of HC and freeze-thaw cycles.

where P is the relative dynamic modulus of elasticity; is the compressive strength, MPa; A, B, and t are constants.

According to Fig. 7, the fitted relationships between compressive strength and relative dynamic elastic modulus for SDHC and SMHC were expressed by the equations: and respectively. The goodness of fit (R²) for the relationships between relative dynamic elastic modulus and compressive strength was 0.97 for SDHC and 0.99 for SMHC. This indicated a strong exponential relationship between the relative dynamic elastic modulus and compressive strength of HC.

Pore structure characteristics

T₂ curve change rule

The NMR T₂ spectrum curve can reflect the pore structure information, and the relaxation time and signal amplitude are positively correlated with the pore size and pore number, respectively. The larger the relaxation time is, the larger the aperture is. The higher the signal amplitude, the greater the number of pores. The peak area of T₂ spectrum is proportional to the number of pores, and the area proportion of each peak can reflect the different proportion of pores.

The nuclear magnetic resonance relaxation time T₂ spectrum curve of SDHC and SMHC under freeze-thaw cycles was shown in Fig. 8. In addition, the curve area under each peak in the T₂ spectral curve was quantitatively calculated, as shown in Table 4.

Figure 8.

The variation law of nuclear magnetic resonance relaxation time T₂ spectrum of SDHC.

Table 4.

Area of T₂ curve.

	Area
	SDHC-0	SDHC-100	SDHC-200	SDHC-300	SDHC-400	SDHC-500	SDHC-550
Small pore	1525	1512	1804	1791	1759	1786	2427
Medium pore	758	859	654	855	981	751	1321
Large pore	523	376	351	356	419	691	565
	Area
	SMHC-0	SMHC-100	SMHC-200	SMHC-300	SMHC-400	SMHC-475	-
Small pore	1587	1754	1968	2646	2192	2519	-
Medium pore	988	1073	878	873	791	2269	-
Large pore	167	186	308	822	657

The horizontal and vertical coordinates represent the relaxation time and signal amplitude, respectively, corresponding to the size and number of pores. The T₂ spectrum curve of SDHC exhibited three consecutive peaks, corresponding to small pores, medium pores and large pores. Under the action of freeze-thaw cycles, the value of peak 1 (small pore) was significantly higher than that of peak 2 (medium pore) and peak 3 (large pore), and the corresponding areas were 1525,758,523 respectively, indicating that the proportion of small pores in SDHC was much higher than that of medium pores and large pores. As the number of freeze-thaw cycles increased, Peaks 1, 2, and 3 all shifted to the right, indicating an increase in the diameters of small, medium-sized, and large pores.

According to Fig. 8, for SMHC, there were three consecutive peaks corresponding to small, medium-sized, and large pores except for SMHC-475. In the case of SMHC-475, there were two peaks corresponding to small and large pores. Overall, under the influence of freeze-thaw cycling, the values of Peak 1 for both SDHC and SMHC were significantly higher than those of Peaks 2 and 3, indicating that the quantity of small pores was much higher than that of medium-sized and large pores.

Analysis of Peak 1 revealed that, with an increasing number of freeze-thaw cycles, the peak value and relaxation time range of SMHC gradually increased, and the peak exhibited a rightward shift. Besides, the area occupied by small pores in SMHC increased more significantly than that of SDHC. This indicates that SMHC, in comparison to SDHC, has an impact on small pores from the beginning of freeze-thaw cycling, with a significant effect observed starting from 100 freeze-thaw cycles. Analysis of Peaks 2 and 3 indicates that, with an increasing number of freeze-thaw cycles, the average radius of medium-sized pores and the quantity of large pores gradually increased, with the most significant changes occurring during the period of 400–475 freeze-thaw cycles.

