Study on the mechanical properties and pore structure of granulated blast furnace slag self-compacting concrete based on grey correlation theory

ABSTRACT

Variations in the mechanical properties and pore structure of granulated blast furnace slag self-compacting concrete were studied. The grey correlation theory established the relationship between mechanical properties and pore structure. The test results show that with the continuous improvement of age, the mechanical properties decreased with the increase of sand replacement rate in the early stage. In the middle and late stages, the compressive strength and splitting tensile strength of granulated blast furnace slag self-compacting concrete are higher than those of ordinary self-compacting concrete, while the elastic modulus continues to decrease with increasing slag content. After standard curing, the change in the pore structure parameters of ordinary self-compacting concrete is relatively stable. The pore structure parameters of granulated blast furnace slag self-compacting concrete change significantly. Because granulated blast furnace slag has a certain hydraulicity, the strength and strength growth rate of granulated blast furnace slag self-compacting concrete are higher than those of ordinary self-compacting concrete, and the corresponding pore structure parameters change. Through grey correlation analysis, the specific surface area and average chord length structure of granulated blast furnace slag self-compacting concrete are essential factors affecting its mechanical properties.

KEYWORDS:

• Granulated blast furnace slag
• self-compacting concrete
• mechanical properties
• pore structure
• grey correlation degree

1. Introduction

By 2050, the world’s population will reach 10 billion. With the acceleration of urbanization and infrastructure construction, the rise of large cities in developing countries has greatly pressured their construction and infrastructure needs (MEHTA 2002). As one of the most widely used materials in construction engineering, the demand for concrete is increasing year by year. Therefore, the demand for natural aggregates is also increasing year by year. The exploitation of natural aggregates has caused serious damage to the environment (Kang and Weibin 2018). Protecting natural resources, effectively utilizing industrial tributaries, maintaining sustainable urban development, and reducing environmental impact are the main goals of the world’s construction industry. Adding environmentally friendly industrial by-products as fine aggregate in concrete production can not only reduce the cost of building materials but also protect the environment (Alzaza et al. 2022; Batayneh, Marie, and Asi 2007; Zhang et al. 2023).

With the rapid development of high-performance concrete, self-compacting concrete (SCC), as a kind of high-performance concrete, was proposed and developed in the late 1980s (Ouchi and Okamura 1999). Ozawa et al. from Tokyo University successfully prepared vibration-free self-compacting concrete in 1988 (Ozawa et al. 1989). Since the development of SCC, there have been many practical applications worldwide, and an SCC of 100,000 m³ is placed to anchor the frame and anchorage of the AKASHI strait bridge (Uno and Japan 2005). Self-compacting concrete is the most widely used concrete in Japan. By 2004, the total use of self-compacting concrete in Japan exceeded 2.5 million m³ (Yongshun and Yuhongm 2007), and there is an increasing trend year by year. In Europe, Sweden first applied self-compacting concrete to practical projects in the 1990s. In recent years, the amount of self-compacting concrete in Europe has gradually increased (Netherlands, Sweden, France, Poland, and other countries) (Houchan 2012). Since then, SCC applications have generally increased throughout Europe. On May 26–28, 2005, China Central South University and other units hosted the first International Symposium on Design, Performance, and Use of Self-Consolidating Concrete (SCC’2005-China) in Changsha, Hunan Province (Yunhua, Youjun, and Guangcheng 2007). In the past few decades, some attempts have been made to develop new high-performance materials with the advantages and characteristics of self-compacting concrete and lightweight concrete. An innovative lightweight self-compacting concrete (LWSCC) has been developed with the characteristics of both LWC and SCC (Ting et al. 2019). Omar Kouider Djelloul et al. studied the effect of coarse and fine recycled concrete aggregates (RCA) on fresh and hardened properties of self-compacting concrete (SCC) containing ground granulated blast-furnace slag (GGBFS) as cement replacement. It was found that the combined use of RCA with GGBFS had a significant effect on fresh and hardened SCC mixes. Adding fine and coarse recycled aggregates as a substitution for up to 50% of natural aggregates enhances the workability of SCC mixes. In contrast, the addition from 50 to 100% decreases the workability (Djelloul et al. 2018). Indirectly estimating compressive strength through non-destructive testing is to monitor the strength of structural concrete used in construction and repair works. Hammering rebound index and ultrasonic pulse velocity (UPV) were used to predict the compressive strength of high SCC. The development of specific models for high SCC responds to the inappropriateness of traditional models that do not adapt to their high-penalty content. Modeling as a function of UPV or hammering rebound index can obtain accurate prediction (Revilla-Cuesta et al. 2021). Víctor Revilla-Cuesta et al. prepared 19 SCC mixtures. The fluidity reduction, compressive strength, elastic modulus, carbon footprint, and mixing cost were studied at 15 and 60 minutes. It is found that the ideal choice for the rapid pouring of concrete is a combination of GGBS, 100 % coarse RCA, and limestone powder, but conventional cement should be used if SCC must be transported to the pouring point. By limiting the fine RCA content to 50 %, the strength and stiffness can be maximized. The ideal choice for the rapid pouring of concrete is the combination of GGBS, 100 % coarse-grained RCA, and limestone powder, but if SCC must be transported to the concrete pouring point, conventional cement should be used. By limiting the fine RCA content to 50 %, the strength and stiffness can be maximized (Revilla-Cuesta et al. 2021). Replacing cement with materials such as fly ash, metakaolin, and ground granulated blast furnace slag (GGBS) can reduce 5–7 % of carbon dioxide emissions in cement. This study will provide a scientific basis for the potential design of SCC materials for concrete structures (Dey et al. 2021). Fractal analysis and 3D X-ray computed tomography accompanied by digital image analysis techniques are used to quantitatively evaluate segregation resistance, static strength, and corrosion-induced cracking in normal self-compacting concrete and self-compacting lightweight concrete. It is found that the compression capacity of self-compacting lightweight concrete is weaker than that of ordinary self-compacting concrete, mainly due to the uneven internal structure (Erdem 2014). Alberti, MG et al. studied the mechanical properties of self-compacting concrete with a low, medium, and high fiber content of large polyolefin fibers. Their fracture behaviors were compared with those of ordinary self-compacting concrete and steel fiber-reinforced self-compacting concrete. It is found that polyolefin fiber-reinforced self-compacting concrete has similar fracture properties to steel fiber-reinforced self-compacting concrete (Alberti, Enfedaque, and Gálvez 2014). High calcium fly ash (HCFA) is used as an additive in concrete (up to 30 %) or as a major cement component. The study confirms that HCFA can be used for self-compacting concrete while maintaining the assumed workability of fresh concrete and the compressive strength of hardened concrete. HCFA should be ground, and its content in the mixture should not be higher than 30 % of the cement mass. Cement with HCFA as the main component can be used in ordinary and high-performance self-compacting concrete (Ponikiewski and Gołaszewski 2014). Information on the fresh and hardening properties of different forms of self-compacting concrete is developed using recycled concrete aggregates combined with recycled crumb rubber or lightweight aggregates. The optimum mix design of recycled concrete and crumb rubber aggregate self-compacting concrete was evaluated to optimize fresh and hardening properties. The proposed SCC mixture can reduce the amount of waste cement to 40 %. In addition, with the increase of the recycled aggregate replacement ratio, the fluidity and passing capacity of the SCC mixture decreased (Aslani et al. 2018). Granulated blast furnace slag as fine aggregate has been successfully applied in ordinary concrete, so its adaptability has been verified (Rashad, Sadek, and Hassan 2016; Yüksel, Bilir, and Ö 2007).

