Experimental Study on Diffusion Process of Sulfate Ion in Cemented Gangue Backfill Material

Cemented gangue backfill material (CGBM) is made of coal gangue, fly ash, cement, and water. ,e backfill body will be corroded by mine water that contains different kinds of corrosive ions. ,e paper mainly aimed to study the diffusion process of sulfate ion (SO2− 4 ) in CGBM. Soluble salt solutions with different concentrations are prepared to simulate various mine water. ,e SO 2− 4 concentration was measured by layered samplingmethod and chemical analyzing method.,e diffusion coefficient was calculated according to the second Fick’s law. Scanning electron microscope (SEM) and X-ray diffraction (XRD) were used to analyze the degradation mechanisms. ,e experimental results showed that the SO2− 4 concentration increases in CGBM when the external sulfate solutions concentration increases. With the increasing of magnesium ion (Mg) concentration and bicarbonate ion (HCO−3 ) concentration in the external corrosion solutions, the diffusion coefficient of SO 2− 4 was increased, and HCO − 3 has more significant effects than Mg. SO2− 4 reacting with CGBM produced ettringite and gypsum. ,e ettringite and gypsum changed the pore structure of hardened CGBM and affected the compressive strength of hardened CGBM. Studying the diffusion of SO2− 4 can contribute to predicting the service life of CGBM.


Introduction
Backfill mining is taken to solve the problem of surface subsidence caused by underground coal mining [1]. It has many benefits, such as reducing the accumulation of solid waste, and the occupation of cultivated land, developing and utilizing underground space [2], and protecting groundwater and environment [3]. Cemented gangue backfill material (CGBM), one of the common backfill materials, is made of coal gangue, fly ash, cement, and water [4]. Comparing to other backfill materials, the main raw materials of CGBM, such as coal gangue and fly ash, are plentiful and cheap, and its performance meets the workability and strength requirements of mining.
Due to the different levels of mine water, which contain different kinds of corrosive ions in the mine, the backfill body will be corroded by mine water during the service period. Zhang et al. found that the composition of mine water under the mine was complex and diverse, and most of them have SO 2− 4 , HCO − 3 , Cl − , Mg 2+ , Na + , and Ga 2+ [5]. e mine water composition of 37 measuring points in 12 mining areas in Shanxi and Inner Mongolia was investigated. Most of the mine water contains corrosive ions such as Mg 2+ , HCO − 3 , and SO 2− 4 , and the ion concentration in the mine water varies greatly. e concentrations of Mg 2+ , HCO − 3 , and SO 2− 4 are 3.88∼225.00 mg/L, 221.000∼3446.045 mg/L, and 73.89∼3314.00 mg/L, respectively. ese ions can be detrimental for hydrated cement in an aqueous environment and for integrity of backfill material consequently [6]. erefore, it is essential to understand the diffusion process of corrosive ion and the deterioration mechanism of the compressive strength of backfill body.
Scholars have conducted a lot of research on the influence of corrosive media on the strength of cement-based materials. Fall et al. found that the strength of the backfill materials under sulfate attack is related to the concentration of sulfate solution, the amount of cement, and the chemical composition [7]. Sun et al. found that the change of backfill body strength under Cl − , SO 2− 4 , and Mg 2+ corrosion is divided into slow growth segment and accelerated reduction segment, and the greater the concentration, the greater the reduction in strength [8]. Zhao et al. found that the strength of concrete increases first and then decreases in Na 2 SO 4 and Na 2 SO 4 and NaHCO 3 complex salt solution and the concrete strength loss rate in the composite solution is greater than the single solution [9]. e effective section size of the backfill body will be reduced under corrosive mine water corrosion, and then the bearing capacity will be reduced, which lead the instability to occur. Exploring the diffusion process of corrosive ions inside materials is the basis for determining the redundancy of the section size as the backfill design. Benoit et al. found that sulfate attack was a diffusion reaction process of concrete when exposed to environment with sulfate [10]. Wang et al. immersed cement mortar in sulfate solutions used layered sampling method combined with chemical analysis, and calculated diffusion coefficients of SO 2− 4 used XRD and SEM to analyze the formation of reaction products. e experimental results showed that in different kinds of sulfate solutions, cement mortars were immersed in (NH4) 2 SO 4 solutions firstly, MgSO 4 solutions took the second place, and Na 2 SO 4 solutions are the last [11]. Zuo and Sun found the SO 2− 4 concentration in the concrete had a gradual increase with the increase of diffusion time; finally, the diffusion and reaction reach a dynamic equilibrium [12]. Idiart et al. accounted for the effect of discrete cracks on the transport of ions, and experimental observation indicated ettringite penetration to make an impact on crack propagation [13]. Tai et al. considered that the distribution of pores had influence for the diffusion of SO 2− 4 in concrete specimens. Ettringite could fill pores, which would change the diffusion path of the ions [14].
Some scholars have establishing models about diffusion coefficient. Nicola et al. used external sulfate to attack concrete structures under partially or fully saturated conditions and established a diffusion model to account for chemical and mechanical damage [15,16]. In order to calculate the chloride diffusion coefficient (D) in concrete, 3 factors (chloride concentration, curing, and environment temperature) were considered and used to predict concrete's life of service [17,18]. Wang et al. used Fick's second law to calculate diffusion coefficient of chloride ion [19][20][21].
Corrosion of backfill materials by soluble salts is a complex physical and chemical process. Revealing the performance degradation mechanism of backfill materials under corrosive action plays an important role in understanding the deterioration of material properties. Fall et al. found that C-S-H gel in tailings cemented filler material absorbs sulfate and causes its structural quality to decline. e expanded mineral ettringite in the pores of the paste material dissolves at high temperature to roughen the pores of the paste [22]. A few investigators found sulfate attack produced ettringite, and this process had two stages. e ettringite was strengthened due to its crystallization in the first stage; the ettringite was weakened because of overexpansion and modeling to verify its rationality and validity in the second stage [23,24]. Some investigators also used high resolution synchrotron X-ray diffraction (SyXRD) to analyze microstructural profile of concrete deterioration which was attacked by sulfate [25][26][27].
At present, a lot of researches have been carried out on the strength and corrosive ion diffusion laws of cementbased composite materials such as concrete under salt corrosion environment, and especially the research results of concrete materials are fruitful. But at the same time, it can be found that due to various materials, different corrosive media and test methods, various factors, and research results varying widely, only qualitative results or laws can be referenced and borrowed, and special research should be carried out for different materials in combination with actual working conditions. e main objective of this paper is to study the diffusion process of SO 2− 4 and investigate the relationship between compressive strength and diffusion and analyze the products using XRD and SEM. e paper also considers the time factor to establish a prediction model which is about CGBM's length of service, which can contribute to predicting the service life of CGBM. e coal gangue samples were obtained from Xinyang Colliery, through breaking, and divided into fine aggregate (<5 mm) and coarse aggregate (5∼15 mm) through breaking; their chemical compositions and physical properties are listed in Table 1. e mixture proportion of CGBM is shown in Table 2.