The T₂ spectrum curves of SDHC and SMHC without freeze-thaw cycles were compared and analyzed as shown in Fig. 9. The relaxation time and peak value of peak 1 of SDHC were 0.51–4.20 ms and 96.05, respectively. The peak 1 relaxation time and peak value of SMHC were 0.60–4.94 ms and 101.79, respectively. Compared with SDHC, the relaxation time range of peak 1 of SMHC increased, the peak shifted to the right, and the peak increased, indicating that the average pore size and number of small pores in SMHC were slightly larger than those in SDHC. This is consistent with the corresponding curve area of small pores in SMHC and SDHC, which is 1587 and 1525 respectively.

Figure 9.

T₂ spectrum curves of SDHC and SMHC without freeze-thaw cycles.

The peak 2 of SMHC also showed a trend of right shift and increase, indicating that the average pore size and number of medium pores of SMHC were larger than those of SDHC. The peak 3 of SMHC showed a significant right shift and a decreasing trend, indicating that although the number of large pores of SMHC was less than that of SDHC, its average pore size was significantly larger than that of SDHC.

In summary, the average pore size of small, medium-sized, and large pores in SMHC was larger than that in SDHC. The quantity of small and medium-sized pores was slightly higher, and although the number of large pores was fewer, their average pore size was significantly larger than in SDHC. This indicates that the pores in SMHC exhibited a coarser structure, resulting in a higher porosity compared to SDHC.

Pore distribution of HC specimens

According to the research of Wu et al⁴⁴., the pore size was divided into harmless pores (< 20 nm), less harmful pores (20–100 nm), harmful pores (100–200 nm) and multi-harmful pores (> 200 nm). The influence of different pore sizes in concrete on the frost resistance of HC was further studied.

The stacked column chart in Fig. 10 illustrates the differential pore size distribution of SDHC and SMHC at the 60-day curing age under specific curing conditions. Before the freeze-thaw cycle, the proportion of harmless pores, less harmful pores, harmful pores and multi-harmful pores in SDHC was 23.45%, 33.12%, 7.92%, and 35.52% respectively. The number of multi-harmful pores accounted for the largest proportion, followed by less harmful pores and harmless pores, with the least number of harmful pores. Similarly, the proportion of various pores in SMHC was 17.50%, 40.01%, 7.00%, and 35.48%, respectively, mainly less harmful pores, followed by multi-harmful pores and harmless pores, and the least harmful pores. This indicated that the internal pore structure of SMHC and SDHC was mainly composed of less harmful pores and multi-harmful pores.

Figure 10.

Stomatal size distribution of SDHC and SMHC without freeze-thaw cycles.

There was a difference in pore distribution between SDHC-0 and SMHC-0. Compared with SDHC, the harmless pore of SMHC was 5.95% less, the less harmful pore was 6.89% more, the harmful pore was 0.92% less, and the multi-harmful pore was 0.04% less. It showed that the harmful pores and multi-harmful pores of SDHC and SMHC were equivalent, but the harmless pores in SMHC were less and the less harmful pores were more. It can be seen that steam curing mainly reduced the proportion of harmless pores and increased the proportion of less harmful pores, making the pore structure coarse, which was consistent with the analysis results of porosity and T₂ spectrum curve.

Under the action of freeze-thaw cycles, the stacking histogram of different pore size distribution in SDHC and SMHC was shown in Fig. 11. In the first 100 freeze-thaw cycles of SDHC, the proportion of harmless pores increased from 23.45 to 25.26%, an increase of 1.81%, while the proportion of less harmful pores, harmful pores and multi-harmful pores decreased or remained unchanged, indicating that new harmless pores were generated during this period. However, when the number of freeze-thaw cycles increased from 200 to 550, the proportion of harmless pores and less harmful pores decreased significantly, and the proportion of harmful pores and multi-harmful pores increased. This showed that after more than 200 freeze-thaw cycles, harmless pores and less harmful pores were obviously transformed into harmful pores and multi-harmful pores.

Figure 11.

The change of pore size distribution in SDHC and SMHC under freeze-thaw cycles.