This paper mainly introduces the preparation of self-compacting concrete using granulated blast furnace slag as fine aggregate. While effectively utilizing industrial tributaries, it also draws on the advantages of self-compacting concrete, which can not only alleviate the problem of insufficient supply of natural sand in China, but also enable the construction industry to develop green, healthy, and sustainable. It can also effectively play the advantages of high-performance concrete. Evaluations of the mechanical properties mainly include the cube compressive strength test, splitting tensile strength test, and static compression elastic modulus test. Pore structure research mainly includes optical methods for measuring pore structure and nuclear magnetic resonance analysis. Finally, the compressive strength and pore structure parameters are correlated by grey correlation analysis. Using multiple angles to explore it is changing rules provides a reference for accelerating the engineering application of granulated blast furnace slag self-compacting concrete (GBFS-SCC).

2. Materials and methods

2.1. Materials

Granulated blast furnace slag comes from Baotou Iron and Steel (Group) Co., Ltd., Inner Mongolia. The sand comes from the natural washing sand of the Dahei River in Hohhot. The gravel comes from the first-grade granite crushed in Daqing Mountain in Hohhot. Table 1 shows the basic performance index of the aggregate. The test standard is based on GB/T14684–2022 “sand for construction” and GB/T14685–2022 “pebbles and gravels for construction”. The cement is P·O 42.5 ordinary Portland cement. Table 2 shows the chemical composition of the granulated blast furnace slag, cement clinker, and fly ash. The fly ash is sourced from the secondary fly ash produced by a power plant in Hohhot. The water-reducing agent is a polycarboxylate superplasticizer. Granulated blast furnace slag and cement clinker are similar, with a certain hydraulicity (Portland activity).

Table 1. Index of aggregate parameters.

Sample category	GBFS	Natural sand	Gravel
Loose bulk density（kg/m3）	1058	1460	1310
Compacted bulk density（kg/m3）	1230	1620	—
Apparent density（kg/m3）	2308	2660	2760
Crushing index value（%）	39.0	6.9	9.9

Table 2. Chemical composition of granulated blast furnace slag and cement clinker.

Materials	Chemical composition（%）
	CaO	MgO	SiO2	Fe2O3	Al2O3
GBFS	35.82	0.58	33.39	7.59	12.92
Cement clinker	64.00	1.00	23.44	2.96	7.19
Fly ash	3.71	0.58	49.11	3.21	38.99

The design strength in the mix ratio test is C40, and three sand replacement rates of 0%, 50%, and 100% are set. The full calculation method (Jiankui and Dongmin 2000) is used to design the mix ratio. After multiple adaptations, the team obtains the mix ratio of granulated blast furnace slag self-compacting concrete that meets the working performance (i.e., fluidity, filling, gap passing, segregation resistance, etc.), as shown in Table 3. Because the density of granulated blast furnace slag is similar to that of natural sand, both of which are between 2.5 and 2.6 g·cm⁻³, for the convenience of engineering application, considering the quality of fine aggregate as a variable, the natural sand is replaced by granulated blast furnace slag in a ratio of 50 % and 100 %. There may be a few deviations in this method, but it has little effect on the whole mixture.

Table 3. Optimum mix proportion design of GBFS-SCC (kg/m³).

W	C	FA	S	G	PS	GBFS	GBFS ratio	SP	W/B	SF(mm)
170	341	85.2	937.0	846.7	2.925	0	0%	52.50%	0.399	615
170	341	85.2	458.5	846.7	3.327	458.5	50%	52.50%	0.399	703
170	341	85.2	0	846.7	7.785	937.0	100%	52.50%	0.399	625

Note; the symbols in the table: W: water, C: cement, FA: fly ash, S: natural sand, G: gravel, PS: polycarboxylic superplasticizer, GBFS: granulated blast furnace slag, GBFS ratio: granulated blast furnace slag replacement rate, SP: sand percentage, W/B: water-binder ratio, SF: Slump-flow.

2.2. Test methods

The concrete mechanical properties were tested using the 100 mm³ cube test block specification, and the static compression elastic modulus test was performed using the 100 × 100× 300 mm specification. Each group of test specimens was three, according to GB/T 50,081–2019 “concrete physical and mechanical properties test method standard”. The ordinary SCC specimens (control group) and GBFS-SCC specimens were placed in the standard curing room for standard curing for 7 d, 14 d, 28 d, and 180 d. The cube compressive strength, splitting tensile strength, and static compressive elastic modulus of SCC were tested.

