Experimental Study on the Cross-Scale Relationship of Cemented Backﬁll under the Action of an Air-Entraining Agent

: Air-entraining agents have the function of optimizing pores and improving the performance of backﬁll. In this study, we used tailings and cement as the main raw materials and added different amounts of air-entraining agents to make backﬁll samples. By testing the uniaxial compressive strength (UCS) and microstructure, macro-and micro characteristics were studied. Nuclear magnetic resonance technology was used to explore pore characteristics, and fractal theory was used to quantitatively discuss the complexity of pore structure. Finally, a cross-scale relationship model between UCS and pores was established. The main conclusions are as follows: (1) Adding the appropriate amount of air-entraining agents can optimize pore structure and increase the UCS of backﬁll materials, which is beneﬁcial to backﬁll materials. (2) The pores of backﬁll materials have fractal characteristics, the fractal effects of pores with different pore size ranges are different, and the air-entraining agent has a certain inﬂuence on the fractal characteristics of the pores. (3) There are inverse relationships between UCS and different pore size ranges.


Introduction
Backfill materials are filled into goaf, which can not only avoid surface subsidence, but also improve the safety of mining; as the source of backfill materials is solid waste, this can also reduce environmental pollution.Therefore, backfill materials can not only solve the problem of mine safety but also solve the problem of environmental pollution [1][2][3].However, mines also have certain requirements for backfill materials, with the basic requirement being to achieve a certain level of fluidity and strength [4,5].Adding an air-entraining agent (AEA) can improve the flowability of the filling slurry, but it also has a certain impact on the strength [6,7].The AEA mainly changes the pore structure of the backfill material, and it also has a certain impact on the hydration reactions, thereby affecting the strength.At present, there are corresponding testing methods for studying pore characteristics and hydration products, mainly including mercury intrusion technology, nuclear magnetic resonance (NMR) technology, and scanning electron microscopy (SEM) technology [8][9][10].
NMR technology is a non-destructive testing technique that does not require the destruction of the sample to ensure its original morphology.It is mainly used to test pore characteristics and obtain the pore size distribution and content of backfill materials [11,12].Jianhua Hu et al. used NMR technology to test the pore size distribution and content of backfill materials under different curing humidity levels [12].SEM is a technique that uses magnification to observe the internal structure of backfill materials.When magnification is low, the distribution of pores and particles can be observed; in contrast, when magnification is high, hydration products and pore shapes can be observed [13,14].Jiaxu Jin et al. used SEM technology to analyze the hydration products of backfill materials at high magnification and the micro-cracks and pores of backfill materials at low magnification [13].Further analysis of test data can provide more information.For SEM image treatment, the product category is generally judged according to the morphology of the hydration product, so it can only be qualitatively analyzed.For NMR data processing, some scholars have introduced fractal theory and used it to study the complexity of pores, thereby carrying out quantitative analysis [15][16][17].Kang Zhao et al. studied the pore fractal characteristics of backfill materials with different cement-tailing ratios and different fiber types, eventually determining the influence relationship between various factors and pores [16].According to different classification standards, pores can be classified into different categories.Depending on different peaks, they can be divided into large and small pores, and according to the degree of damage, they can be divided into harmful and harmless pores [11,15,18].The fractal results vary depending on the type of pore.
Based on the above research foundation and shortcomings, this study uses tailings and cement as raw materials and adds different amounts of air-entraining agents to create backfill materials.Their macroscopic and microscopic characteristics are tested using a uniaxial compression test, NMR, and SEM, and fractal theory is used to analyze pore characteristics; finally, a cross-scale relationship between strength and pore characteristics is established.Thus, the macroscopic and microscopic characteristics of backfill materials and their relationships are studied under the action of air-entraining agents.

Raw Materials
The tailings used in the experiment were graded tailings, and their particle size distribution is shown in Figure 1 after testing with a laser particle size analyzer.The physical properties of graded tailings were tested according to the GB/T 14684-2011 standard [19], and the results are shown in Table 1.The cement used was a composite Portland cement produced in Changsha.The experimental water used was daily drinking water in Changsha, and the AEA used was a commercially available product, with the main component being K12.