For SMHC, Fig. 11 showed that during the 0-100 freeze-thaw cycles, the proportion of harmless pores in SMHC decreased by 4.74%, the proportion of less harmful pores increased by 4.77%, the proportion of harmful pores decreased by 0.68%, and the proportion of multi-harmful pores increased by 0.66%. This indicated that during the first 100 freeze-thaw cycles, the number of harmless pores in SMHC was lower than the number of harmful pores, harmful pores and multi-harmful pores. During 100–200 freeze-thaw cycles, the proportion of harmless pores increased by 10.14%, the proportion of less harmful pores decreased by 8.21%, and the proportion of harmful pores decreased by 0.45%, the proportion of harmful pores decreased by 1.61%. The proportion of harmless pores in SMHC was greater than the proportion of conversions to less harmful pores, harmful pores and multi-harmful pores. During the 200–475 freeze-thaw cycles, the proportion of harmless pores, less harmful pores and harmful pores in SMHC decreased, while the proportion of multi-harmful pores increased significantly, indicating that harmless pores, less harmful pores and harmful pores began to transform into multi-harmful pores during this period.

In summary, after more than 200 freeze-thaw cycles, the proportion of multi-harmful pores in SDHC and SMHC began to increase significantly. However, the increase in the number of harmful pores in the SMHC was significantly greater than that in SDHC, resulting in the damage of SMHC after 475 freeze-thaw cycles, while SDHC was destroyed after 550 freeze-thaw cycles.

Porosity change rule

Before the freeze-thaw cycle, the porosity of SMHC and SDHC was 8.31% and 7.96%, respectively. It can be seen that the steam curing system caused the internal porosity of HC to increase, which was consistent with the law of low-grade concrete performance^45–47. The variation of the total porosity of HC after freeze-thaw cycles with the number of freeze-thaw cycles was shown in Fig. 12.

Figure 12.

Porosity of HC under freeze-thaw cycles.

As the number of freeze-thaw cycles increased, the total porosity of SDHC and SMHC gradually increased, but the increase gradient gradually slowed down until it was destroyed. Under 100, 200, 300, 400, and 475 freeze-thaw cycles, the porosity of SMHC was greater than that in SDHC, and the difference was 0.34%, 0.56%, 1.47%, 1.23%, and 2.05%, respectively. When the number of freeze-thaw cycles exceeded 100 times, the porosity growth rate of SMHC was greater than that of SDHC. The total porosity of concrete in SDHC increased greatly after 300 freeze-thaw cycles, while that in SMHC increased significantly after 200 freeze-thaw cycles. It can be seen that under the action of freeze-thaw cycles, the pore deterioration of SMHC was faster.

Analysis of frost resistance of HC based on fractal dimension

From the above analysis, it can be concluded that the freeze-thaw cycling process causes an increase in the porosity and pore size of HC, leading to a decrease in compressive strength. Therefore, under the influence of freeze-thaw cycling, there is an inherent correlation between the deterioration pattern of pore structure and the macroscopic performance degradation of concrete. Fractal dimension is used to characterize the relationship between pore structure and frost resistance.

Principle of pore volume fractal dimension

The existing research shows that^48,49, the relationship between the number of pores N and the pore size r in concrete satisfies the following relationship:

4

where, is the maximum pore radius, µm; is the pore size distribution density function; is a proportional constant; D is the pore fractal dimension.

By derivation of both ends of Eq. (4), the aperture distribution density function can be obtained, as shown in Eq. (5) :

5

Where, is the proportional constant.

The cumulative volume of pores with pore diameter less than r in concrete can be expressed by Eq. (6) :

6

Where,α = 4π/3, r_min is the minimum pore radius (µm) in the pore.

According to Eq. (5) and Eq. (6), Eq. (7) can be derived:

7

Therefore, the total pore volume of concrete can be expressed by Eq. (8) :

8

From this, the expression of cumulative pore volume fraction S_V with aperture less than V_r can be derived as Eq. (9) :

9

Also because of , it is possible to simplify Eq. (9) into the form of Eq. (10) :

10

Take the logarithm of both sides of Eq. (10) and derive Eq. (11):

11

Let lgu = y, lg(r/r_max)=x, the Eq. (12) can be obtained:

12

Finally, the linear regression equation is established by Eq. (12), and the fractal dimension D of the pore volume of high-strength concrete based on the pore size distribution can be obtained.

Fractal characteristics of pore size of HC

According to Eq. (12), the linear regression equation of pore size and pore volume was established, and then the fractal dimension of HC was calculated according to the slope of the linear regression equation. The fitting results of the fractal dimension of the internal pores of the HC specimens without freeze-thaw cycles were shown in Fig. 13.

Figure 13.

Fitting curve of pore fractal dimension

From Fig. 13, it can be observed that the fractal dimension fitting coefficients (R²) for all pores inside SDHC and SMHC were 0.54 and 0.41, respectively, indicating a poor fitting effect. The reason was that the internal pore size of HC spanned micro and macro scales, making it challenging to express them uniformly with a fractal dimension. Therefore, in this study, the pore size distribution was narrowed down, focusing only on the fractal dimension of multi-harmful pores. The fitting results are shown in Fig. 14.

Figure 14.

Fitting curve of multi-harmful pore fractal dimension.

It can be observed that the fractal dimension fitting relationships of the multi-harmful pores in SDHC and SMHC were and , with fitting coefficients (R²) of 0.94 and 0.91, respectively. This indicates a good fitting effect. Therefore, this section exclusively focuses on the fractal characteristics of multi-harmful pores in HC for analysis and study.

The change rule of fractal dimension of HC under freeze-thaw cycles

According to Eq. (12), the fractal dimension of multi-harmful pore volume of specimens in SDHC and SMHC under freeze-thaw cycles was calculated respectively. The results were shown in Table 5.

Table 5.

Fractal dimension of pore volume of HC under freeze-thaw cycles.

Number	D	R 2	Number	D	R 2
B-0	2.956	0.94	Z-0	2.948	0.91
B-50	2.947	0.97	Z-50	2.948	0.94
B-100	2.947	0.96	Z-100	2.946	0.94
B-150	2.943	0.96	Z-150	2.945	0.96
B-200	2.935	0.98	Z-200	2.945	0.94
B-250	2.932	0.98	Z-250	2.932	0.98
B-300	2.932	0.96	Z-300	2.925	0.95
B-350	2.927	0.99	Z-350	2.921	0.98
B-400	2.923	0.96	Z-400	2.920	0.99
B-450	2.919	0.95	Z-450	2.911	0.95
B-500	2.914	0.98	Z-475	2.905	0.99
B-550	2.914	0.99	-	-	-

The fractal dimension can quantitatively characterize the complexity of the pore structure inside concrete, where a higher fractal dimension value indicates a more complex pore characteristic. As shown in Table 5, the minimum value of the fractal dimension fitting degree R² of the multi-harmful pore was 0.91, suggesting a good fitting effect. For both SDHC and SMHC specimens, the fractal dimension values exhibited a decreasing trend during the freeze-thaw cycling period. The primary reason for this phenomenon is the transformation of small pores into larger pores within multi-harmful pores under the influence of freeze-thaw cycling, leading to a reduction in the complexity of the pore distribution.

The fractal dimension of SMHC and SDHC decreased slightly with the freeze-thaw cycle, the average reduction rate of the fractal dimension of SDHC and SMHC was 0.22% and 0.35% per 100 freeze-thaw cycles, respectively. The decline rate of SMHC fractal dimension is slightly higher than that of SDHC, which indicates to a certain extent that SMHC has a higher deterioration rate under freeze-thaw cycles, and the deterioration degree under the same freeze-thaw cycles is also greater.

The relationship between fractal dimension and relative dynamic elastic modulus

The relationship between the fractal dimension and the relative dynamic elastic modulus of the specimens in SDHC and SMHC was shown in Fig. 15.

Figure 15.

Fitting relationship between fractal dimension and relative dynamic elastic modulus.