The pore structure of GBFS-SCC was measured by an optical method using a Rapid Air 457 hardened concrete pore structure analyzer. The Rapid Air 457 concrete pore structure analyzer is manufactured by Concrete Experts International, Denmark. It includes an automatic analysis system, a computer control unit (PC), a color monitor, a camera lens, and a microscope objective lens mounted on a mobile workbench. The variation in the pore structure of the concrete is evaluated by analyzing parameters such as the air content, pore spacing coefficient, and average chord length of the bubble (Liu and Liu 2021).

Nuclear magnetic resonance tests were performed using a nuclear magnetic resonance instrument (MesoMR-60S) for pore structure analysis. The standard specimen size used in this test is 50 mm in diameter and 50 mm in height. Before the first test, the GBFS-SCC specimen must be calibrated to determine the quality of the water inside the specimen. Before each test, the test piece needs to be saturated under high pressure so that the internal holes of the test piece are filled with distilled water. After the parameters such as pore size distribution and porosity inside the concrete test piece are measured by a nuclear magnetic resonance instrument, the test piece continues to be held in a standard curing room for curing. The signal intensity reflects the amount of hydrogen protons in liquid water in the pores. The higher the signal intensity is, the greater the water content (Revilla-Cuesta et al. 2021). The T₂ spectrum of the concrete specimens is analyzed, and the influence of different GBFS contents on the SCC pore structure is analyzed and evaluated from the microscopic point of view.

3. Results and discussion

3.1. Mechanical properties test results and analysis

As shown in Figure 1, the mechanical properties of GBFS-SCC and ordinary SCC are similar, with the increase of age, compressive strength, and splitting tensile strength increasing gradually. The early strength shows that the compressive strength gradually decreases with an increasing sand replacement rate. The reason is that the shape of granulated blast furnace slag is irregular. In the case of no vibration, the internal harmful pores (d >200 nm) and harmful pores (200 nm ≥d >100 nm) (Zhongwei and Zhang 1990)are in the majority, which makes the strength decrease with increasing sand replacement rate. Figure 1(a) is the compressive strength test results of different ages, in the 7-day age compressive strength test group. The compressive strength of 50% GBFS-SCC is 93.4% of that of ordinary SCC, and the compressive strength of 100% GBFS-SCC is 78.9% of that of ordinary SCC. However, in the 28-day compressive strength test group, the strength of GBFS-SCC with a 50% sand replacement rate is higher than that of ordinary SCC. The compressive strength of GBFS-SCC with a 100% sand replacement rate is increased to 84.0% of that of ordinary concrete. When the age reaches 180 days, the compressive strength of 50 % GBFS-SCC is 116.5 % of that of ordinary SCC, and the compressive strength of 100 % GBFS-SCC is 107.3 % of that of ordinary SCC. As shown in Figure 1(b), Similarly, there are still similar changes in the splitting tensile strength test. In the 7-day tensile strength test group, the tensile strength of 50 % GBFS-SCC is 73.1 % of that of ordinary SCC, and the compressive strength of 100 % GBFS-SCC is 58.2 % of that of ordinary SCC. At the age of 14 days, the tensile strength of 50 % GBFS-SCC is slightly higher than that of ordinary concrete. The tensile strength of 50 % GBFS-SCC is 105.2 % of that of ordinary SCC. The tensile strength of 28 and 180 days has the same rule. However, the growth rate of splitting tensile strength of GBFS-SCC with 100 % sand replacement rate at 28–180 days was significantly higher than that of the other two test groups. This represents that the potential activity of granulated blast furnace slag is stimulated after long-term curing, which is consistent with the change rule of the compressive strength test.

Figure 1. Cubic compressive strength of specimens at different ages.

The potential hydraulicity of granulated blast furnace slag is promoted in this process so that the internal macropores (d >1000 nm) and capillary pores (1000 nm ≥d >100 nm) of concrete are filled, gradually reduced, and transformed into excessive pores (100 nm ≥d >10 nm) and gel pores (d ≤10 nm) (Dongli et al. 2021). This shows that the hydraulicity of GBFS improves the strength of concrete to a certain extent.

Figure 1(c) shows the elastic modulus test results. The elastic modulus of the first 7 d is lower than 24.0 GPa, and the three groups of tests are between 30.0–34.0 GPa at the age of 28 d, which is similar to the mechanical properties of SCC and ordinary concrete found in the research results of P.L. Domone (Domone 2007). In the whole test process, the elastic modulus of GBFS-SCC is similar to that of ordinary SCC, and both increase with increasing age, but GBFS-SCC is always lower than ordinary SCC. This shows that the ability of GBFS-SCC to resist deformation is still lower than that of ordinary SCC during 28 d of standard curing. The elastic modulus at the age of 180 d is 50 % > 0 % > 100 %. After long-term standard curing, the elastic modulus of the 50 % replacement rate test group has been significantly improved and slightly higher than the replacement rate of 0 % (control group). However, the test group with a 100 % replacement rate is still less than 0 %. The possible reason is that GBFS-SCC, with a 100 % replacement rate, has more macropores, and there are still more holes on the surface and inside of the specimen compared with 0 % and 50 %, so the ability to resist deformation is relatively weak.

Granulated blast furnace slag has irregular particles, many needle-like flakes, and a sizeable crushing value. Compared with ordinary self-compacting concrete, the number of pores in granulated blast furnace slag self-compacting concrete is larger, which affects the mechanical properties of self-compacting concrete. The granulated blast furnace slag has hydraulicity, and the internal pore structure of the concrete is optimized to a certain extent under the condition of long-age curing. The strength growth rate of long-age granulated blast furnace slag self-compacting concrete is greater than that of ordinary self-compacting concrete. These two factors highly affect the mechanical properties of GBFS-SCC.