Jin et al. used SEM technology to analyze the hydration products of backfill materials at
high magnification and the micro-cracks and pores of backfill materials at low magnification [13].Further analysis of test data can provide more information.For SEM image treatment, the product category is generally judged according to the morphology of the hydration product, so it can only be qualitatively analyzed.For NMR data processing, some scholars have introduced fractal theory and used it to study the complexity of pores, thereby carrying out quantitative analysis [15][16][17].Kang Zhao et al. studied the pore fractal characteristics of backfill materials with different cement-tailing ratios and different fiber types, eventually determining the influence relationship between various factors and pores [16].According to different classification standards, pores can be classified into different categories.Depending on different peaks, they can be divided into large and small pores, and according to the degree of damage, they can be divided into harmful and harmless pores [11,15,18].The fractal results vary depending on the type of pore.
Based on the above research foundation and shortcomings, this study uses tailings and cement as raw materials and adds different amounts of air-entraining agents to create backfill materials.Their macroscopic and microscopic characteristics are tested using a uniaxial compression test, NMR, and SEM, and fractal theory is used to analyze pore characteristics; finally, a cross-scale relationship between strength and pore characteristics is established.Thus, the macroscopic and microscopic characteristics of backfill materials and their relationships are studied under the action of air-entraining agents.

Raw Materials
The tailings used in the experiment were graded tailings, and their particle size distribution is shown in Figure 1 after testing with a laser particle size analyzer.The physical properties of graded tailings were tested according to the GB/T 14684-2011 standard [19], and the results are shown in Table 1.The cement used was a composite Portland cement produced in Changsha.The experimental water used was daily drinking water in Changsha, and the AEA used was a commercially available product, with the main component being K12.

Experimental Scheme
The slurry concentration used in this experiment was 70%, the cement/sand ratio was 1:8, and the additive was an air-entraining agent.The cement addition amounts were 0%, 0.2%, 0.4%, 0.6%, and 0.8%, respectively, denoted as A0, A1, A2, A3, and A4.There were 6 samples in each group and a total of 30 samples, among which 3 samples were used for strength testing and 3 samples were used for NMR testing.The samples used for SEM were taken from the damaged fragments after strength testing.The sample preparation and testing methods were as follows: The filling slurry was prepared according to the ratio and then injected into the standard mold (50 × 100 mm); after demolding, it was placed in a curing box for 14 days, and finally, various tests were conducted.The strength test was conducted using the WHY-300/10 pressure testing machine produced by Shanghai Hualong Testing Instrument Co., Ltd.The testing loading rate was 0.2 kN/s, and the sample was placed at the center of the loading plate.After the samples were tested, the fragments were selected from the center of the damaged samples, dried, sprayed with gold, and finally observed via SEM.The testing process of NMR was to first saturate the sample with water, wrap it with cling film, and finally use an NMR instrument for testing.

Strength
The strength characteristics of the backfill under the action of the AEA are shown in Figure 2. It can be observed in Figure 2 that the strength increases after adding AEA, but the excessive addition of AEA is harmful to the strength of the backfill, which illustrates that adding an appropriate amount of AEA has the effect of optimizing the pores of the backfill.This is because adding an appropriate amount of AEA in the same volume can introduce a small number of tiny bubbles, forming harmless pores, but when the content of AEA is too high, resulting in a large increase in the number of bubbles, the large number of bubbles gathered together will lead to an increase in the volume of the bubbles, resulting in the formation of harmful pores and reducing the strength.In the application process, the amount of AEA used was not too high so as to demonstrate its positive effect.

Experimental Scheme
The slurry concentration used in this experiment was 70%, the cement/sand ratio was 1:8, and the additive was an air-entraining agent.The cement addition amounts were 0%, 0.2%, 0.4%, 0.6%, and 0.8%, respectively, denoted as A0, A1, A2, A3, and A4.There were 6 samples in each group and a total of 30 samples, among which 3 samples were used for strength testing and 3 samples were used for NMR testing.The samples used for SEM were taken from the damaged fragments after strength testing.The sample preparation and testing methods were as follows: The filling slurry was prepared according to the ratio and then injected into the standard mold (50 × 100 mm); after demolding, it was placed in a curing box for 14 days, and finally, various tests were conducted.The strength test was conducted using the WHY-300/10 pressure testing machine produced by Shanghai Hualong Testing Instrument Co., Ltd.The testing loading rate was 0.2 kN/s, and the sample was placed at the center of the loading plate.After the samples were tested, the fragments were selected from the center of the damaged samples, dried, sprayed with gold, and finally observed via SEM.The testing process of NMR was to first saturate the sample with water, wrap it with cling film, and finally use an NMR instrument for testing.