Specimen's Preparation.
e specimen's preparation was according to Chinese standard GB/T50081-2002. e cube specimens with size of 100 mm × 100 mm × 100 mm were casted. e specimens were cured under the temperature of 23 ± 2°C and RH was not less than 90% in molds for 24 hours. en the specimens were demolded and cured in water under the temperature of 23 ± 1°C for 28 days. Namely, curing time of specimens was 28 days before the immersion test. Specimens were sealed with epoxy resin on the five opposite sides, and one side was exposed to subsequent sulfate attack experiments [11].

Salt Solution Corrosion
Conditions. Specimens were soaked in different salt solutions; salt mediums were sodium sulfate (Na 2 SO 4 ) solutions, magnesium sulfate (MgSO 4 ) solution, and sodium bicarbonate (NaHCO 3 ) solution; and the proportions of these solutions are listed in Table 3. S3, S5, and S10 represent 3%, 5%, and 10% Na 2 SO 4 solutions; M3 and M5 represent 3% and 5% MgSO 4 solutions; and H3 and H5 represent 3% and 5% NaHCO 3 solutions. To keep the concentration constant, the solutions were renewed for three days.

Layered Sampling Method.
Specimens immersed in different salt solutions at the schedule age (30 d/60 d/120 d/ 180 d) were taken out and dried under the temperature of 60°C for about 24 hours to make the surface dry and easily sampled. en every 3 mm layered sampling was taken from the exposed surface to center by precision lathe and the powder samples were collected, respectively. After vacuum drying for 24 hours under the temperature of 105 ± 5°C, the samples were sealed for the next experiment. Cutting depth of each specimen was usually six layers which is 18-20 mm. e test process is shown in Figure 1.

Determination of SO 2− 4 of Specimens.
Chemical analysis method was carried out to determine the sulfate ion (SO 2− 4 ) concentration of powder samples in different depths of specimens. Analysis method was according to Chinese standard GB/T 176-2008 "Methods for Chemical Analysis of Cement". e powder samples were collected by the method of layered sampling, weighed accurately, dissolved by hot hydrochloric acid and filtered. en the filtrate and Barium chloride solution (BaCl 2 ) was mixed to produce precipitate which was filtered again, and weighed after drying under the 900°C [11]. SO 2− 4 concentration was calculated according to the following: where m is the mass of powder sample, g; m 1 is the mass of crucible, g; and m 2 is the total mass of precipitate and crucible, g.

Testing Compressive Strength.
Compressive strength test was conducted with a YAW-200B-type compressiontesting machine. e load was implemented at a relatively slow rate (0.3 KN/s). Each test was repeated at least three times and the average value was calculated as the compressive strength of specimens.

Diffusion Coefficient Calculation of SO
Fick's second law of diffusion was widely used to describe kinds of ions diffusion into concrete [18]. In general, the diffusion of SO 2− 4 in CGBM obeyed Fick's second law. In this paper, the CGBM was assumed as a semi-infinite homogeneous medium and SO 2− 4 was not bound to material when they diffused, so the coefficient of SO 2− 4 was constant [28], and the following one-dimensional equation was used: where C is the SO 2− 4 concentration, cm 2 /s; t is the period of corrosion, s; x is the corrosion depth, cm; and D is the diffusion coefficient, cm 2 /s. When the initial condition was t � 0, x > 0, C � 0; boundary condition was x � 0, t > 0, C�C s . e solutions were evolved into the following equation: where C s is the concentration of SO 2− 4 on the surface, cm 2 /s, and erf is the error function, erf u 0 e − t 2 dt. en diffusion coefficient was evolved into the following equations: where Φ − 1 (m i ) can be traceable standard normal distribution table.
Advances in Civil Engineering e SO 2− 4 concentration on the surface and coefficient of variation was evolved into the following equations: where n is the number of measured points of the specimen and Var is the coefficient of variation.

Influence of Concentration in Diffusion.
Specimens were immersed in 3%, 5%, and 10% Na 2 SO 4 solutions; SO 2− 4 concentration at different depths in the specimen was obtained according to the above method. e results are shown in Figure 2.
It can be seen that the closer to the surface of the specimens, the higher the concentration of SO 2− 4 . e SO 2− 4 concentration is decreased with increasing depth of specimens. And the deceleration rate is faster before 6 mm. e SO 2− 4 concentration in the specimens decreases slowly and linearly after 6 mm. Because SO 2− 4 reacts with CGBM to form gypsum and ettringite, the product will block the surface pores of the materials and change the ion diffusion path, leading to rapid decrease in ion diffusion rate and then slowing down [6,14]. At 180 days, when the concentration of the external solution Na 2 SO 4 solution is 3%, 5%, and 10%, the SO 2− 4 concentration is 0.4634%, 0.5215%, and 0.6712% from the surface of the specimens at 3 mm. SO 2− 4 of high concentration in external solution can accelerate the ion diffusion, which indicates that the reaction product is increased, so that the internal pores are expanded in CGBM [29].

Influence of Different Kinds of Salt Solutions in Diffusion.
Specimens were immersed in Na 2 SO 4 + MgSO 4 , Na 2 SO 4 + NaHCO 3 , and Na 2 SO 4 + MgSO 4 + NaHCO 3 composite solution; SO 2− 4 concentration at different depths in the specimen was obtained according to the above method. e results are shown in Figure 3.
It can be seen that the change trend of SO 2− 4 concentration is basically consistent with single sulfate corrosion; all of them presented the trend that SO 2− 4 concentration is high in outside section and low in inside section. At the same corrosion depth, the concentrations of Mg 2+ and HCO − 3 are higher in the external composite solutions, and concentration of SO 2− 4 is higher in the specimens. As is shown in Figures 3(a)-3(e), at 180 days, the SO 2− 4 concentrations are 0.495%, 0.5373%, 0.5291%, 0.6011%, and 6471% from the surface of the specimens at 3 mm. It can be found that when the concentration of MgSO 4 solution is 3% in external solution, the diffusion of SO 2− 4 is inhibited, and when the concentration is 5%, it will accelerate the diffusion of SO 2− 4 . When the external solution contains HCO − 3 , it also accelerates the diffusion of SO 2− 4 . And the effect is greater than that of Mg 2+ . When both ions are present at the same time, the effect is the greatest.
Effects of different ions on diffusion coefficient of SO 2− 4 in specimens are shown in Figure 5. e changed trend of its diffusion coefficient is divided into two stages: a fast-linear falling section at 30-60 d and a slow falling section after 60 d. e precorrosion period is due to the reaction product blocking the surface pores of the specimens [11,14], so that the diffusion coefficient is rapidly reduced. As the corrosion time increases, the concentration difference between the inside and the outside gradually becomes balanced, so the diffusion rate slowly decreases.
By changing the external solutions from 5% Na 2 SO 4 solutions to 5% Na 2 SO 4 + 3% MgSO 4 composite solutions, as can be seen from Figure 4(a), the SO 2− 4 concentration is decreased by 23%, 35%, 17%, and 8% in 30-, 60-, 120-, and 180-day specimens, respectively. As can be seen from Figure 5(a), the diffusion coefficient of SO 2− 4 is decreased by 19%, 13%, and 4% and increased by 15% in 30-, 60-, 120-, and 180-day specimens, respectively. At the early age, whether MgSO 4 solution is less than 3% can be found, which can inhibit the diffusion of SO 2− 4 in CGBM. at is because a small amount of Mg 2+ enters into CGBM in the early age and reacts with the hydration product to form brucite  [13,25]. ese are all water-insoluble precipitate, which can fill the pores of CGBM to improve its compressive strength and prevent SO 2− 4 to penetrate [29,30]. As time goes on, SO 2− 4 penetrates the pores gradually and reactants increase, which leads to internal crack expansion in CGBM [31]. Lastly, it will accelerate the diffusion of ions, and the compressive strength decreases.

Time Influences for Diffusion Coefficient of SO
where D(t) is the diffusion coefficient of SO 2− 4 at time t, cm 2 / year; D 1 is the diffusion coefficient of sulfate ion at 1 year, cm 2 /year; and m is the empirical coefficient.
Establishing a diffusion model to use diffusion coefficients D 1 , m and surface concentration C s , the diffusion model evolves into the following equation: e comparison between considering time and not considering time to observe the diffusion coefficients of SO 2− 4 in CGBM is shown in Table 4. e model of diffusion under the composite solutions is shown in Table 5.

Using XRD and SEM to Analyze Reaction Products in CGBM
Reaction products of CGBM were immersed in Na 2 SO 4 , Na 2 SO 4 + MgSO 4 , Na 2 SO 4 + NaHCO 3 and Na 2 SO 4 + MgSO 4 + NaHCO 3 composite solution separately, then SEM 5% + 0% + 0% 5% + 5% + 0% 5% + 0% + 5% 5% + 5% + 5% Compressive strength (MPa) 5% + 0% 5% + 3% 5% + 5% Compressive strength (MPa) 5% + 0% 5% + 3% 5% + 5% Compressive strength (MPa) 5% + 0% + 0% 5% + 5% + 0% 5% + 0% + 5% 5% + 5% + 5% (c) Figure 6: Effect of different ions on compressive strength of SO 4 2− in CGBM. (a) Na 2 SO 4 + MgSO 4 , (b) Na 2 SO 4 + NaHCO 3 , and (c) Na 2 SO 4 + 5% MgSO 4 + 5% NaHCO 3 . Advances in Civil Engineering 9 and XRD were used to observe the microstructure of reaction products. Test results are shown in Figure 7. It can be observed from Figure 7(a) that the internal structure is complete, which contains a large amount of calcium hydroxide (Ca(OH) 2 ). Observe Figure 7(b) and find that, when immersed in a solution containing SO 2− 4 , the Ca(OH) 2 concentration is reduced and the calcium carbonate (CaCO 3 ) is increased, and there are ettringite and gypsum formation. Its chemical reaction is as follows: It can be observed from Figure 7(c) that there is much columnar crystal in CGBM after corrosion with SO 2− 4 and Mg 2+ for 180 d [28], which is arranged orderly. At the same time, a large amount of amorphous matter is wrapped around the columnar crystal [29], its main products are Mg(OH) 2 , gypsum, ettringite, and M-S-H. e diffraction peaks intensity of M-H-S and Mg(OH) 2 is low in the low concentration solutions. It is verified that the formation of Mg(OH) 2 can improve sulfate resistance of CGBM in the early composite solutions, so the compressive strength is increased. e number of diffraction peaks of M-H-S and Mg(OH) 2 is increased when CGBM is immersed in composite solutions for 180 d, and the high concentration solutions have higher diffraction peaks intensity. In addition, there are also CaCO 3 and gypsum with large diffraction peaks intensity. It is indicated that as the concentration of Mg 2+ increases and the corrosion time prolongs, SO 2− 4 and Mg 2+ continuously invade CGBM to form CaSO 4 . When the protective film of Mg(OH) 2 is eroded, SO 2− 4 and Mg 2+ continuously infiltrate into the interior of CGBM. e C-H-S is decomposed to form M-H-S without bond properties, making the structure of CGBM worse. Its chemical reaction is as follows: It can be observed from Figure 7(d) that a large amount of flocculent material forms in CGBM after corrosion with SO 2− 4 and HCO − 3 for 180 d. In addition, there is much columnar crystal arranged disorderly, which is dispersed in the middle of flocculent material. e flocculent material is gypsum, ettringite, C-S-H, and thaumasite. After immersing for 30 days, the diffraction peaks intensity of Ca(OH) 2 is large; it is the hydration product of CGBM. CGBM is immersed in SO 2− 4 and HCO − 3 composite solutions, and the reaction product is CaCO 3 and thaumasite. After 180 d, the number of diffraction peaks of ettringite and gypsum increases significantly, and the diffraction peaks intensity of CaCO 3 and thaumasite is also increased significantly. Under long-term effects, Ca(OH) 2 is increasing because Portland cement contains more C 2 S and its hydration product is enough, which provides enough reactants to form thaumasite, and CGBM is gradually corroded. Its internal structure is attacked seriously compared to a single sulfate.
Most studies on the formation of thaumasite show that it is easy to form at temperatures below 15°C, especially at 4°C to 5°C. However, in recent years, many studies have shown that thaumasite can still be formed at temperatures above 15°C. According to Brown's research, thaumasite can also be formed at room temperature [33]. Juanhong Liu et al. found that water-rich filling materials in the sodium carbonate solution at a temperature of about 20°C generated a large amount of carbon thaumasite [34]. Cemented gangue backfill material (CGBM) also formed thaumasite at room temperature.
Its chemical reaction is as follows: It can be observed from Figure 7(e) that there is much columnar crystal neatly arranged in CGBM when CGBM is etched by SO 2− 4 , Mg 2+ , and HCO 3 − for 180 d [35][36][37]. e crystal is sharp and angular, and the surface is straight and smooth. In addition, there are M-S-H, C-S-H, gypsum, ettringite, and thaumasite in CGBM. And the number of diffraction peaks of ettringite and gypsum increases at 180 d. At the same time, the diffraction peaks intensity of M-H-S and thaumasite is increased significantly. When SO 2− 4 , Mg 2+ , and HCO − 3 exist simultaneously, the hydration product of the cement is OH − in CGBM, which combines with the soluble metal cation to produce more harmful corrosion products [38]. It can reduce the alkalinity of cement and decompose hydrated gel gradually. e corrosion products decompose the structure of CGBM, resulting in loss of its strength.

Conclusion
Based on the results presented in this paper, the following conclusions are offered: ( (3) Gypsum and ettringite are formed by the reaction of SO 2− 4 into the CGBM. In the early 60 days, the reaction product will block the pores on the surface of the material, delay the diffusion reaction speed of the ions, and lead to an increase in strength. After 60 days, due to the increase of reaction products, the pores inside the material expand, which accelerates the diffusion reaction of ions, resulting in a decrease in strength.

Data Availability
e data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that they have no conflicts of interest. 12 Advances in Civil Engineering