3.2. Pore structure test results and analysis

The main reason for the decrease in the strength of granulated blast furnace slag self-compacting concrete is that the incorporation of a large amount of granulated blast furnace slag will change the pore structure of the sample, thereby increasing the porosity of the concrete and resulting in a decrease in mechanical properties (Han and Xing 2017). Porosity greatly influences the water absorption, impermeability, and frost resistance of concrete materials, and the high porosity and water absorption will increase. The weight of concrete materials will increase, the strength will decrease, the thermal insulation performance will decrease, and the frost resistance will become worse. The permeability of concrete directly reflects the impermeability. The higher the permeability is, the worse the impermeability is. Impermeability is the most important factor determining the durability of concrete. The permeability of concrete affects the rate of liquid (or gas) invasion. When harmful liquid or gas penetrates the concrete, a series of physical, chemical, and mechanical effects will occur on the concrete composition. Impermeability is the main performance that must be controlled first to improve and ensure durability. Three main types of concrete impermeability are water permeability, air permeability, and resistance to chloride ion permeability. The impermeability of concrete is directly related to water, which mainly refers to its ability to resist water and oil infiltration, and whether it can effectively prevent water from infiltrating the concrete through pores.

3.2.1. Measuring pore structure by the optical method

As shown in Figure 2(a), the air content of ordinary SCC is relatively stable, which means that ordinary SCC has completed hydration in the early stage. The hydration effect of 14–180 days is relatively small, while the air content of GBFS-SCC with 50 % and 100 % content is relatively high in 0–28 days. This is because GBFS is irregular, making the internal macropores in the majority, which is consistent with the trend of surface morphology in Figure 2(a). With the increase in sand replacement rate, the number, density, and size of pores are significantly improved. However, there was a significant downward trend after 7–180 days, which proved that the potential activity of GBFS was stimulated during 7–180 days, participating in hydration and continuously generating hydration products, so that the internal voids were optimized and filled, and the gas in the pores was excluded, resulting in a significant decrease in the gas content of GBFS-SCC.

Figure 2. Air-void structure parameters of specimens at different ages.

As shown in Figure 2(b), the specific surface area of ordinary SCC shows a relatively stable change rule, while the specific surface area of the GBFS-SCC test group with a sand replacement rate of 50 % and 100 has a relatively significant increase. The reason is that GBFS has certain hydraulicity. With the increase of age, the hydration reaction products will continue to increase, increasing specific surface area, indicating that the potential hydraulicity of GBFS can be stimulated by sufficient standard curing, thereby optimizing its internal pore structure. After 180 days of standard curing, the specific surface area of GBFS-SCC with a 50 % sand replacement rate is greater than that of ordinary SCC, and during the 180 days of curing, the specific surface area of GBFS-SCC has always maintained an increasing trend, but the specific surface area of 0–14 days The change range is relatively small, and the growth rate is relatively obvious in 14–180 days. This indicates that the potential hydraulicity of granulated blast furnace slag can be brought into play after long-term curing, thereby improving the pore structure and affecting the change of pore structure parameters.

As shown in Figure 2(c), the ordinary SCC showed a relatively stable change rule, and GBFS-SCC showed a significant downward trend. The pore spacing coefficient of concrete decreases, manifested by the optimization of pore structure, indicating that the mineral admixtures in concrete have not been fully hydrated, and the pores are still hydrated to fill the pores, making the concrete structure denser (Yanwen et al. 2020). In the process of 7–28 days of standard curing, the pore spacing coefficient decreased significantly, but the difference between 180 days and 28 days was not significant. The possible reason was that it had reached a stable state at 28–180 days, and after 28 days, the pore spacing coefficient of GBFS-SCC was significantly lower than that of ordinary SCC, which represented that the average distance from any point in the concrete to the pore was significantly reduced, which indicated that the hydration products produced by continuous hydration filled some pores during the test. Another reason for the decrease in the pore spacing coefficient is the decrease in the gas content. As mentioned above, the formation of hydration products leads to the filling of holes, which leads to the decrease of the gas content, and the decrease of the gas content will also lead to the decrease of the pore spacing coefficient.

As shown in Figure 2(d), with the increase of age, ordinary SCC is stable, while the average chord length of GBFS-SCC has a significant downward trend, which indicates that the internal pore size of concrete becomes smaller. Combined with Figure 2(d), it can be seen that with the increase of age, the pore size of GBFS-SCC decreases obviously. The change in the average chord length at the age of 7–180 days is relatively obvious. Because of the activation of the activity of the granulated blast furnace slag, the internal pore size has been filled and optimized by the hydration products, and finally, the average chord length of the pores of GBFS-SCC has been significantly reduced. The pore size of ordinary SCC is relatively stable and always maintains a low value. It can also be seen intuitively from Figure 2(d). However, in the 100 % sand replacement group, the average chord length of the pores at the age of 14 days is slightly higher than that of 7 days, and there is a slight increase in the 50 % sand replacement group at the age of 180 days. The possible reason is that the concrete itself has a certain degree of dispersion, so it cannot be analyzed from a single perspective.

As shown in Figure 3, it can be seen that with the increase of sand replacement rate, the number of pores in concrete increases. However, with the increase of age, the number of pores in GBFS-SCC decreases, the pore structure is optimized, and the number of macropores decreases obviously. However, with the increase of sand replacement rate, the number of pores increases continuously. Among them, GBFS-SCC with a 100 % replacement rate is still the most, which is also the reason for its low strength.

Figure 3. Scanning analysis of the pore structure of each group of specimens at different ages.

Note: 7d-0% means that the sand ratio of 7 d of curing age is 0%, and so on.

3.2.2. Nuclear magnetic resonance analysis

As shown in Figure 4, the change rules of the T₂ spectra of ordinary SCC and GBFS-SCC in the standard curing process are the same. With the increase in sand replacement rate, the overall number of pores continues to increase, and with the change in curing age, each peak has a certain degree of reduction. The T₂ spectrum mainly shows three peaks (a, b, and c peaks). With increasing age, the signal intensity of the T₂ spectrum decreases to a certain extent, which indicates that the overall porosity of concrete under standard curing has been reduced to a certain extent. At the same time, comparing Figs. 4(a,b), at the age of 28 d, the signal intensity of peak b is significantly reduced, and peak b shifts to peak a, which represents the continuous hydration inside the SCC, and then the large pores are filled and optimized. The original large pores gradually change to small pores, which also confirms the reason for the increase in strength and strength growth rate of GBFS-SCC shown above.