Strength
The strength characteristics of the backfill under the action of the AEA are shown in Figure 2. It can be observed in Figure 2 that the strength increases after adding AEA, but the excessive addition of AEA is harmful to the strength of the backfill, which illustrates that adding an appropriate amount of AEA has the effect of optimizing the pores of the backfill.This is because adding an appropriate amount of AEA in the same volume can introduce a small number of tiny bubbles, forming harmless pores, but when the content of AEA is too high, resulting in a large increase in the number of bubbles, the large number of bubbles gathered together will lead to an increase in the volume of the bubbles, resulting in the formation of harmful pores and reducing the strength.In the application process, the amount of AEA used was not too high so as to demonstrate its positive effect.

NMR Characteristics
Pore characteristics are important parameters of backfill materials.According to relevant studies [11,15], pores can be divided into four categories according to pore size: harmless pores (<20 nm), less harmful pores (20~100 nm), harmful pores (100~200 nm), and multi-harmful pores (>200 nm).NMR can non-destructively test pore characteristics, and the results are shown in Figure 3.According to relevant research [20,21], there is a certain relationship between pore size and T 2 value.Therefore, the T 2 value can reflect the distribution of pore size, and the relationship between them can be expressed as follows: where r represents the pore size (nm), T 2 represents the transverse relaxation time (ms), ρ 2 represents the transverse surface relaxation intensity (taken as 12 nm/ms), and Fs represents the pore shape factor (considered spherical, taken as 3) [22,23].
certain relationship between pore size and T2 value.Therefore, the T2 value can re distribution of pore size, and the relationship between them can be expressed as f where r represents the pore size (nm), T2 represents the transverse relaxation time represents the transverse surface relaxation intensity (taken as 12 nm/ms), and F sents the pore shape factor (considered spherical, taken as 3) [22,23].It can be observed in Figure 3 that there are three peaks in the T2 spectrum, in that the pores in the backfill can be divided into three categories, which are sm dium, and large pores.The larger the peak area, the greater the pore content, so the pores in the backfill are small pores.Some pores in small pores are harmles others are less harmful.As the content of AEA increases, the porosity shows a creasing and then increasing trend, which indicates that an appropriate amount has the effect of optimizing pores and reducing pore volumes.

Microstructure
SEM technology can magnify the substance thousands of times to observe th structure characteristics of the substance, but the SEM image can only qualitativ lyze the apparent characteristics of the substance.Figure 4 shows a SEM imag backfill material magnified by 5000 times.From the SEM image, it can be seen hydration products are mainly acicular crystals (AFt) and flocculent (C-S-H), pores are filled with hydration products in a staggered manner.The smaller the p the easier it is to fill, and the denser the backfill material.Conversely, the looser the material, the lower its strength.The macroscopic changes in backfill materials can qualitatively explained via microscopic characteristics.It can be observed in Figure 3 that there are three peaks in the T 2 spectrum, indicating that the pores in the backfill can be divided into three categories, which are small, medium, and large pores.The larger the peak area, the greater the pore content, so most of the pores in the backfill are small pores.Some pores in small pores are harmless, while others are less harmful.As the content of AEA increases, the porosity shows a first decreasing and then increasing trend, which indicates that an appropriate amount of AEA has the effect of optimizing pores and reducing pore volumes.

Microstructure
SEM technology can magnify the substance thousands of times to observe the microstructure characteristics of the substance, but the SEM image can only qualitatively analyze the apparent characteristics of the substance.Figure 4 shows a SEM image of the backfill material magnified by 5000 times.From the SEM image, it can be seen that the hydration products are mainly acicular crystals (AFt) and flocculent (C-S-H), and the pores are filled with hydration products in a staggered manner.The smaller the pore size, the easier it is to fill, and the denser the backfill material.Conversely, the looser the backfill material, the lower its strength.The macroscopic changes in backfill materials can also be qualitatively explained via microscopic characteristics.