For SDHC specimens, the fitting curve relationship between the fractal dimension and relative dynamic modulus was , with a fitting coefficient (R²) of 0.92. For SMHC specimens, the fitting curve relationship between the fractal dimension and relative dynamic modulus was , with a fitting coefficient (R²) of 0.93. In both standard and steam-curing environments, HC exhibited a quadratic relationship between relative dynamic modulus and fractal dimension. The relative dynamic modulus gradually increased with an increase in fractal dimension, but the rate of increase decreased.

Compared with the specimens of SDHC, with the decrease of fractal dimension, the relative dynamic elastic modulus of SMHC decreased more, indicating that SMHC was severely damaged under the action of freeze-thaw cycles, and the degradation rate was also faster. Under the same fractal dimension, the relative dynamic elastic modulus of SMHC was smaller, indicating that its internal deterioration damage degree was higher than that of SDHC. The main reason is that steam curing will lead to more pores in HC, which aggravates the expansion and connection of pore structure of HC.

The relationship between fractal dimension and compressive strength

The relationship between the fractal dimension and the compressive strength of SDHC and SMHC was shown in Fig. 16.

Figure 16.

The relationship between fractal dimension and compressive strength.

The relationship between the fractal dimension and the compressive strength of the specimens in SDHC was , with a fitting coefficient (R²) of 0.86. The fitting curve relationship between the fractal dimension and the cube compressive strength of SMHC was , with a fitting coefficient (R²) of 0.94. It showed that there was a good linear relationship between compressive strength and fractal dimension of HC under standard curing and steam curing environment, and the compressive strength increased with the increase of fractal dimension. Compared with SDHC, with the decrease of fractal dimension, the compressive strength of SMHC decreased more, indicating that the degree of internal deterioration damage was higher than that of SDHC.

Discussions

Since the internal structure of HC is more dense, some researchers believe that the effect of steam curing regimes on HC is negligible, and there are some controversies on the study of pore structure of SMHC. Therefore, the progress of freeze-thaw damage of HC under two curing conditions was studied in this paper, and the fundamental mechanism driving the difference between SDHC and SMHC has been discussed:

The main reason of concrete damage under freeze-thaw cycle is the generation, expansion and development of micro-cracks in concrete. The experimental results of Luan et al⁵⁰. show that the water absorption and water saturation of concrete increase significantly after freezing and thawing. When the temperature drops below 0 °C, the water in the pores inside concrete forms ice and expands to about 9% of its volume⁵¹. During the freezing process, unfrozen water gradually migrates around the frozen macropores, and the migration of pore solution eventually produces hydrostatic pressure and osmotic pressure. When the expansion force exceeds the tensile strength of the capillary wall, microcracks begin to expand around and gradually penetrate into the cement.

For SMHC, the curing process leads to higher hydration degree of cement slurry, but the coarse-grained semi-microporous structure with high pore connectivity and low fractal dimension is formed in the later stage. This phenomenon is known as the “thermal damage effect”⁵². Under high temperature conditions, the growth and diffusion of hydration products are subjected to the pressure of water vapor evaporation. During the cooling phase of the steam curing process, as the ambient temperature begins to decrease, the water vapor in the formed pores condenses, resulting in a decrease in the pressure in the pores. At the same time, the cement paste is hardened and cannot be deformed freely. As a result, local stresses are generated, leading to the appearance of micro-cracks. This is also the fundamental reason that the effect of steam curing on the progress of freeze-thaw damage is different from that of standard curing.

According to the above analysis, with the increase of freeze-thaw cycles, both compressive strength and relative dynamic elastic modulus gradually decreased. The average pore size and proportion of large pores in SMHC were higher than those in SDHC, and the rate of pore conversion into harmful pores in SMHC was significantly higher than that in SDHC, because steam curing enhanced the mutual permeability of pores, forming a continuous seepage channel. During freeze-thaw cycle, ice expansion force leads to more serious freeze-thaw damage and deterioration degree of SMHC which also indicates that the pore structure of SMHC has a certain impact on mechanical properties and durability, and can not be ignored.

In addition, water-cement ratio, curing time and curing temperature are important factors affecting the development of pore structure under freeze-thaw cycle⁵³. In the future, the effects of water-cement ratio, steam curing temperature and curing time on the pore structure and mechanics of concrete can be further investigated.

Conclusions

The pore structure evolution of SMHC under freeze-thaw cycles was studied systematically for the first time. The change of pore structure by two curing systems under freeze-thaw cycle was analyzed, and the influence of microstructure on its properties and the correlation between internal microstructure and macro behavior were studied. The findings are summarized as follows:

1. With the increase of freeze-thaw cycles, the appearance characteristics of SDHC and SMHC became more and more rough, and pores appeared on the surface of the specimens obviously. Microcracks appeared and slight mortar detachment occurred of SMHC. The apparent damage of SMHC was more serious than that of SDHC.

2. After freeze-thaw cycles, the mass loss rates of SDHC and SMHC were 0.43% and 0.50%, respectively, which did not exceed 5%. Mainly due to the dense internal structure of HC, only a small part of the mortar fell off after freeze-thaw damage.

3. The compressive strength loss rates of SDHC during 0-350 and 350–550 freeze-thaw cycles were 6.65% and 26.47%, respectively. While during 0-350 and 350–475 freeze-thaw cycles the compressive strength loss rates of SMHC were 9.66% and 20.00%, respectively. SMHC was destroyed earlier than SDHC. The relative dynamic elastic modulus of SDHC and SMHC decreased significantly after 425 and 350 freeze-thaw cycles, respectively. The relationship between the relative dynamic elastic modulus and compressive strength of SDHC and SMHC was exponential function.

4. The steam curing regimes led to an increased porosity within HC. After freeze-thaw damage, SMHC exhibited larger average pore sizes and quantities of small and medium-sized pores compared to SDHC. Additionally, the average pore size of large pores in SMHC was significantly larger than that in SDHC. Under the influence of freeze-thaw cycles, the pores in SMHC became coarser.

5. When the freeze-thaw cycles reached 200 times, both SDHC and SMHC exhibited a noticeable increase in the quantity of harmful pores. However, after exceeding 200 cycles, the rate of transformation from internal pores to harmful pores in SMHC was significantly higher than that in SDHC. The specimens of SMHC experienced damage after 475 freeze-thaw cycles, while SDHC specimens was damaged after 550 freeze-thaw cycles.

6. The fractal dimension can reflect the complexity of the internal pores of HC in different freeze-thaw stages. With the increase of freeze-thaw cycles, the fractal dimension of concrete decreased gradually, the total porosity increased, the proportion of harmless pores, less harmful pores and harmful pores in concrete decreased, and the proportion of multi-harmful pores increased gradually.In addition, the compressive strength and relative dynamic elastic modulus showed a downward trend, and the degree of internal deterioration of concrete gradually became more severe.For instance, after 475 freeze-thaw cycles, the fractal dimension decreased by 1.46%, the compressive strength and relative dynamic elastic modulus decreased by 27.7% and 48.77%, respectively, and the proportion of multi-harmful pores increased by 33.54% of SMHC. The fractal dimension reflects the influence of the pore structure on the mechanical properties and frost resistance of concrete after freeze-thaw cycle by evaluating the change of the pore structure inside concrete, and then evaluates the freeze-thaw damage of HC.

In conclusion, through the research, it is found that the pore structure has a significant impact on the mechanical properties and durability of HC. This paper serves as a catalyst for further exploration, and in the future, more in-depth research can be carried out.

Notation

P

the relative dynamic elastic modulus

f_c

the compressive strength

D

fractal dimension

Author contributions

Runfang Zhou: investigation, data curation, writing - original draft, writing - review & editing. Haitao Mao: methodology, writing - review & editing, resources. Shuai Yang: investigation, writing - review & editing. Zhengcheng Wang: validation, writing - review & editing. Xiaobing He: data curation. All authors have read and agreed to the published version of the manuscript.

Data availability

Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare no competing interests.