Figure 4. Nuclear magnetic resonance T₂ spectrum curves of different age groups.

The pore radius is proportional to the transverse relaxation time T₂, so the transverse relaxation time T₂ signal intensity of the nuclear magnetic resonance test represents the proportion of the corresponding pore size (Gong et al. 2022). After 7 d and 28 d of standard curing, nuclear magnetic resonance tests were carried out. As shown in Figure 4, with increasing age, the peak value of the T₂ spectrum decreases and the curve of the T₂ relaxation time spectrum tends to shift to the left, which shows that the relaxation time is short, mainly in the form of bound flow, the relaxation time is faster, and the specimen is mainly composed of micro holes. Therefore, the internal pores of GBFS-SCC decrease with increasing curing age.

According to the different influences of pore size on strength, the internal pores in concrete are divided into four categories: harmless pores, less harmful pores, harmful pores, and more harmful pores (Zhongwei and Zhang 1990). Figure 5 shows that with the increase in sand replacement rate, harmless pores and less harmful pores gradually decrease, and harmful pores and more harmful pores gradually increase. At the 7-day curing age, the harmless pores and less harmful pores of ordinary SCC accounted for 94.913 %, GBFS-SCC harmless pores and less harmful pores with a sand replacement rate of 50 % accounted for 92.387 %, and the GBFS-SCC harmless pores and less harmful pores with a sand replacement rate of 100 % accounted for 89.910 %. As the curing age reaches 28 days, the harmless hole and less harmful hole of ordinary SCC increase by 0.246 %, while the sum of 100 % harmless hole and less harmful hole of 50 % increases by 2.458 % and 3.905 % respectively. As the curing age reaches 180 days, the harmless hole and harmful hole of ordinary SCC increase by 0.382 %, while the sum of 100 % harmless hole and less harmful hole of 50 % increases by 2.062 % and 4.296 % respectively. After long-term standard curing. After long-term standard curing, the internal pore structure of SCC shows that the number of harmful pores and multi-harmful pores decreases as a whole, and the harmful pores decrease more obviously with the increase of sand replacement rate. This represents that the internal pore structure of harmful pores and multi-harmful pores is optimized, and the pore diameter is reduced. At the same time, it can be seen that the proportion of harmless pores is significantly increased. The hydraulic action of GBFS improves the distribution of the internal pore structure of concrete, improves the homogeneity of concrete, and thus improves its strength.

Figure 5. Pore size distribution of specimens at different ages.

As shown in Table 4, the granulated blast furnace slag self-compacting concrete and ordinary self-compacting concrete have similar changes. With the increase of age, the peak increases significantly, and the peaks b, c, and d decrease significantly. This indicates that the pores of small pore size increase and the pores of large pore size decrease. It indicates that after standard curing, the large pores migrate towards the small pores, and the internal pores are optimized. At the same time, compared with ordinary self-compacting concrete, the change of granulated blast furnace slag self-compacting concrete is more obvious, while the ordinary self-compacting concrete is relatively more stable, which is consistent with the change rule in the optical method test. It further proves the potential hydraulicity of granulated blast furnace slag, and more hydration products will be produced to optimize the internal pore structure.

Table 4. Nuclear magnetic resonance peak ratio of each group of specimens at different ages.

Group	GBFS ratio	Testing items	7d	28d	180d
1	0%	Peak a (%)	88.3	93.2	95.5
2		Peak b (%)	7.8	6.3	4.1
3		Peak c (%)	3.5	0.5	0.3
4		Peak d (%)	0.3	0	0
5	50%	Peak a (%)	86.2	92.8	95.9
6		Peak b (%)	9.0	6.3	3.4
7		Peak c (%)	3.1	0.8	0.2
8		Peak d (%)	1.6	0	0.4
9	100%	Peak a (%)	86.4	90.3	95.1
10		Peak b (%)	8.5	7.3	3.6
11		Peak c (%)	3.1	2.2	1.2
12		Peak d (%)	2.0	0.1	0.1

It can be seen from Tables 5 and 6 that compared with ordinary self-compacting concrete, the effective porosity of granulated blast furnace slag self-compacting concrete is larger, and the effective porosity will decrease after standard curing similar to ordinary concrete. After 180 days of long-term curing, the effective porosity and free flow saturation of GBFS-SCC are significantly reduced, and the reduction is more obvious with the increase of sand replacement rate. This proves that after long-term standard curing, the internal pores are filled, which means that the internal pores are filled, and a small part of the pores are densely filled and transformed into cementitious pores. The saturation of the bound flow is improved, and the gas phase permeability of the gas-water transition zone decreases round by round (see Table 5). After the influence of long-term curing, ‘water seal air’ is formed (Xinhua et al. 2023), which gradually reduces the pore space, increases the number of closed holes in GBFS-SCC, and reduces the number of connected holes.

Table 5. Effective porosity and permeability of each group of specimens at different ages.

Group	GBFS ratio	Testing items	7d	28d	180d
1	0%	Effective	6.6134	6.4966	5.8907
		porosity (%)
2		Permeability	0.0006	0.0006	0.0002
3	50%	Effective	9.5789	9.1681	7.4743
		porosity (%)
4		Permeability	0.0025	0.0025	0.0004
5	100%	Effective	12.8278	12.3736	8.9610
		porosity (%)
6		Permeability	0.0181	0.0104	0.0013

Table 6. Bound flow saturation and Free flow saturation of specimens at different ages.

Group	GBFS ratio	Testing items	7d	28d	180d
1	0%	Bound flow	94.7558	94.4758	95.1810
		saturation (%)
2		Free flow	5.2442	5.5242	4.8190
		saturation (%)
3	50%	Bound flow	94.8391	94.4560	96.4677
		saturation (%)
4		Free flow	5.1609	5.5440	3.5323
		saturation (%)
5	100%	Bound flow	92.4489	93.7571	95.7577
		saturation (%)
6		Free flow	7.5511	6.2429	4.2423
		saturation (%)

The permeability increases with the increase of the sand replacement rate, which indicates that the permeability resistance is a downward trend. The higher the sand replacement rate, the more significant the permeability reduction. At the same time, the permeability will increase with the increase of sand replacement rate, which again proves the view that the bubbles increase with the increase of sand replacement rate because there are many bubbles and the pore size is large, which makes the permeability increase. With the increase of curing age, the higher the replacement rate of sand, the more obvious the decrease of GBFS-SCC permeability, which represents that after long-term curing, the internal pore structure is optimized, which makes the permeability decrease and the anti-permeability ability increase. Because the granulated blast furnace slag has a certain potential hydraulicity, after long-term standard curing, its potential hydraulicity is stimulated, and certain hydration products are produced. The formation of hydration products makes up for the high porosity and large pore size in the early stage.

4. Relationship between the compressive strength and pore structure based on grey correlation degree

According to the grey system theory established by Deng (Julong 1990) and Liu (Sifeng 2010). Grey correlation analysis theory is to seek the main relationship between the factors in the system to find out the important factors affecting the target value to grasp the main characteristics of things to promote and guide the rapid and effective development of the system (Hong-Qiang and Lin-Hua 2009). The basic idea of grey correlation analysis is to judge whether the relationship between different sequences is close according to the similarity of the geometric shape of the sequence curve. The basic idea is to transform the discrete behavior observations of system factors into piecewise continuous broken lines by linear parenthesis method and then construct a model to measure the degree of correlation according to the geometric characteristics of broken lines. The closer the broken line geometry is, the greater the correlation between the corresponding sequences and vice versa.

4.1. Grey correlation analysis

For any discrete and random complex system, the grey correlation theory is mainly used to determine the degree of correlation between the behavioral characteristics of the system (system characteristic behavior sequence and related factor behavior sequence). The basic idea is to dimensionless process the original observation data of the evaluation index, calculate the correlation coefficient and correlation degree, and sort the identification index according to the size of the correlation degree (Zongping and Wudang 2016). This method can better reveal the characteristics and degree of the correlation between things and has the advantages of less sample demand, no typical distribution law, a small amount of calculation, and good consistency between quantitative results and qualitative analysis (Liu and H-BQ-T 2013). It can be seen that the grey correlation analysis theory can reasonably determine the relationship between the strengthening and pore structure of granulated blast furnace slag self-compacting concrete.

Let $X_0=\left(x_0\left(1\right),x_0\left(2\right),\dots ,x_0\left(\mathit{n}\right)\right)$be the characteristic behavior sequence of the system, and

(1) $\left.\begin{array}{c}{X}_1=\left(x_1\left(1\right),x_1\left(2\right),\dots ,x_1\left(\mathit{n}\right)\right)\\ \dots \\ X_i=\left(x_i\left(1\right),x_i\left(2\right),\dots ,x_i\left(\mathit{n}\right)\right)\\ \dots \\ X_m=\left(x_m\left(1\right),x_m\left(2\right),\dots ,x_m\left(\mathit{n}\right)\right)\end{array}\right\}$(1)

Given a real number $\mathit{\gamma }\left(x_0\left(\mathit{k}\right),x_i\left(\mathit{k}\right)\right)$for a sequence of correlated factors, if

(2) $\mathit{\gamma }\left(X_0\left(\mathit{k}\right),X_i\left(\mathit{k}\right)\right)=\frac{1}{n}{\sum }_{k=1}^n\mathit{\gamma }\left(x_0\left(\mathit{k}\right),x_i\left(\mathit{k}\right)\right)$(2)

Satisfy:

(a) normative

0 < $\mathit{\gamma }\left(X_0\left(\mathit{k}\right),X_i\left(\mathit{k}\right)\right)$ ≤1，$\mathit{\gamma }\left(X_0\left(\mathit{k}\right),X_i\left(\mathit{k}\right)\right)=1\Leftarrow X_0=X_i$

(b) proximity

The smaller$x_0\left(\mathit{k}\right)-x_i\left(\mathit{k}\right)$ is， $\mathrm{thelarger}\mathit{\gamma }\left(x_0\left(\mathit{k}\right),x_i\left(\mathit{k}\right)\right)$

Then, $\mathit{\gamma }\left(X_0,X_i\right)$ is called the grey correlation degree between $X_i$and $X_0$, $\mathit{\gamma }\left(x_0\left(\mathit{k}\right),x_i\left(\mathit{k}\right)\right)$ is the correlation coefficient between $X_i$ and $X_0$ at point k, conditions (a) and (b) are called the grey correlation axioms.

$\mathit{\gamma }\left(X_0,X_i\right)$ ∈(0,1] indicates that any two behavior sequences in the system are not strictly unrelated.

The normalization limits the value of the grey correlation degree to the interval of [0,1], and the proximity shows that Deng’s grey correlation analysis model measures the similarity of the changing trend of system factors based on the distance between the corresponding points of two behavior sequences.