Fractal Characteristics
Pores are complex structures, and in order to characterize their complexity theory has been introduced in relevant studies [15,17,24,25].Research has sho there is a certain functional relationship between the pore's size and its volume and there is also a certain functional relationship between T2 value and pore size can be transformed.The relationship between pore size and volume is as follows where Sv represents the cumulative pore volume, r represents the pore size, rmax re the max pore size, and D represents the fractal dimension of pores.We substitute E (1) into Equation ( 2) to obtain the relationship between T2 value and volume: The fractal dimension of the pore can be obtained via the linear fitting of lg lg(T2).Taking group A0 as an example that needs solving, the results are shown i 5. From Figure 5, it can be seen that the fitting effect of pores within each range size is good, and the larger the pore size, the greater the fractal dimension.When size range increases for fitting, the fitting effect deteriorates because the pore size is large, which weakens the similarity between larger and smaller pore sizes.
Each group is calculated according to the above calculation methods, and th are shown in Table 2. From the table, it can be seen that the fractal dimensions within some ranges of pore sizes have a certain regularity.For example, the fracta sions of pores within the range of 20~100 nm show a first decreasing and then in trend with respect to the groups, and the fitting effect within this range is good.Th dimensions of some pores also have no regularity; for example, pores within the

Fractal Characteristics
Pores are complex structures, and in order to characterize their complexity, fractal theory has been introduced in relevant studies [15,17,24,25].Research has shown that there is a certain functional relationship between the pore's size and its volume content, and there is also a certain functional relationship between T 2 value and pore size, so they can be transformed.The relationship between pore size and volume is as follows: where S v represents the cumulative pore volume, r represents the pore size, r max represents the max pore size, and D represents the fractal dimension of pores.We substitute Equation (1) into Equation ( 2) to obtain the relationship between T 2 value and volume: where T 2max represents the max transverse relaxation time.The functional relationship of the fractal dimension is obtained by taking the logarithm of both sides of Equation (3): The fractal dimension of the pore can be obtained via the linear fitting of lg(S v ) and lg(T 2 ).Taking group A0 as an example that needs solving, the results are shown in Figure 5.
From Figure 5, it can be seen that the fitting effect of pores within each range of pore size is good, and the larger the pore size, the greater the fractal dimension.When the pore size range increases for fitting, the fitting effect deteriorates because the pore size spacing is large, which weakens the similarity between larger and smaller pore sizes.

The Relationship between Strength and Pores
The pore content in the backfill material has a certain influence on strength, but th influence does not exhibit the following: the higher the pore content, the lower th strength.Only when the harmful pores in the backfill material increase do they have a certain impact on strength.The relationship between pore content and strength was es tablished, and the results are shown in Figure 6.It can be observed in Figure 6 that both porosity and harmful pore content increase, leading to a decrease in strength.The rela tionships between them are as follows: where x represents pore content (%), and y represents strength (MPa).It can be observed in Formula (5) that the strength decreases linearly with the pore content.Therefore, re ducing the porosity and reducing the harmful pore content are effective methods for im proving strength.Adding an appropriate amount of AEA can not only reduce porosity but also optimize the pore structure, which has an improved effect on strength.However adding too much AEA should be avoided; otherwise, it will increase harmful pore con tents and reduce the strength of the backfill.Each group is calculated according to the above calculation methods, and the results are shown in Table 2. From the table, it can be seen that the fractal dimensions of pores within some ranges of pore sizes have a certain regularity.For example, the fractal dimensions of pores within the range of 20~100 nm show a first decreasing and then increasing trend with respect to the groups, and the fitting effect within this range is good.The fractal dimensions of some pores also have no regularity; for example, pores within the range of >200 nm have no regularity.This also indicates that the air-entraining agent mainly acts on small pores.

The Relationship between Strength and Pores
The pore content in the backfill material has a certain influence on strength, but the influence does not exhibit the following: the higher the pore content, the lower the strength.Only when the harmful pores in the backfill material increase do they have a certain impact on strength.The relationship between pore content and strength was established, and the results are shown in Figure 6.It can be observed in Figure 6 that both porosity and harmful pore content increase, leading to a decrease in strength.The relationships between them are as follows: y = −0.272x+ 2.245 y = −1.366x+ 3.827 (5) where x represents pore content (%), and y represents strength (MPa).It can be observed in Formula (5) that the strength decreases linearly with the pore content.Therefore, reducing the porosity and reducing the harmful pore content are effective methods for improving strength.Adding an appropriate amount of AEA can not only reduce porosity but also optimize the pore structure, which has an improved effect on strength.However, adding too much AEA should be avoided; otherwise, it will increase harmful pore contents and reduce the strength of the backfill.