Set the system behavior sequence

(3) $\left.\begin{array}{c}{X}_0=\left(x_0\left(1\right),x_0\left(2\right),\dots ,x_0\left(\mathit{n}\right)\right)\\ X_1=\left(x_1\left(1\right),x_1\left(2\right),\dots ,x_1\left(\mathit{n}\right)\right)\\ \dots \\ X_i=\left(x_i\left(1\right),x_i\left(2\right),\dots ,x_i\left(\mathit{n}\right)\right)\\ \dots \\ X_m=\left(x_m\left(1\right),x_m\left(2\right),\dots ,x_m\left(\mathit{n}\right)\right)\end{array}\right\}$(3)

For $\mathit{\xi }\in \left(0,1\right)$, let

(4) $\mathit{\gamma }\left(x_0\left(\mathit{k}\right),x_i\left(\mathit{k}\right)\right)=\frac{\begin{array}{c}\underset{i}{\mathit{min}}\underset{k}{\mathit{min}}\left|x_0\left(\mathit{k}\right)-x_i\left(\mathit{k}\right)\right|\\ +\mathit{\xi }\underset{i}{\mathit{max}}\underset{k}{\mathit{max}}\left|x_0\left(\mathit{k}\right)-x_i\left(\mathit{k}\right)\right|\end{array}}{\begin{array}{c}\left|x_0\left(\mathit{k}\right)-x_i\left(\mathit{k}\right)\right|\\ +\mathit{\xi }\underset{i}{\mathit{max}}\underset{k}{\mathit{max}}\left|x_0\left(\mathit{k}\right)-x_i\left(\mathit{k}\right)\right|\end{array}}$(4)

(5) $\mathit{\gamma }\left(X_0,X_i\right)=\frac{1}{n}\sum _{\mathit{k}-1}^n\mathit{\gamma }\left(x_0\left(\mathit{k}\right),x_i\left(\mathit{k}\right)\right)$(5)

Then, $\mathit{\gamma }\left(X_0,X_i\right)$ satisfies the grey correlation theory, where $\mathit{\xi }$ is called the resolution coefficient. $\mathit{\gamma }\left(X_0,X_i\right)$ is called the grey correlation degree between $X_0$ and $X_i$.

The grey correlation degree $\mathit{\gamma }\left(X_0,X_i\right)$ is often abbreviated as ${\gamma }_{0\mathit{i}}$, and the k-point correlation coefficient $\mathit{\gamma }\left(x_0\left(\mathit{k}\right),x_i\left(\mathit{k}\right)\right)$ is abbreviated as ${\gamma }_{0\mathit{i}}\left(\mathit{k}\right)$.

According to Formula (3), the calculation steps of the grey correlation degree are as follows.

Step 1: Find the initial value of each sequence (or mean). Let

(6) $X_i^{\prime }=\frac{X_i}{x_i}=\left(x_i^{\prime }\left(1\right),x_i^{\prime }\left(2\right),\dots ,x_i^{\prime }\left(\mathit{n}\right)\right),\mathit{i}=0,1,2,\dots ,\mathit{m}$(6)

Step 2: Find the absolute value sequence of the difference between the components corresponding to the initial value image (or mean term) of $X_0$ and $X_i$. Record

(7) ${\mathrm{\Delta }}_i\left(\mathit{k}\right)=/x_0^{\prime }\left(\mathit{k}\right)-x_i^{\prime }\left(\mathit{k}\right)/,{\mathrm{\Delta }}_i=\left({\mathrm{\Delta }}_i\left(1\right),{\mathrm{\Delta }}_i\left(2\right),\dots {\mathrm{\Delta }}_i\left(\mathit{n}\right)\right),\mathit{i}=0,1,2,\dots ,\mathit{m}$(7)

Step 3: The third step is to find ${\mathrm{\Delta }}_i\left(\mathit{k}\right)=/x_0^{\prime }\left(\mathit{k}\right)-x_i^{\prime }\left(\mathit{k}\right)/,\mathit{k}=1,2,\dots ,\mathit{n};\mathit{i}=1,2,\dots ,\mathit{m}$ the maximum and minimum. Record, respectively

(8) $\mathit{M}=\underset{i}{\mathit{max}}\underset{k}{\mathit{max}}{\mathrm{\Delta }}_i\left(\mathit{k}\right),\mathit{m}=\underset{i}{\mathit{min}}\underset{k}{\mathit{min}}{\mathrm{\Delta }}_i\left(\mathit{k}\right)$(8)

Step 4: Calculate the correlation coefficient.

(9) $\begin{array}{rl}& {\gamma }_{0\mathit{i}}\left(\mathit{k}\right)=\frac{\mathit{m}+\mathit{\xi M}}{{\mathrm{\Delta }}_i\left(\mathit{k}\right)+\mathit{\xi M}},\mathit{\xi }\in \left(0,1\right),\mathit{k}=1,2,\dots ,\mathit{n};\\ & \mathit{i}=1,2,\dots ,\mathit{m}\end{array}$(9)

Step 5: Find the average value of the correlation coefficient, that is the degree of correlation.

(10) ${\gamma }_{0\mathit{i}}=\frac{1}{n}{\sum }_{k=1}^n{\gamma }_{0\mathit{i}}\left(\mathit{k}\right),\mathit{i}=1,2,\dots ,\mathit{m}$(10)

4.2. Compressive strength and pore structure establishment of model

Taking the compressive strength of GBFS-SCC at different ages as the reference Column (Y) and the air content, specific surface, spacing factor, void frequency, and average chord length of pores as the comparison columns (X₁, X₂, X₃, X₄, X₅), the correlation between compressive strength and pore parameters is explored.

Step 1: Set the initial sequence, as shown in Table 7.

Table 7. The original sequence of each group of trials.

GBFS ratio	Index	Age
		7d	14d	28d	180d
0%	Y	34.60	38.20	39.40	45.50
	X1	1.880	1.200	1.410	1.290
	X2	169.160	168.010	164.760	166.160
0%	X3	0.086	0.092	0.088	0.097
	X4	0.794	0.504	0.580	0.398
	X5	0.024	0.024	0.024	0.023
50%	Y	32.30	33.10	41.40	53.00
	X1	4.440	3.890	1.810	1.610
	X2	98.840	112.390	156.140	168.600
	X3	0.091	0.061	0.117	0.067
	X4	1.094	1.517	0.508	0.477
	X5	0.040	0.036	0.026	0.029
100%	Y	27.30	27.80	33.10	48.80
	X1	5.180	3.720	2.100	1.730
	X2	84.550	81.610	132.740	150.430
	X3	0.151	0.100	0.073	0.073
	X4	1.098	1.233	0.428	0.715
	X5	0.047	0.049	0.030	0.031

Step 2: Calculate the initial value of each sequence (or mean), as shown in Table 8.

Table 8. Initial value image of each group test.

GBFS ratio	Index	Age
		7d	14d	28d	180d
0	Y	1.0000	1.1040	1.1387	1.3150
	X1	1.0000	0.6383	0.7500	0.6862
	X2	1.0000	0.9932	0.9740	0.9823
	X3	1.0000	1.0698	1.0233	1.1279
	X4	1.0000	0.6348	0.7305	0.5013
	X5	1.0000	1.0000	1.0000	0.9583
50	Y	1.0000	1.0248	1.2817	1.6409
	X1	1.0000	0.8761	0.4077	0.3626
	X2	1.0000	1.1371	1.5797	1.7058
	X3	1.0000	0.7778	0.5231	0.5690
	X4	1.0000	1.3867	0.4644	0.4360
	X5	1.0000	0.9000	0.6500	0.7250
100	Y	1.0000	1.0183	1.2125	1.7875
	X1	1.0000	0.7181	0.4054	0.3340
	X2	1.0000	0.9652	1.5700	1.7792
	X3	1.0000	0.6623	0.4854	0.4828
	X4	1.0000	1.1230	0.7541	0.6512
	X5	1.0000	1.0426	0.6383	0.6596

Step 3: Find the absolute value sequence of the difference between the initial value image (or mean term) of $X_0$ and $X_i$, as shown in Table 9.

Table 9. Difference sequence of tests in each group.

GBFS ratio	Index	Age
		7d	14d	28d	180d
0%	X1	0	0.4657	0.3887	0.6289
	X2	0	0.1108	0.1647	0.3328
	X3	0	0.0343	0.1155	0.1871
	X4	0	0.4693	0.4082	0.8138
	X5	0	0.1040	0.1387	0.3567
50%	X1	0	0.1486	0.8741	1.2783
	X2	0	0.1123	0.2980	0.0649
	X3	0	0.2470	0.7587	1.0719
	X4	0	0.3619	0.8174	1.2049
	X5	0	0.1248	0.6317	0.9159
100%	X1	0	0.3002	0.8070	1.4536
	X2	0	0.0531	0.3575	0.0084
	X3	0	0.3561	0.7270	1.3048
	X4	0	0.1046	0.4584	1.1364
	X5	0	0.0242	0.5742	1.1280

Step 4: Calculate the correlation coefficient, as shown in Table 10.

Table 10. The correlation coefficient of each group of trials.

GBFS ratio	Index	Age
		7d	14d	28d	180d
0%	X1	1.0000	0.4663	0.5114	0.3928
	X2	1.0000	0.7859	0.7118	0.5501
	X3	1.0000	0.9223	0.7789	0.6850
	X4	1.0000	0.4644	0.4992	0.3333
	X5	1.0000	0.7964	0.7457	0.5329
50%	X1	1.0000	0.8113	0.4224	0.3333
	X2	1.0000	0.8505	0.6820	0.9078
	X3	1.0000	0.7213	0.4572	0.3735
	X4	1.0000	0.6385	0.4388	0.3466
	X5	1.0000	0.8367	0.5029	0.4110
100%	X1	1.0000	0.7077	0.4738	0.3333
	X2	1.0000	0.9319	0.6703	0.9886
	X3	1.0000	0.6712	0.4999	0.3577
	X4	1.0000	0.8741	0.6132	0.3901
	X5	1.0000	0.9677	0.5587	0.3918

Step 5: Find the average value of the correlation coefficient, the correlation degree, as shown in Figure 6.

Figure 6. Grey correlation degree between the compressive strength and pore structure parameters of different sand replacement rates.

It can be seen from Figure 6 that the specific surface area and the average chord length of bubbles are highly and stably correlated with GBFS-SCC. It is indicated that the specific surface area and average chord length are important factors affecting the strength of GBFS-SCC, and the pores are relatively small for the 0 % and 50 % sand replacement rate groups. The grey correlation degree between the pore spacing coefficient and the compressive strength is the highest, but the correlation degree drops sharply for the 100 % sand replacement rate group. Considering that the specimens with a 100 % sand replacement rate are mostly large pores, the bubble size is larger, and the effective porosity is higher than the first two groups, the corresponding variation law appears. At the same time, it shows that the number of pores in the internal pore structure of concrete greatly influences compressive strength.

5. Conclusion

1. The compressive strength, splitting tensile strength, and elastic modulus of granulated blast furnace slag self-compacting concrete at short age (0-14d) are lower than those of ordinary self-compacting concrete. However, after long age (14-180d) standard curing, the strength and strength growth rate of granulated blast furnace slag self-compacting concrete are improved. This is because granulated blast furnace slag has certain potential hydraulicity, and granulated blast furnace slag will continue to produce additional hydration products after standard curing so that the compressive strength and strength growth rate are improved to a certain extent.

2. After standard curing, the pore structure parameters of ordinary SCC show a relatively stable variation. The air content, pore spacing coefficient, and average chord length of GBFS-SCC decrease, the specific surface area increases obviously, the pore radius decreases gradually, and the number of pores decreases slightly. Compared with ordinary SCC, GBFS-SCC has a better hydration effect, which optimizes the internal pore structure of concrete to a certain extent.

3. Through the grey correlation analysis method, the compressive strength is correlated with the gas content, specific surface area, pore spacing coefficient, pore frequency, and average pore chord length. It is concluded that the specific surface area and the average chord length of bubbles are highly correlated with the compressive strength of GBFS-SCC and are relatively stable. These two points are the main factors affecting the mechanical properties of GBFS-SCC.

Acknowledgements

The authors thank the National Natural Science Foundation of China (52068058), Ordos Science and Technology Plan Project (2022YY006) and Inner Mongolia ‘Grassland Talent’ Project (CYYC5039) for their financial support.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [52068058]; Ordos Science and Technology Plan Project [2022YY006]; Inner Mongolia ’grassland talent’ [CYYC5039].