The Relationship between Strength and Fractal Dimension
The fractal dimension reflects the complexity of pores, and pores have a certain impact on strength, so there is a certain functional relationship between fractal dimensions and strength.Figure 7 shows the functional relationship between strength and fractal dimensions.It can be observed in the figure that strength decreases as the fractal dimension increases, which is consistent with the research results of other scholars [15,17] where x represents the fractal dimension, and y represents strength (MPa).It can be observed in the formulas that the relationships differ within the different pore size ranges.
There is an exponential decreasing relationship between them within the range of 20~100 nm and a linear decreasing relationship between them within the range of 20~200 nm and >20 nm.This also indicates that different pore sizes have different effects on strength, and as the pore size range increases, the effect of fractal dimensions on strength tends to become simplified.The comparative analysis indirectly reflects that the AEA has a significant impact on small pores.

The Relationship between Strength and Fractal Dimension
The fractal dimension reflects the complexity of pores, and pores have a certain impact on strength, so there is a certain functional relationship between fractal dimensions and strength.Figure 7 shows the functional relationship between strength and fractal dimensions.It can be observed in the figure that strength decreases as the fractal dimension increases, which is consistent with the research results of other scholars [15,17].Their relationships are as follows: y = −0.007e (66.667×(x−2.711))+ 0.890 (6) y = −7.981x+ 23.488 (7) y = −13.144x+ 39.417 (8) where x represents the fractal dimension, and y represents strength (MPa).It can be observed in the formulas that the relationships differ within the different pore size ranges.
There is an exponential decreasing relationship between them within the range of 20~100 nm and a linear decreasing relationship between them within the range of 20~200 nm and >20 nm.This also indicates that different pore sizes have different effects on strength, and as the pore size range increases, the effect of fractal dimensions on strength tends to become simplified.The comparative analysis indirectly reflects that the AEA has a significant impact on small pores.

Conclusions
The addition of AEA has a certain impact on the performance of backfill materials.This study utilized a uniaxial compression test, NMR, and SEM to study the macroscopic and microscopic characteristics of backfill materials.Fractal theory was used to analyze the complexity of the pore structure, and a cross-scale relationship model was established.The main conclusions are as follows: (1) AEA has the effect of optimizing the pore's structure.Adding an appropriate amount of AEA can reduce pore contents and increase the strength of the backfill material, which is beneficial for the backfill material.

Conclusions
The addition of AEA has a certain impact on the performance of backfill materials.This study utilized a uniaxial compression test, NMR, and SEM to study the macroscopic and microscopic characteristics of backfill materials.Fractal theory was used to analyze the complexity of the pore structure, and a cross-scale relationship model was established.The main conclusions are as follows:

Figure 2 .
Figure 2. The strength characteristics of backfill materials.

Figure 2 .
Figure 2. The strength characteristics of backfill materials.

Figure 3 .
Figure 3.The T 2 spectrum of backfill materials.

Figure 4 .
Figure 4.The SEM image of backfill materials magnified 5000 times.

Figure 4 .
Figure 4.The SEM image of backfill materials magnified 5000 times.

FractalFigure 5 .
Figure 5.The fractal dimension of pores within each range of pore size (group A0).

Figure 5 .
Figure 5.The fractal dimension of pores within each range of pore size (group A0).

Fractal 10 Figure 6 .
Figure 6.The relationship between pores and strength.

Figure 6 .
Figure 6.The relationship between pores and strength.

Figure 7 .
Figure 7.The relationship between fractal dimensions and strength.

Figure 7 .
Figure 7.The relationship between fractal dimensions and strength.

Table 1 .
Physical properties of graded tailings.

Table 2 .
The fractal dimensions of all groups' backfill.
D R

Table 2 .
The fractal dimensions of all groups' backfill.
. Their relationships are as follows: