**Study on Visible Light Catalysis of Graphite Carbon Nitride-Silica Composite Material and Its Surface Treatment of Cement**

#### **Weiguang Zhong, Dan Wang, Congcong Jiang, Xiaolei Lu, Lina Zhang \* and Xin Cheng \***

Shandong Provincial Key Laboratory of Preparation and Measurement of Building Materials, University of Jinan, Jinan 250022, China; 20172120540@mail.ujn.edu.cn (W.Z.); mse\_wangd@ujn.edu.cn (D.W.); mse\_jiangcc@ujn.edu.cn (C.J.); mse\_luxl@ujn.edu.cn (X.L.)

**\*** Correspondence: mes\_zhangln@ujn.edu.cn (L.Z.); mse\_chengx@ujn.edu.cn (X.C.)

Received: 24 May 2020; Accepted: 5 June 2020; Published: 7 June 2020

**Abstract:** Cement-based composite is one of the essential building materials that has been widely used in infrastructure and facilities. During the service of cement-based materials, the performance of cement-based materials will be affected after the cement surface is exposed to pollutants. Not only can the surface of cement treated with a photocatalyst degrade pollutants, but it can also protect the cement-based materials from being destroyed. In this study, graphite carbon nitride-silica composite materials were synthesized by thermal polymerization using nanosilica and urea as raw materials. The effect of nanosilica content and specific surface area were investigated with the optimal condition attained to be 0.15 g and 300 m2/g, respectively. An X-ray diffractometer, thermogravimetric analyzer, scanning electron microscope, a Brunauer–Emmett–Teller (BET) specific surface area analyzer and ultraviolet-visible spectrophotometer were utilized for the characterization of as-prepared graphite carbon nitride-silica composite materials. Subsequently, the surface of cement-based materials was treated with graphite carbon nitride-silica composite materials by the one-sided immersion and brushing methods for the study of photocatalytic performance. By comparing the degradation effect of Rhodamine B, it was found that the painting method is more suitable for the surface treatment of cement. In addition, through the reaction of calcium hydroxide and graphite carbon nitride-silica composite materials, it was found that the combination of graphite carbon nitride-silica composite materials and cement is through C-S-H gel.

**Keywords:** graphite carbon nitride; silica; visible light catalysis; cement

#### **1. Introduction**

In recent years, with the continuous improvement of the level of economic development and industrialization, pollution has become more and more serious, and the environment has been greatly damaged and even threatens human health [1,2]. In order to counter these problems, photocatalytic technology has attracted widespread attention as one of the most promising methods for controlling environmental pollution [3–6]. As the most widely used civil engineering material, cement-based composite is widely used in the construction sector in various countries and regions. It has been suggested to combine photocatalytic technology with building materials [7–10]. Based on building materials, photocatalytic catalysts are easily excited by the energy of sunlight and can degrade surrounding pollutants [11–13]. So far, many efforts have been made to combine TiO2 photocatalysts with cement [14,15] to achieve photocatalytic degradation capabilities [16–18] and self-cleaning capabilities [19–23]. With the deepening of research, the emergence of some problems has also hindered the development of titanium dioxide photocatalytic cement [24,25]. First, TiO2 with a wide band gap

(3.2 eV) cannot use visible light. Most of the energy of sunlight cannot be used by it, which causes energy to be wasted. Second, after the photocatalyst is coated on the cement surface, the binding between the catalyst and the cement is poor, which will cause the catalyst to fall off during use and thus reduce the photocatalytic efficiency. Therefore, a new type of visible light photocatalytic cement with a stable structure should be designed to solve the above problems.

As for the first problem, although there are a large number of methods reported to extend the spectral response range of photocatalysts [26–28], there have been few reports applied to cement materials so far. This may be due to their low activity and poor stability. However, the combination of cement and visible light photocatalysis technology will be an indispensable new requirement for the construction industry. Fortunately, graphite carbon nitride (g-C3N4) has been discovered as a stable visible light photocatalyst since 2008 [29]. Due to its narrow band gap (2.7 eV), g-C3N4 can make full use of visible light for photocatalytic water decomposition [30–32], organic matter degradation [33,34], and outdoor pollution control [35–37]. In contrast to traditional visible light photocatalysts, g-C3N4 is a polymer semiconductor similar to graphene and has good chemical and thermal stability [38,39].

Regarding the second problem, some scholars have prepared a SiO2/g-C3N4 [40] composite material by heating a mixture of SiO2 and melamine. The specific surface area of the obtained composite material increases, and the degree of aggregation of the graphite carbon nitride decreases. This can improve the catalyst's adsorption of pollutants so that the SiO2/g-C3N4 composite has higher activity in the process of the photocatalytic degradation of pollutants. In addition, highly reactive nanosilica can react with cement to produce C-S-H gel. The functional layer and the cement matrix are combined by C-S-H gel [41]. This provides a way to counter the problem of bonding.

In this paper, by controlling the specific surface area and the additional amount of nanosilica, the optimal preparation conditions of graphite carbon nitride-silica composite materials are discussed. The effect of nanosilica on the modification of graphite carbon nitride is explored by XRD, TGA SEM, UV–Vis, and Brunauer–Emmett–Teller (BET) methods. Subsequently, the prepared graphite carbon nitride-silica composite material is used to treat the cement surface, and its photocatalytic ability is studied by degrading the dye under visible light. At the same time, the reaction mechanism of graphite carbon nitride-silica composite material and calcium hydroxide is explored.

#### **2. Materials and Methods**

#### *2.1. Materials*

Rhodamine B (RhB) and urea were purchased from Sinopharm Chemical Reagent Co. Ltd. (Shanghai, China) without any purification. RhB was prepared as a 10 mg/l solution for use. Nanosilica was purchased from Aladdin Reagent Co. Ltd. (Shanghai, China). Its specific surface areas are 200 and 300 m2/g, respectively. P.W 525 white cement was purchased from Shandong Shanshui Cement Co. Ltd. (Jinan, Shandong, China). Its density is 3.2 g/cm3. Distilled water obtained from a water purification system (Direct-Q® 3.5.8, Millipore Co. Ltd., Burlington, MA, USA).

#### *2.2. Preparation of Graphite Carbon Nitride-Silica Composite Materials*

First, 50 mL deionized water was added to a 100 mL crucible. Nanosilica with a specific surface area of 200 m2/g was then added to the crucible. The amount of nanosilica added was controlled to 0.05 g, 0.10 g, 0.15 g, and 0.20 g. The nanosilica solution was sonicated for 30 min by using an ultrasonic cell grinder. The purpose was to uniformly disperse the nanosilica in deionized water, and then 12 g urea was added to the crucible. After stirring for 30 s with a glass rod, the crucible was placed in an ultrasonic cleaning machine for 30 min for ultrasonic treatment, with the purpose to completely dissolve the urea. After the treatment, the crucible was dried in an oven at 70 ◦C. After drying, the crucible was taken out; the crucible mouth was covered with aluminum foil paper, and the crucible lid was covered. The crucible was placed in a muffle furnace and heated to 550 ◦C in an air atmosphere. The temperature increase rate was 5 ◦C/min, and the holding time was 2 h. The obtained graphite carbon nitride-silica composite material (g-C3N4-SiO2) was taken out from the crucible after natural cooling, and it could then be used after grinding. By adjusting the specific surface area of SiO2 to 300 m2/g, several other samples were prepared by the same method. It was named CS005-200, CS011-200, CS015-200, CS020-200, CS005-300, CS010-300 CS015-300, CS020-300 according to the amount and specific surface area of nanosilica.

#### *2.3. Characterization of g-C3N4-SiO2*

The crystal structure of the sample was determined by an X-ray diffractometer (XRD, D8 Advance, Bruker Co. Ltd., Karlsruhe, Ban-Württemberg, Germany). A thermal gravimetric analyzer (TGA/DSC 1, Mettler, Switzerland) was used to determine the sample composition. The field emission scanning electron microscope (QUANTA 250 FEG, FEI Co. Ltd., Hillsboro, OR, USA) was used to observe the micromorphology of the samples. Its acceleration voltage is 20 kV. The band gap was characterized by a UV–Vis DRS spectrum by an ultraviolet-visible spectrophotometer (U-4100 Hitachi Co. Ltd., Tokyo, Japan). The photocatalytic activity of g-C3N4-SiO2 was evaluated by the degradation of RhB (10 mg/l) under visible light in a photo reactor (Beijing Princes Co. Ltd., Beijing, China). The light source is a xenon lamp with a power of 350 W. The absorbance of RhB was measured by an ultraviolet-visible spectrophotometer (U-4100, Hitachi Co. Ltd., Tokyo, Japan). The degradation rate was calculated by dividing the absorbance of the sample by its original absorbance. The specific surface area was measured by the Brunauer–Emmett–Teller (BET) method using a specific surface area analysis tester (MFA-140 Beijing Peaudi Co. Ltd., Beijing, China).

#### *2.4. Surface Treatment of Cement with g-C3N4-SiO2*

Cement paste produced with white cement was made into a cube of 20 mm × 20 mm × 20 mm with a water–cement ratio of 0.35. The cement sample was placed in the curing room for 7 days. The g-C3N4-SiO2 was mixed with water to make a 1 mg/mL suspension. The photocatalyst was attached to the surface of cement by the one-sided immersion method and the brushing method. For the one-sided immersion method, the flank of cement was covered with adhesive tape, and the top surface was surrounded. The suspension was sucked by using a dropper, and it was evenly dropped to the top surface. For the brushing method, the dispersion liquid was dipped by using a brush and then repeatedly brushed onto the cement surface. The treated cement samples were placed in a dark curing cabinet for 7 days. The temperature was 25 ◦C. The humidity was 50%.

#### *2.5. Evaluation of Visible Light Catalytic Performance of Photocatalytic Cement*

The cement sample was taken out of the curing box. The RhB solution (10 mg/L) was sprayed evenly onto the treated surface. The sprayed cement was put in the dark for curing for 24 h. After the RhB solution on the surface of the sample was dried, it was taken out of the curing box. It was placed in the photocatalytic reactor and the test surface was aimed at the light source. Under the condition of visible light irradiation, the picture was taken every 30 min, and its color change was compared.

#### *2.6. Exploration of the Binding Mechanism of Graphite Carbon Nitride-Silicon Dioxide Composite Materials and Cement*

We added 60 ml of a saturated calcium hydroxide solution to the plastic bottle. Then, 0.15 g of CS015-300 was added to the solution. After stirring evenly, the pH value of the solution was measured with a pH test paper. The plastic bottle was sealed, and it was stirred at 1000 rpm on the magnetic stirrer for 7 days. After stirring, the resulting sample was taken out, and the pH of the solution was measured again. After the measurement was completed, the sample was dried in a vacuum drying oven, and then it was ground and tested.

#### **3. Results and Discussion**

#### *3.1. Crystal Structure*

In order to analyze the crystal structure of the synthesized of g-C3N4-SiO2, we characterized it with an X-ray diffractometer. Figure 1a is the XRD pattern of g-C3N4-SiO2 synthesized with SiO2 with a specific surface area of 200 m2/g. There is no obvious diffraction peak in the XRD pattern of SiO2, but there is a steamed bread around 2θ = 23◦. The reason is that gas-phase nano-SiO2 is amorphous [42]. This is also the reason why there are only two diffraction peaks of 2θ = 12.9◦ and 2θ = 27.5◦ in the XRD pattern of the g-C3N4-SiO2. Here, 2θ = 12.9◦ and 2θ = 27.5◦ correspond to the (100) and (002) crystal planes of g-C3N4, respectively [43]. After the addition of SiO2, the intensity of the diffraction peak at 2θ = 12.9◦ is weaker than that of the single g-C3N4. With the increase of the amount of SiO2 added, the intensity of the diffraction peak showed a trend of gradually decreasing. The change law of the diffraction peak intensity at 2θ = 27.5◦ is consistent with the change law of the diffraction peak intensity at 2θ = 12.9◦. This may be related to the decrease of the proportion of g-C3N4 when the amount of SiO2 in the sample is increased. Figure 1b is the XRD pattern of g-C3N4-SiO2 synthesized with SiO2 with a specific surface area of 300 m2/g. An analysis of the changes in the diffraction peaks of the two graphs reveals that they are basically the same as those shown in Figure 1a. Their rule is that there is no change in the position of the diffraction peak, and the intensity of the same diffraction peak decreases as the amount of SiO2 added increases. This can also be attributed to the reduction of graphite carbon nitride content in the sample. From a comprehensive analysis of Figure 1a,b, it can be concluded that the change in the specific surface area of SiO2 will not affect the crystal structure of the g-C3N4-SiO2.

**Figure 1.** The XRD patterns of SiO2-200, g-C3N4, CS005-200, CS010-200, CS015-200, CS020-200 (**a**) and SiO2-300, g-C3N4, CS005-300, CS010-300, CS015-300, CS020-300 (**b**).

#### *3.2. Composition*

g

Figure 2 shows the TG curve of SiO2, g-C3N4 and g-C3N4-SiO2, CS005-200, CS010-200, CS015-200, CS020-200, CS005-300, CS010-300, CS015-300, CS020-300. Below 580 ◦C, the quality of g-C3N4 is basically unchanged. This shows that g-C3N4 has stable chemical properties below 580 ◦C. The reason is that the internal structure is an aromatic ring conjugated system connected by a covalent bond of carbon and nitrogen. On the other hand, g-C3N4 has a layered structure similar to graphite. The van der Waals force between layers is relatively strong [44]. From the beginning of 580 ◦C, as the temperature is increased, g-C3N4 is decomposed. The g-C3N4 is completely decomposed at 750 ◦C. At this time, the mass of g-C3N4 is 0. This corresponds to the position of the inflection point in the curve. SiO2 basically has no mass loss below 900 ◦C. It has excellent thermochemical stability below 900 ◦C [45]. According to the characteristics of g-C3N4 and SiO2 in the TG curve, we can determine the proportion of SiO2 in different samples according to the value of the inflection point in the curve. In CS005-200, the content of SiO2 is 16.48%. In CS010-200, the content of SiO2 is 29.66%. In CS015-200, the content of SiO2 is 31.24%. In CS020-200, the content of SiO2 is 35.62%. In CS005-300, the content of

SiO2 is 12.40%. In CS010-300, the content of SiO2 is 28.41%. In CS015-300, the content of SiO2 is 36.26%. In CS020-300, the content of SiO2 is 41.28%.

**Figure 2.** The TGA analysis of SiO2-200, g-C3N4, CS005-200, CS010-200, CS015-200, CS020-200 (**a**) and SiO2-300, g-C3N4, CS005-300, CS010-300, CS015-300, CS020-300 (**b**).

#### *3.3. Surface Morphology and Structure*

As shown in Figure 3, the structure of CS005-200 is a stacked layer. The spacing between the slices is very obvious; there are holes in the middle of the block. At the same time, there are a few spherical SiO2 particles in the middle of the block, which are attached to both sides of the part of the plate. Obviously, more spherical SiO2 particles were observed in CS010-200 than in CS005-200. The degree of stacking between the sheets becomes weak. The form is developed into a three-dimensional structure. There are more g-C3N4 flakes in the sample than spherical SiO2 particles, which leads to uneven distribution. The spherical SiO2 particles in CS015-200 are evenly embedded in the holes of the g-C3N4 sheet. In CS020-300, spherical SiO2 increased significantly, while g-C3N4 flakes decreased. The distribution of SiO2 and g-C3N4 is also uneven. As the SiO2 content increases, more SiO2 particles are introduced into the pores of the g-C3N4 flake. When the added amount reached 0.15 g, the SiO2 particles evenly entered the pores of the g-C3N4. At this time, the modification effect is the best. The amount of SiO2 continued to increase, and SiO2 was distributed on the surface. Moreover, the porosity in the sample is also reduced, which leads to a poor modification effect. The SEM changes of CS005-300, CS010-300, CS015-300, and CS020-300 are similar to those of the CS200 series. It should be noted that the holes in the CS300 series samples are smaller than those in the CS200 series. The increase in porosity will increase the specific surface area, thereby improving the photocatalytic activity. Therefore, when the specific surface area of SiO2 is 300 m2/g SiO2 and the addition amount is 0.15 g, the obtained g-C3N4-SiO2 has the best performance. The results of the EDS analysis are shown in Figure 4. CS015-300 contains four elements of C, N, Si, and O. Both C and N come from g-C3N4, while Si and O come from SiO2. This indicates that g-C3N4-SiO2 has been successfully synthesized.

**Figure 3.** SEM images of CS005-200, CS010-200, CS015-200, CS020-200, CS005-300, CS010-300, CS015-300, CS020-300.

**Figure 4.** The EDS analysis of CS015-300.

#### *3.4. Specific Surface Area and Porosity*

Figure 5 is the nitrogen adsorption and desorption isotherms of g-C3N4, CS015-200, and CS015-300. The specific surface area, the total pore volume and the average pore radius measured by the N2 adsorption-desorption experimental data and the BET model are listed in Table 1. The adsorption-desorption curves of g-C3N4 and CS015-300 indicate a type Π isotherm, which is the characteristic of microporous materials. It can be seen from Table 1 that after the addition of nano-SiO2, the specific surface area of the sample became larger, the total pore volume became smaller, and the average pore radius became smaller. The specific surface area of CS015-200 was increased by 61.68%, the total pore volume was expanded by 56.13%, and the average pore radius was reduced by 3.41%. The specific surface area of CS015-300 was increased by 126.35%, the total pore volume was expanded by 15.70%, and the average pore radius was reduced by 52.99%. The reason is that more pores were introduced with the addition of nano-SiO2, which caused the pore volume to be reduced and the pore size to become smaller. This caused the specific surface area to be increased. Although it was concluded from the previous analysis that the addition of SiO2 has little effect on the band structure of the sample, the specific surface area has greatly improved. As the specific surface area is increased, more active sites are provided [46]. This is conducive to the improvement of catalytic capacity.

**Figure 5.** N2 adsorption-desorption isotherms of g-C3N4, CS015-200, and CS015-300.


**Table 1.** The specific surface area, total pore volume, and average hole radius of g-C3N4, CS015-200 and CS015-300.

#### *3.5. Band Gap and Absorption Edge*

As can be seen from Figure 6a, the UV–Vis spectral curve of CS005-200 and of CS010-200 are similar to that of g-C3N4. The absorption edge does not move. The absorption edge of CS015-200 has a slight red shift. The UV–Vis spectrum of CS020-200 is different from that of the previous materials; its absorption edge has a slight blue shift. Their change rule is that the UV–Vis spectrum of the sample does not change when the amount of SiO2 is low. As the amount of SiO2 is increased, the absorption edge of the sample is red-shifted, but the degree of shift is not large. As the amount of SiO2 is continuously increased, the absorption edge of the sample has a blue shift. This shows that the low additional amount of SiO2 will not affect the visible light absorption range. The addition of SiO2 will expand the visible light absorption range of the sample under the appropriate addition amount. However, when the blending amount is too large, the negative effect will appear. From Figure 6b, we can find that the width of the band gap of CS005-200 and CS010-200 is the same as that of g-C3N4, both of which are 2.7 eV. The width of the forbidden band of CS015-200 was reduced to 2.65 eV, and the absorption edge was increased to 471 nm. The band gap of CS020-200 was expanded to 2.8 eV, and the absorption edge was reduced to 468 nm. The variation law of the band gap of each sample is the same as that of its corresponding ultraviolet-visible diffuse reflection spectrum.

**Figure 6.** UV–Vis spectra (**a**) and band gap (**b**) of g-C3N4, CS005-200, CS010-200, CS015-200, CS020-200.

The UV–Vis spectrum of the g-C3N4-SiO2 prepared with SiO2 with a specific surface area of 300 m2/g is shown in Figure 7a. The absorption edge of the sample changed. The absorption edge of CS005-300 and CS020-300 has a slight blue shift compared to g-C3N4. The movement of CS005-300 was slightly larger than that of CS020-300. The curve of CS010-300 coincides with the curve of g-C3N4, and the absorption edge did not change. A slight red shift occurred in the absorption edge of CS015-300. The difference with the graphite carbon nitride-silica (SBET = 200 m2/g) composite material is that the absorption edge of the sample had a blue shift at lower dosing levels and too much doping. The corresponding absorption of visible light was also reduced. From Figure 7b, it can be found that the band gap of CS005-300 expanded to 2.8 eV, and the absorption edge was reduced to 442 nm. The band gaps of CS010-300 and CS015-300 were reduced to 2.68 eV, and the absorption edge expanded to 462 nm. The band gap of CS020-300 expanded to 2.75 eV, and the absorption edge was reduced to 451 nm. The band gap of g-C3N4 is still 2.7 eV. The absorption edge is 460 nm. Because the added SiO2 is amorphous, the changes in the band gap and the absorption edge of g-C3N4-SiO2 were very

slight. The change in band gap is due to the quantum size effect of the smaller size g-C3N4 generated on the surface of nano-SiO2 [47].

**Figure 7.** UV–Vis spectra (**a**) and band gap (**b**) of g-C3N4, CS005-300, CS010-300, CS015-300, CS020-300.

#### *3.6. Photocatalytic Evaluation*

As shown in Figure 8a, RhB is not degraded without adding a catalyst. After 1 h of dark treatment, g-C3N4 has the same dye adsorption rate as the other four samples, which is about 27%. With the extension of visible light exposure time, the absorbance of the dye is gradually reduced, and the dye is continuously degraded. The minimum degradation time of CS015-200 is 55 min. Secondly, the degradation time of CS005-200 is 60 min. Thirdly, the degradation time of CS010-200 is 70 min. Fourthly, the degradation time of g-C3N4 is 75 min. The maximum degradation time of CS020-200 is 90 min. The catalytic performance from strong to weak is ranked as CS015-200, CS005-200, CS010-200, g-C3N4, CS020-200. The reason for the reduced efficiency of CS020-200 may be related to the reduced visible light absorption range caused by the reduction of the absorption edge. Among all the samples, the improvement of the CS015-200 is the most obvious, and the performance has improved by 26.67% compared with the g-C3N4.

**Figure 8.** Photocatalytic activities (**a**) and their kinetic constants (**b**) of g-C3N4, CS005-200, CS010-200, CS015-200, CS020-200.

From Figure 8b, it can be concluded that the largest k value of CS015-200 is 0.067. Secondly, the k value of CS010-200 is 0.052. Thirdly, the k value of CS005-200 is 0.048. Fourthly, the k value of g-C3N4 is 0.033. The minimum k value of CS020-200 is 0.025. After silica is added, the k value of each sample is changed to varying degrees. CS015-200 is 103.03% higher than g-C3N4. CS010-200 is 57.57% higher than g-C3N4. CS005-200 is 45.45% higher than g-C3N4, and CS020-200 is 24.24% lower than g-C3N4. The performance of CS015-200 is the best among all the samples in the picture.

As shown in Figure 9a, after 1 h of dark treatment, different samples have different adsorption rates for dyes. The adsorption rate of composite materials is higher than that of the single g-C3N4, and the adsorption rate of g-C3N4 is about 27%. The adsorption rate of CS010-300 and CS020-300 is about 33%. The adsorption rate of CS005-300 and CS015-300 is about 39%. The minimum degradation time of CS015-300 is 50 min. Secondly, the degradation time of CS005-300 and CS010-300 is 60 min. Thirdly, the degradation time of CS0020-300 is 70 min. The maximum degradation time of g-C3N4 is 75 min. The catalytic performance from strong to weak is ranked as CS015-300, CS005-300 (CS010-300), CS0020-300, g-C3N4. Compared with g-C3N4, the visible light catalytic ability of each sample has improved. This shows that the visible light catalytic ability of the sample is increased with the addition of SiO2 with a specific surface area of 300 m2/g.

**Figure 9.** Photocatalytic activities (**a**) and their kinetic constants (**b**) of g-C3N4, CS005-300, CS010-300, CS015-300, CS020-300.

From Figure 9b, the maximum k value of CS015-300 is 0.072. Secondly, the k value of CS010-300 is 0.054. Thirdly, the k value of CS010-300 is 0.049. Fourthly, the k value of CS020-300 is 0.045. The minimum k value of g-C3N4 is 0.033. The difference from Figure 9 is that after adding nanosilica with a specific surface area of 300 m2/g, the k value of all samples has improved. CS015-300 is 118.18% higher than g-C3N4. CS010-200 is 63.63% higher than g-C3N4. CS005-200 is 48.48% higher than g-C3N4. CS020-200 is 36.36% higher than g-C3N4. The performance of CS015-300 is the best among all the samples in the picture.

By comparing the degradation rate constants of the two types of samples, we find that the g-C3N4-SiO2 prepared using SiO2 with a specific surface area of 300 m2/g has the best visible light catalytic performance. When the same amount is added, the degradation rate constant is always higher than that of g-C3N4-SiO2 prepared with SiO2 with a specific surface area of 200 m2/g. In addition, the degradation rate constant of heterogeneous graphite carbon nitride-silica prepared with SiO2 with a specific surface area of 300 m2/g is higher than that of g-C3N4. The phenomenon of reduced catalytic performance did not occur.

#### *3.7. Surface Treatment Evaluation*

As can be seen from Figure 10, the catalyst distribution on the surface of the cement material treated by the one-sided immersion method is uneven, and the thickness of the coating is different. The color in the middle of the sample is obviously lighter than the color at the edge of the sample. This shows that there are more catalysts on the cement edge than in the middle. Cracking and shedding of the coating appear on the edge of the cement block. The reason is that the solution was dripping onto the cement surface, and the liquid level is affected by the surface tension; it appears to be high in the surroundings and low in the middle [48]. As the water evaporated, the water in the middle disappeared firstly and then gradually spread to the surroundings. This caused the surrounding coating to be too thick, which caused cracking and shedding. The color distribution of the surface of the cement material treated was relatively uniform by the brushing method, which indicates that the distribution of the catalyst was relatively uniform. There is no cracking and shedding of the catalyst on the cement surface, which indicates that the catalyst did not appear on the cement surface. The reason is that

the brush dipped in less solution during the application process, and when applied to the cement surface, the surface tension is less affected. At the same time, the catalyst is further uniformly dispersed in the process of the repeated three times of brushing, thereby avoiding cracking and shedding caused by the aggregation of the catalyst.

**Figure 10.** Surface treatment of cement by the one-sided immersion method and brushing method.

#### *3.8. Performance Evaluation of Photocatalytic Cement*

Figure 11 is the color change of RhB after the photocatalytic cement prepared by the one-sided immersion method was exposed to visible light. As shown in Figure 11, comparing the photos of the cement under visible light irradiation, it was found that with the increase of light time, the color of the surface without surface treatment is basically unchanged, but the color of all surface-treated samples was lightened to varying degrees. This shows that the cement had a self-cleaning function after surface treatment. The reason is that the catalyst on the cement surface captures the pollutants, and the dye was degraded under the irradiation of visible light. However, the self-cleaning efficiency of cement materials treated with different catalysts varies. After 60 min of irradiation, the degree of discoloration is ranked as CS015-300, CS010-300, CS005-300, CS020-300, g-C3N4 in order from large to small. This is consistent with the rule of g-C3N4-SiO2 degrading RhB in solution. This shows that the performance of the catalyst did not change after being applied to the cement surface.

**Figure 11.** Photocatalytic performance of surface treatment cement with the one-sided immersion method.

Figure 12 is the color change of RhB after the photocatalytic cement prepared by the brushing method was exposed to visible light. After 60 min of irradiation, the degree of discoloration was ranked as CS015-300, CS010-300, CS005-300, CS020-300, g-C3N4 in order from large to small. The discoloration of CS015-300 is most obvious. However, since the catalyst dispersion on the cement surface treated by the brushing method was more uniform, the color change was more obvious than that of the one-sided immersion method. The performance of the photocatalytic cement obtained by the brushing method was more excellent.

**Figure 12.** Photocatalytic performance of surface treatment cement by the brushing method.

#### *3.9. Exploration of Binding Mechanism*

In order to explore the binding mechanism of g-C3N4-SiO2 and cement, we used saturated calcium hydroxide solution to simulate the alkaline environment of cement, and then an appropriate amount of CS015-300 was added. Under sealed conditions, the two substances are reacted. The resulting product was analyzed.

As can be seen from Figure 13, after adding CS015-300 to the saturated calcium hydroxide solution, the pH value of the test mixed solution is 13. After 7 days of reaction, the pH of the solution was reduced to 9. This indicates that the content of OH- in the solution was reduced, and a part of calcium hydroxide was reacted because SiO2 can react with calcium hydroxide by pozzolanic reaction [49]. According to existing research, it has been found that the product is C-S-H gel after the reaction [41,50]. We think that the nanosilica in CS015-300 reacted with the calcium hydroxide in the solution to form C-S-H, and the calcium hydroxide was consumed.

**Figure 13.** The pH of solution before and after reaction.

As can be seen from Figure 14, comparing the SEM pictures of the samples before and after the reaction, it was found that the microscopic morphology of the sample changed significantly after the reaction with calcium hydroxide. The microstructure of CS015-300 changed from the previous nanosilica embedded in the pores of g-C3N4 to the accumulation of irregular lumps. After further zooming, the rod was found. This point was analyzed by EDS, and the results are shown in Figure 15. It can be observed from Figure 15 that the main chemical composition of the rod is C, N, Si, O, and Ca. By analyzing the distribution of the four elements C, N, Si, and Ca in the pink area, it was found

that the distribution of the four elements is very uniform and no aggregation occurred. This further illustrates that CS015-300 reacted with calcium hydroxide rather than simply piled together. This can further explain that CS015-300 reacted with calcium hydroxide to form a C-S-H gel [50]. Through the simulation experiments of CS015-300 and calcium hydroxide, we can draw the conclusion that the calcium hydroxide produced by cement hydration reacts with the nanosilica in the composite material to form C-S-H gel. The g-C3N4-SiO2 and cement material are combined by C-S-H gel.

**Figure 15.** The EDS of CS015-300 after reaction.

#### **4. Conclusions**

In summary, the g-C3N4-SiO2 was synthesized by mixing and heating nanosilica and urea. By controlling the amount and the specific surface area of nanosilica, the best synthesis conditions were selected. In this way, the band gap of the graphite carbon nitride was changed, and the specific surface area was increased. The visible light catalytic performance of the material has improved. After the graphite carbon nitride-silicon dioxide composite material was treated by brushing and by one-sided immersion, the cement obtained the photocatalytic function. By comparing the photocatalytic efficiency, the brushing method was more suitable for the surface treatment of cement than the one-sided immersion method. The combination mechanism of calcium hydroxide and g-C3N4-SiO2 was explored. It was found that g-C3N4-SiO2 and cement material were combined by C-S-H gel.

**Author Contributions:** Conceptualization: W.Z. and X.L.; methodology: all authors; validation: W.Z., D.W., and L.Z.; formal analysis: all authors; investigation: W.Z., L.Z., and C.J.; resources: all authors; writing—original draft preparation: W.Z.; writing—review and editing: all authors; visualization: all authors; supervision: all authors; project administration: L.Z.; funding acquisition: L.Z. and X.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Program for Taishan Scholars Program, the Case-by-Case Project for Top Outstanding Talents of Jinan, the Distinguished Taishan Scholars in Climbing Plan, the Science and Technology Innovation Support Plan for Young Researchers in Institutes of Higher Education in Shandong (2019KJA017), the National Natural Science Foundation of China (Grant No. 51872121, 51632003, and 51902129), the National Key Research and Development Program of China (Grant No. 2016YFB0303505) and the 111 Project of International Corporation on Advanced Cement-based Materials (No.D17001).

**Acknowledgments:** The authors wish to gratefully thank Shandong Provincial Key Laboratory of Preparation and Measurement of Building Materials, University of Jinan for their support of this work.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Inverse Estimation Method of Material Randomness Using Observation**

#### **Dae-Young Kim 1, Pawel Sikora 2,3, Krystyna Araszkiewicz <sup>3</sup> and Sang-Yeop Chung 1,\***


Received: 16 April 2020; Accepted: 15 June 2020; Published: 16 June 2020

**Abstract:** This study proposes a method for inversely estimating the spatial distribution characteristic of a material's elastic modulus using the measured value of the observation data and the distance between the measurement points. The structural factors in the structural system possess temporal and spatial randomness. One of the representative structural factors, the material's elastic modulus, possesses temporal and spatial randomness in the stiffness of the plate structure. The structural factors with randomness are typically modeled as having a certain probability distribution (probability density function) and a probability characteristic (mean and standard deviation). However, this method does not consider spatial randomness. Even if considered, the existing method presents limitations because it does not know the randomness of the actual material. To overcome the limitations, we propose a method to numerically define the spatial randomness of the material's elastic modulus and confirm factors such as response variability and response variance.

**Keywords:** Bayesian updating; spatial randomness; uncertainty; correlation distance; stochastic field

#### **1. Introduction**

Research toward the development and incorporation of new building materials in modern engineering structures in order to meet sustainability goals has gathered substantial attention in recent years. Various new cement-based composites have been investigated including lightweight materials (foamed concrete and lightweight aggregates concretes) [1], pervious concretes [2], nano-modified, and self-cleaning materials [3,4]. However, due to the relatively higher production costs of modern building materials than in the case of conventional ones, it is still imperative to find a solution to support the simulating techniques and their accuracy toward decreasing the number of site trials, thus reducing the costs and environmental impact of material.

In general, structural material analysis can be classified into a deterministic or a probabilistic method [5]. The deterministic method uses finite element analysis (FEA) considering the material properties, geometry, and forces. In other words, the various internal and external factors that can exist in a structure are represented by constants. However, these factors are all assumptions, and in the case of actual structures, it would be more reasonable to assume that the factors have different values depending on the position vector in the structural domain.

The probabilistic method assumes that the structure possesses arbitrary material properties, loads, and geometries, and generates a random sample with some statistical characteristics. A deterministic FEA is repeatedly performed on the generated samples to obtain the characteristic behavior of

the structure [6,7]. Structural uncertainty, in terms of numerical considerations, can be classified as intrinsic, measurement, and statistical uncertainty, or uncertainty in the mathematical model [8,9]. In each case, the measurement uncertainty is that involved in establishing uncertainty factors through experiments. Experimental and statistical uncertainty is that obtained due to the lack of data due to limited time and space information. Uncertainty in the mathematical model implies uncertainty due to the difference between the actual model of the uncertainty coefficient and the simulated mathematical model. Intrinsic uncertainty is an uncertainty in the structural material, geometric factors expressing the shape of structures, and applied loads [10,11]. These uncertainties are generally considered, both in the actual behavior of the structure and in the reliability analysis. Among them, the stochastic finite element method (SFEM) is mainly focused on the intrinsic uncertainty with the greatest influence. SFEM is a combination of a stochastic method and FEM. The purpose of SFEM is to estimate the uncertain response variation of the structure with respect to the spatial and temporal randomness of the factors in the structural system [12,13]. SFEM is divided into statistical and non-statistical methods in terms of analytical methodology.

There are many analytical methods such as the K-L Expansion [14], Polynomial Chaos Expansion [15], perturbation methods [16], and the weighted integration method that is based on non-statistical methods [17–22]. However, the non-statistical method is mainly based on the first-order expansion or the second-order series expansion for the main variables and is applicable only when the coefficient of variation (COV) of the stochastic fields is low [23]. In fact, when COV (=σ/μ) of the stochastic field is large, it is accurate and shows a significant difference from the Monte-Carlo simulation (MCS).

The MCS, which is a representative statistical method, has the advantage of providing a solution to most stochastic problems. However, to obtain a MCS with high efficiency and accuracy, a proper algorithm and considerable time is also required for analysis. This study focuses on estimating the spatial randomness of materials through observation (partial elastic modulus) and overcoming the limitations of the existing statistical methods. For this purpose, a method to numerically define the spatial randomness of the material's elastic modulus was proposed, and the obtained results were demonstrated using factors such as response variability and response variance.

#### **2. Disadvantage of Current Statistical Methods**

#### *2.1. Statistical Methods without Considering Spatial Randomness*

In the current statistical method, the target random variable, which is the elastic modulus, is assumed to be a normal distribution (N(μ, σ)). In this case, a random process satisfying a specific normal distribution is generated as a pseudo time process (here, the random variable satisfies *rt* = *r*(*t*), *t* ∈ (0, *T*) and an analysis is performed for generated N constant to satisfy the normal distribution (N(μ, σ)).

However, as shown in Figure 1, the factor of the actual material's elastic modulus does not have the same value according to the position vector. Therefore, the current method of using a constant field is different from the actual material, and a random sample of the statistical method should satisfy both functions simultaneously.

**Figure 1.** Different elastic modulus in different positions due to material heterogeneity.

#### *2.2. Statistical Methods Considering Spatial Randomness*

The spatial randomness distribution of the uncertainty factor is represented by *f*(*x*)in the stochastic field function, stochastic field *f*(*xi*), and at any point *xi* ∈ Ω*str*, belonging to the structural domain Ω*str*, which must satisfy the probability density function (PDF). At the same time, it must also satisfy the spectral density function (SDF) (or autocorrelation function) representing the aspect existing in the structural domain [24]. Even in the case of a stochastic field with the same mean and standard deviation, the actual shape of the stochastic field can exist in various forms (μ*<sup>k</sup> <sup>i</sup>* <sup>=</sup> <sup>μ</sup>*<sup>k</sup> j* ). This variance is due to the characteristics of the stochastic field based on the ensemble concept, which is a statistical characteristic in a direction orthogonal to the stochastic plane.

In general, the distribution characteristic of the stochastic field is determined by the correlation distance. The stochastic field can have two extreme conditions: *f*(*x*; *d* = 0) and *f*(*x*; *d* = ∞). In the former case, the stochastic field appears in the form of a white noise field and contains all the theoretically possible spectra. In the latter, the stochastic field is a constant field with one value, which is called the random variable state [25]. For example, d is infinite when spatial randomness is not taken into consideration.

The distribution of the stochastic field using the correlation distance can simulate (imitate) the spatial randomness of the material. However, it is difficult to determine the spatial randomness of the actual material with this approach. Various methods are available to compute the elastic modulus of concrete, but the spatial randomness is difficult to identify. To investigate the spatial randomness of a target objective, the stochastic field with a correlation distance (d) ranging from zero to infinity needs to be generated. In addition, this spatial characteristic can be examined by the COV trend obtained from the Monte-Carlo simulation, as shown in Figure 2 [26,27].

**Figure 2.** The schematic of the response variability according to the correlation distance (d).

However, since the actual correlation distance (d) of the target elastic modulus cannot be known, the exact result is unknown (which is not a meaningful result). Therefore, we aimed to overcome the problem (disadvantages) of the existing statistical methods.

#### *2.3. Objective and Methods*

In this study, we proposed a method of inversely estimating the correlation distance using the observed values and the distance between the observation points. In particular, the population can be predicted using some samples. Then, the obtained real correlation distance d1 (from the population) is compared with the d2 (predicted from samples). Once the correlation distance of the actual material is found using the proposed method, the exact behavior of structures by the actual material can be described instead of using the tendency of COV. The process is described in the following three steps. First, generate the stochastic field using the spectral representation method [28,29]. The purpose of creating a sample by applying the algorithm is because the exact d value corresponding to the samples through the algorithm is known. If the proposed inverse estimation method correctly traces d, it starts from the assumption that some data of the actual structure can be used to obtain an actual d corresponding to the structure. Second, we assumed values at some locations to be used as sample data, as shown in Figure 3, and compared the estimated correlation distance (using only some observation) and the correlation distance of the stochastic field. Third, the probability characteristics are obtained using the Bayesian method. This is a method of obtaining new probability characteristics (posterior) by updating the prior probability characteristics based on new test data [30].

**Figure 3.** Observation in the stochastic field with spatial randomness.

#### **3. Investigation Procedures and Their Examples**

#### *3.1. Consideration Method of Spatial Randomness of Material's Elastic Modulus*

For every real-valued 2D-1V homogeneous stochastic field *f*0(*x*1, *x*2) with the mean value equal to zero and a bi-quadrant SDF as *Gf*<sup>0</sup> *<sup>f</sup>*<sup>0</sup> (κ1, κ2), two mutually orthogonal real processes *u*(κ1, κ2) and *v*(κ1, κ2) with orthogonal increments *du*(κ1, κ2) and *dv*(κ1, κ2) can be assigned so that:

$$f\_0(\mathbf{x}\_1, \mathbf{x}\_2) = \int\_{-\infty}^{\infty} [\cos(\mathbf{x}\_1 \mathbf{x}\_1 + \mathbf{x}\_2 \mathbf{x}\_2) d\mathbf{u}(\mathbf{x}\_1, \mathbf{x}\_2) + \sin(\mathbf{x}\_1 \mathbf{x}\_1 + \mathbf{x}\_2 \mathbf{x}\_2) d\mathbf{v}(\mathbf{x}\_1, \mathbf{x}\_2)] \tag{1}$$

$$E(\mathbf{x}, y) = \overline{E}(\mathbf{1} + f\_i(\mathbf{x}, y)) \tag{2}$$

$$R(\xi\_1, \xi\_2) = \sigma\_0^2 \exp\left\{-\left(\frac{\Delta \xi\_1}{d\_1}\right) - \left(\frac{\Delta \xi\_2}{d\_2}\right)\right\} \tag{3}$$

In the generation of homogeneous random fields, the spectral representation method [31–33] can be employed, which takes advantage of fast Fourier transform. In the random fields of elastic modulus, the stiffness of the elastic modulus is assumed to be homogeneous Gaussian and represented by Equation (2), where *E* is the mean value of the elastic modulus and *fi*(*x*, *y*) is a homogeneous random field. The auto-correlation functions for the respective random field *fi*(*x*, *y*) are assumed by Equation (3) [34]. In the spectral representation scheme, the numerical generation of a homogeneous

uni-variate i-th random sample *fi*(*x*, *y*) with a zero mean in two dimensions can be generated via the summation of the cosine functions, as shown in Equation (4) [35,36].

$$f\_{l}(\mathbf{x}, y) = \sqrt{2} \sum\_{n1=0}^{N\_{1}-1} \sum\_{n1=0}^{N\_{2}-1} \left[ A\_{n1n2} \cos \left( \kappa\_{1n\_{1}} \mathbf{x} + \kappa\_{2n\_{2}} y + \Phi\_{n\_{1}n\_{2}}^{(1)(i)} \right) \right. \tag{4}$$

$$+ \overleftarrow{A}\_{n1n2} \cos \left( \kappa\_{1n\_{1}} \mathbf{x} - \kappa\_{2n\_{2}} y + \Phi\_{n\_{1}n\_{2}}^{(2)(i)} \right) \Biggr] \tag{4}$$

$$A\_{n1n2} = \sqrt{2S\_{f0f}(\kappa\_{1n\_1}, \kappa\_{2n\_2})\Delta\kappa\_1\Delta\kappa\_2}, \quad \tilde{A}\_{n1n2} = \sqrt{2S\_{f0f}(\kappa\_{1n\_1}, -\kappa\_{2n\_2})\Delta\kappa\_1\Delta\kappa\_2} \tag{5}$$

$$
\kappa\_{1\mathfrak{n}\_1} = n\_1 \Delta \kappa\_1; \qquad \kappa\_{2\mathfrak{n}\_2} = n\_2 \Delta \kappa\_2 \qquad \Delta \kappa\_1 = \kappa\_{1\mathfrak{u}} / N\_1; \qquad \Delta \kappa\_2 = \kappa\_{2\mathfrak{u}} / N\_2 \tag{6}
$$

Since the uniform random phase angle Φ*n*1*n*<sup>2</sup> in Equation (4) is determined depending on *n*<sup>1</sup> and *n*2, it needs to generate two folds of *N*<sup>1</sup> × *N*<sup>2</sup> number of values in the range of [0, 2π]. The upper cut-off limit of wave numbers κ1*u*, κ2*<sup>u</sup>* in the SDF *Sf* <sup>0</sup> *<sup>f</sup>* <sup>0</sup>(κ1, κ1) can be determined by:

$$\int\_{0}^{\kappa\_{1u}} \int\_{-\kappa\_{2u}}^{\kappa\_{2u}} S\_{f \circ f \circ}(\kappa\_1, \kappa\_2) d\kappa\_1 d\kappa\_2 = (1 - \varepsilon) \int\_{0}^{\infty} \int\_{-\infty}^{\infty} S\_{f \circ f \circ}(\kappa\_1, \kappa\_2) d\kappa\_1 d\kappa\_2 \tag{7}$$

where ε is set to be 0.001(0.1%) in the numerical generation.

In the basic spectral representation method, as shown in Figure 4, 2D-1V can be expressed as a stochastic field, depending on the mean, standard deviation, and the correlation distance between variables [37].

**Figure 4.** Stochastic field (2D-1V): (**a**) d = 1.0; (**b**) d = 5.0; (**c**) d = 10.0; (**d**) d = 50.0.

#### *3.2. Bayesian Method*

Bayesian inference is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. Bayesian inference is an important technique in statistics, especially in mathematical statistics. Bayesian updating is particularly important in the dynamic analysis of a sequence of data.

Bayesian inference derives the posterior probability as a consequence of two antecedents: a prior probability and a "likelihood function" derived from a statistical model for the observed data. Bayesian inference computes the posterior probability according to Bayes' theorem:

$$
\lambda \, posterior \propto likelihood \times prior \tag{8}
$$

$$p(\theta|\text{data}) \propto p(\text{data}|\theta) \times p(\theta) \tag{9}$$

where θ stands for any hypothesis whose probability may be affected by data (called evidence below) [38,39]. Often, there are competing hypotheses, and the task is to determine which is the most probable. *p*(θ), the prior probability, is the estimate of the probability of the hypothesis θ before the "*data*," the current evidence, is observed. The evidence "*data*" corresponds to new data that was not used in computing the prior probability.

*p*(θ|*data*), the posterior probability, is the probability of θ given "*data*", after the "data" are observed. This is what we want to know: the probability of a hypothesis given the observed evidence. *p*(*data*|θ) is the probability of observing "*data*" given θ, and is called the likelihood. The likelihood function is a function of the evidence, data, while the posterior probability is a function of the hypothesis, θ and can be expressed by the process as shown in Figure 3 [40].

$$\begin{array}{l} p(\mu, \sigma^2) \propto \sigma^{-1} \left(\sigma^2\right)^{-\left(\nu\_0/2 + 1\right)} \exp\left[-\frac{1}{2\sigma^2} \left\{\nu\_0 \sigma\_0^2 + \kappa\_0 \left(\mu - \mu\_0\right)^2\right\}\right] \\ \times \left(\sigma^2\right)^{-n/2} \exp\left[-\frac{1}{2\sigma^2} \left\{(n-1)s^2 + n(\overline{y} - \mu)^2\right\}\right] \end{array} \tag{10}$$

$$
\mu\_n = \frac{\kappa\_0}{\kappa\_0 + n} \mu\_0 + \frac{n}{\kappa\_0 + n} \overline{y} \tag{11}
$$

$$\kappa\_n = \kappa\_0 + n; \upsilon\_n = \upsilon\_0 + n; \quad \kappa\_0 = s^2/\sigma\_0^2 \tag{12}$$

$$
\omega\_n \sigma\_n^2 = \nu\_0 \sigma\_0^2 + (n-1)s^2 + \frac{\kappa\_0 n}{\kappa\_0 + n} (\overline{y} - \mu\_0)^2 \tag{13}
$$

It is expressed as the product of likelihood and prior probability if expanded to a probability distribution, as shown in Equation (10) (posterior probability) [41]. Here, μ0, μ*<sup>n</sup>* denotes the prior/posterior mean, σ0, σ*<sup>n</sup>* denotes the prior/posterior standard deviation, and υ0, υ*<sup>n</sup>* denotes the prior/posterior degree of freedom. Similarly, *y*, *s*, and *n* are the test mean, test standard deviation, and test count, respectively, where *<sup>s</sup>*<sup>2</sup> <sup>=</sup> (*y*<sup>1</sup> − *y*) <sup>2</sup> <sup>+</sup> ··· + (*yn* <sup>−</sup> *<sup>y</sup>*) 2 /*n*.

#### *3.3. Consideration of Inverse Estimation (Prediction) Method*

For visualization purposes, we considered only 1-axis direction (y = constant or x = constant) of the 2D-1V stochastic field *f*0(*x*), as shown in Figure 5a. The method of estimating the correlation distance, expressing the spatial distribution state, is as follows [42]. First, within the stochastic field, each random variable has an irregular value. Second, the difference in value between two consecutive random variables also has an irregular value, but when d = 1, it will be larger than d = 10. Similarly, as shown in Figure 5c, it is assumed that the non-continuous random variables are also the same. Third, if the two random variables are equal in length, the maximum difference of the value will be similar in the stochastic field, regardless of the position.

(**d**)

**Figure 5.** Difference of value between random variables: (**a**) Stochastic fields (1D-1V); (**b**) Difference of value in two continuous variables; (**c**) Difference of value in two non-continuous variables; (**d**) Comparison in stochastic fields with different correlation distance.

#### **4. Verification of the Proposed Method**

#### *4.1. Example Model and Method*

In this study, the main objective was to find the coefficient (=d) representing the spatial randomness of the elastic modulus using experimental data (=observation) obtained by measuring specific parts of actual samples. However, it is not easy to accurately determine the spatial randomness of material through the measurement of the actual material. This is because there is almost no observed data of the actual structure. Therefore, as mentioned in Section 2, the population was predicted using some samples. Then, we compared the obtained real correlation distance d1 from the population with the d2 predicted from samples. We simulated the samples through an algorithm that knows the correlation distance (d) value correctly. The process is described below.

First, as shown in Figure 6, 3000 stochastic fields are generated. Then, 100 out of the 3000 stochastic fields are selected, and the user arbitrarily determines a specific position of the stochastic field, and random variables at that position are collected. At this time, it is assumed that generated stochastic fields (of 3000) are the population measured using a relatively small number of samples (100 samples in this study). In addition, the collected data are assumed as the observation data. Third, the correlation distance is estimated using the collection of data and the Bayesian method; and the statistical characteristics (μ, σ) are obtained. Finally, the statistical characteristics of 3000 stochastic

fields are compared with the updated statistical characteristics (and to compare the actual field d1 with estimated d2). To verify the performance of the prediction, five cases with different conditions (d = 1, 5, 10, 20, 50) were selected and examined.

**Figure 6.** Procedures for estimation (sampling method).

The spatial randomness of the elastic modulus of the target material can be expressed by Equation (2) by applying the spectral representation method to generate stochastic fields *fi*(*x*, *y*) of 2D-1V. Here, it was assumed that *fi*(*x*, *y*) had a mean value of 0, a standard deviation of 0.1, and the probability density was assumed to be a normal distribution. *E*(= 1.0) denotes the mean modulus of elasticity and *i* (1~3000) denotes the number of stochastic fields. Then, we assumed the randomness of the elastic modulus using Equation (2).

The total number of element e of sample fields was 60 elements in the x-direction and 20 elements in the y-direction, as shown in Figure 7a However, we did not know the number of elements of actual material. Therefore, the correlation distance could be found without knowing the number of elements as shown in Figure 7b, Table 1, summarizes the measured values in Figure 7a.

**Figure 7.** Design domain elements: (**a**) actual material 1200 elements; (**b**) estimated material 6000 elements.


**Table 1.** Observation data at the distance (= 0.5) per correlation distance.

#### *4.2. Results*

Part (a) in Figures 8–12 are the stochastic fields composed of material homogeneity (d = 1, 5, 10, 20, 50). These five observation points are assumed to be material samples. The total population was assumed to be 3000, and the design was made so that the true value (elastic modulus) had a mean of 1.0 and a standard deviation of 0.1. The prior probability was assumed to be unknown, with a mean of 0.8 and a standard deviation of 0.2. A total of 100 out of 3000 stochastic fields were chosen continuously from arbitrary positions, and a Bayesian update of five observation points in each stochastic field was performed.

**Figure 8.** *Cont*.

**Figure 8.** Bayesian updating at the stochastic field of the correlation distance d = 1.0: (**a**) How to perform Bayesian updating; (**b**) Observation point 1; (**c**) Observation point 2; (**d**) Observation point 3; (**e**) Observation point 4; (**f**) Observation point 5.

**Figure 9.** Bayesian updating at the stochastic field of the correlation distance d = 5.0: (**a**) How to perform Bayesian updating; (**b**) Observation point 1; (**c**) Observation point 2; (**d**) Observation point 3; (**e**) Observation point 4; (**f**) Observation point 5.

**Figure 10.** Bayesian updating at the stochastic field of the correlation distance d = 10.0: (**a**) How to perform Bayesian updating; (**b**) Observation point 1; (**c**) Observation point 2; (**d**) Observation point 3; (**e**) Observation point 4; (**f**) Observation point 5.

**Figure 11.** Bayesian updating at the stochastic field of the correlation distance d = 20.0: (**a**) How to perform Bayesian updating; (**b**) Observation point 1; (**c**) Observation point 2; (**d**) Observation point 3; (**e**) Observation point 4; (**f**) Observation point 5.

**Figure 12.** Bayesian updating at the stochastic field of the correlation distance d = 50.0: (**a**) How to perform Bayesian updating; (**b**) Observation point 1; (**c**) Observation point 2; (**d**) Observation point 3; (**e**) Observation point 4; (**f**) Observation point 5.

The elastic modulus values of the observation points (1 to 5) were updated using Bayes' theorem in a direction orthogonal to the stochastic plane. Bayesian updated results for observation points one through five are shown in subimages (b) through (f). The updated posterior probability was similar to the actual value at each position.

Figure 13 shows the comparison between the actual correlation distance and the estimated correlation distance at observation points one to five. Although the errors were different according to the observation positions from (a) to (e), the values achieved between the estimated correlation distance and the actual material showed good agreement. Notably, as the correlation distance (material homogeneity) increased, the correlation distance was accurately detected.

**Figure 13.** Comparison of d for simulated (imitated) material and inversely analyzed d: (**a**) Observation point 1; (**b**) Observation point 2; (**c**) Observation point 3; (**d**) Observation point 4; (**e**) Observation point 5.

#### **5. Conclusions**

The existing design and analysis were based on the deterministic assumption that the design variables had the same value (=constant field) in the structural domain. However, many factors (Poisson's ratio, thickness, etc.) of the actual structure possess temporal and spatial randomness, and the material's elastic modulus contains uncertainties. The results can differ depending on the correlation distance as in the response variance. If the value d in the actual material is not d = ∞, the result will be an under or overestimation.

In this study, we proposed a method of inversely estimating the correlation distance coefficient, which indicates the degree of uncertainty of the material, using the measured value of the observation data and the distance between measurement points. Probability characteristics and spatial randomness of the actual material can be estimated using some data only.

The concluding remarks of this paper can be summarized as follows:


The current probabilistic analysis can simulate spatial randomness through the correlation distance, but it does not know the spatial randomness of the actual material. Therefore, the present results are only assumptions, and their meaning is not conclusive.

In this study, a method of inversely estimating the correlation distance was proposed using measurement (observation), and it was confirmed that the actual correlation distance (d) agreed well with the estimated actual distance. Therefore, we could overcome the current disadvantage and find the true result of the actual structure, and not the assumption. Incidentally, the proposed method has a temporal advantage over the response variance. Verification was performed using an example by assuming that the program running time was 1 min at a time. A total of 100,000 (= 1000 ×1 ×100) minutes of program running time is required in order to analyze 1000 samples per correlation distance for COV from d = 1~100. This means a decrease in the number of interpretations of the Monte-Carlo simulation, and the program running time was reduced to a total of 1000 (= 1000 ×1 ×1) minutes.

Future studies need to be conducted considering the application of Poisson's ratio, cross-section (A), thickness (t), and uncertainty factors. Efforts to increase the accuracy of the estimates and actual values are also required in future study.

**Author Contributions:** Conceptualization, D.-Y.K., P.S., K.A. and S.-Y.C.; Methodology, D.-Y.K. and S.-Y.C.; Software, D.-Y.K. and S.-Y.C.; Validation, D.-Y.K., P.S., K.A. and S.-Y.C.; Formal analysis, D.-Y.K. and S.-Y.C.; Investigation, D.-Y.K. and S.-Y.C.; Resources, S.-Y.C., P.S. and K.A.; Data curation D.-Y.K. and S.-Y.C.; Writing—original draft preparation, D.-Y.K., S.-Y.C., P.S. and K.A.; Writing—review and editing, D.-Y.K., P.S., K.A. and S.-Y.C.; Visualization, D.-Y.K. and S.-Y.C.; Supervision, D.-Y.K. and S.-Y.C.; Project administration, D.-Y.K. and S.-Y.C.; Funding acquisition, D.-Y.K., S.-Y.C. and K.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project was received funding from the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant agreement no. 841592. Pawel Sikora is supported by the Foundation for Polish Science.

**Acknowledgments:** The authors would like to acknowledge that this work was supported by the Korea Agency for Infrastructure Technology Advancement (KAIA) and the grant was funded by the Ministry of Land, Infrastructure and Transport (Grant 13IFIP-C113546-01 and Grant 20NANO-B156177-01).

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

### *Article* **Influence of the Aggregate Surface Conditions on the Strength of Quick-Converting Track Concrete**

**Rahwan Hwang 1, Il-Wha Lee 2, Sukhoon Pyo 3,\* and Dong Joo Kim 1,\***


Received: 25 May 2020; Accepted: 17 June 2020; Published: 24 June 2020

**Abstract:** This experimental study investigates the effects of the aggregate surface conditions on the compressive strength of quick-converting track concrete (QTC). The compressive strength of QTC and interfacial fracture toughness (IFT) were investigated by changing the amount of fine abrasion dust particles (FADPs) on the aggregate surface from 0.00 to 0.15 wt% and the aggregate water saturation from 0 to 100%. The effects of aggregate water saturation on the compressive strength of the QTC and IFT were notably different, corresponding to the amount of FADPs. As the aggregate water saturation increased from 0 to 100%, in the case of 0.00 wt% FADPs, the IFT decreased from 0.91 to 0.58 MPa·mm1/2, and thus, the compressive strength of the QTC decreased from 34.8 to 31.4 MPa because the aggregate water saturation increased the water/cement ratio at the interface and, consequently, the interfacial porosity. However, as the aggregate water saturation increased from 0 to 100%, in the case of 0.15 wt% FADPs, the compressive strength increased from 24.6 to 28.1 MPa, while the IFT increased from 0.41 to 0.88 MPa·mm1/<sup>2</sup> because the water/cement ratio at the interface was reduced as a result of the absorption by the FADPs on the surface of the aggregates and the cleaning effects of the aggregate surface.

**Keywords:** Interfacial transition zone; quick-converting track concrete; aggregate surface condition; railway ballast

#### **1. Introduction**

The traditional track system, a ballasted track, is still widely regarded as one of the favored options for new railway construction projects due to low construction costs and easy maintenance. However, this type of track requires frequent repairs as a result of periodic train loads [1–3]. Lee and Pyo [1] developed a quickly converting track system that converts ballasted railway tracks into concrete tracks using quick-hardening materials.

During the service time of ballasted railway tracks, fine abrasion dust particles (FADPs) of aggregates are generated from the deterioration of aggregates under repeated train loads [2]. Lee et al. [2] experimentally evaluated the influence of FADPs at the interface on the strength of quick-converting track concrete (QTC). They concluded that surface cleaning of aggregates is necessary in order to achieve target strength. Lee et al. [4] additionally assessed the effects of FADPs on interfacial fracture toughness (IFT) between quick-hardening mortar (QM) and ballast aggregates in order to develop a suitable QM with high IFT. They revealed that the use of coarser silica sands and silica fume could produce the required QTC strength with a minimum cleaning process of existing ballast aggregates.

However, the effects of FADPs on the IFT between the aggregate and the QM—and subsequently on the strength of QTC—are not yet fully understood. For instance, ballast aggregates are generally placed in an outside environment and can be easily exposed to water through rain or snow. It is well known that the amount of water in mixing concrete should be adjusted to correspond to the content of water saturation and surface condition of aggregates because the W/C ratio would change if water saturation of the aggregate is not constant [5]. Thus, it can be expected that the water saturation content of the aggregate would substantially affect the compressive strength of QTC.

This experimental study aims to further understand the effects of the aggregate surface condition on the strength development of QTC. The detailed purposes are to experimentally evaluate the effects of FADPs that are adhered to the surface of aggregates and the effects of different water saturation content of the aggregate on the IFT between the aggregate and the QM and, subsequently, on the strength development of QTC.

#### **2. Aggregate Conditions and the Properties of Concrete**

Many studies have been carried out to characterize the influence of aggregate conditions, e.g., aggregate moisture content, type, roughness, and surface deformation, on the mechanical properties of concrete [6–18]. Aggregate water saturation generally produces negative effects on the interfacial bonding between the matrix (cement paste or mortar) and inclusions (coarse aggregate) [6,7]. Oliveira and Vazquez [6] investigated the influence of the moisture of recycled aggregate on the strength and durability of concrete and reported that saturated aggregates showed lower flexural strength. Poon et al. [7] revealed that air-dried aggregates produce a better compressive strength than that of water-saturated aggregates. On the other hand, Lee and Lee [8] reported that saturated surface-dry aggregates exhibit higher concrete strength than air-dried and sun-dried aggregates because oil palm shell aggregates are more efficient for internal curing because of the higher absorption capacity of oil palm shell aggregate.

The aggregate type also significantly affects concrete strength [9–13]. Ozturan and Cecen [9] claimed that basalt and limestone generate higher concrete strength than gravel aggregates. The effects of aggregate type on concrete strength show significantly different results in high-strength concrete [10], where crushed quartzite aggregates indicate higher concrete strength than marble aggregates. Beshr et al. [11] also reported that the influences of the type of aggregate on concrete strength are considerable in high-strength concrete. Petros et al. [12] investigated the interpretation of the adverse effects of the secondary products in two types of rocks during their performance as concrete aggregates. They reported that abnormal hydration reactions and considerable swelling of the smectite result in the appearance of defects in the concrete, hence contributing to its low performance. Petros et al. [13] investigated the effects of the aggregate type on concrete strength. They reported that the mineralogy and microstructure of the coarse aggregates affected the strength of concrete.

Aggregate surface roughness [14,15] and the aggregate shapes [16] also have substantial effects on the mechanical properties of concrete. Rao et al. [14] reported that an increase of the roughness of aggregates contributes to an increase in the interfacial bonding between the aggregate and mortar. In addition, Hong et al. [15] revealed that concrete strength variation would correspond to the roughness of the aggregate. Rocco and Elices [16] reported that the concrete that uses crushed aggregates shows better mechanical properties of concrete than the concrete that uses spherical aggregates.

In addition, surface-coating of the aggregate with pozzolanic materials produces noticeable effects on concrete properties [17–19]. Kong et al. [17] concluded that the surface-coating of the aggregate with pozzolanic particles consumes calcium hydroxide (CH) in the pores and interface between the aggregate and mortar, thus forming new hydration products. This phenomenon improves the microstructures around interfacial transition areas, further enhancing the strength and durability of concrete using the recycled aggregate. Choi et al. [19] revealed that the aggregate coated with inorganic powder strengthens the interfacial transition zone, thereby preventing micro-cracking and improving the mechanical performance of the concrete. Petros et al. [20] investigated the effects of three types of recycled materials (beer green glass, waste tile and asphalt) on concrete strength. In addition, the effects of beer green glass with quartz primer and waste tile with quartz primer on the concrete were studied. They reported that the material coated with quartz primer was suitable for obtaining optimal compressive strength results.

Pyo et al. [21] investigated the mechanical properties of ultra high performance concrete (UHPC) incorporating coarser fine aggregates with maximum particle size of 5 mm. They reported that the UHPC mixtures with dolomite and steel fibers with more than one volume percent achieved more than 150 MPa of compressive strength at the age 56 days, and showed strain hardening behavior and limited decrease in tensile strength compared to typical UHPC without coarser fine aggregates.

As many research studies found in the literature point out, the condition of aggregates is a critical factor for the properties of cement-based materials. However, the effects of aggregate conditions on the QTC strength, especially using quick-hardening mortar, are not fully understood. Specifically, investigation is needed of how aggregate water saturation affects the strength development of QTC. It is important to clarify the influence of aggregate water saturation on QTC strength to obtain the target strength of railway tracks using the proposed quick-converting method because ballast aggregates are under various climate conditions.

#### **3. Materials and Methods**

Figure 1 illustrates the detailed experimental series for clarifying the effects of aggregate surface conditions on IFT and then on the compressive strength of QTC. As shown in the figure, the first terms, "C" and "F," indicate the compressive and IFT tests, respectively. The second terms ("00" and "15") designate the content (0.00 and 0.15 wt%) of FADPs adhered to the surface of the aggregate with the weight ratio. Furthermore, the last term represents the aggregate water saturation content: "50" indicates a 50% aggregate water saturation content. For example, C-15-100 refers to the compressive test on the specimen using aggregates with 0.15 wt% of the FADP amount and a 100% aggregate water saturation content.

**Figure 1.** Details of the experimental program.

#### *3.1. Raw Materials and Fabrication*

Table 1 shows the composition of the QM matrix. Note that high early strength cement was used in this research for the purpose of the fast construction of the converting track. Polycarboxylic acid superplistizer was used as a high-range water-reducing agent (HRWRA), produced by DongNam Co., Ltd. in South Korea. The setting retarder was provided by SsangYong Co. Ltd. in South Korea. The FADPs were produced containing aggregate powder as by-products during granite processing. The maximum particle size of FADPs is 0.075 mm, which is larger than that of cement (0.005~0.03 mm). The chemical components of the used materials are summarized in Table 2. The fineness of the quick hardening cement is 5400 cm2/g, which is greater than 3200 cm2/g for normal cement type I, and the specific gravity is 2.85, which is less than 3.15 for normal cement type I. Both types of sand contained a

large amount of SiO2. The initial setting time of this quick-hardening mortar was 30 min, and more than 30 MPa of compressive strength can be obtained after two hours of curing, as shown in Table 3. It should also be noted that the dosage of the used setting retarder would change, according to the mixing environment and the target curing time.

**Table 1.** Composition of quick-hardening mortar matrix.


§ HRWRA: high-range water-reducing agent. † Maximum grain size of Sand A: 1.20 mm. ‡ Maximum grain size of Sand B: 0.42 mm. \* The amount of setting retarder depends on the temperature at mixing.


**Table 2.** Chemical component of materials.


**Table 3.** Compressive strength of mortar.

Cylinder specimens (100 mm in diameter and 200 mm in height) were prepared for the compressive QTC strength tests conducted according to ASTM C 39 [22]. QTC specimens were prepared by pre-filling the granite coarse aggregate with a size of 22.4 to 63 mm inside the mold and then injecting the QM. It should be noted that a series of compressive strength tests were carried out because compressive strength is one of the direct indications of overall strength of the ballastless track system. To attach the FADPs onto the aggregate surface, the following steps were conducted: the required weight of FADPs was first measured and mixed with wet coarse aggregate; then, the wet aggregate was fully dried. Saturated aggregates were prepared after immersing the aggregates, in which FADPs were applied according to the parameters in water and removing excess moisture. Although loss of FADPs may occur through this process, it is considered to be a similar condition to the actual track system, e.g., under a meteorological phenomenon.

Figure 2 illustrates the geometry of the IFT samples, and Figure 3 provides photos that show the surface condition of aggregates that correspond to different amounts of FADPs and different aggregate water saturations. The granite aggregate was collected from railway ballast. It can be seen that there is about half of the moisture remaining in the aggregate without FADPs and 50% water saturation of the aggregate surface (Figure 3b). In addition, for the aggregate with 100% water saturation, the entire surface is wet. As the content of aggregate water saturation increases, it can be seen that FADPs are mixed with water on the aggregate surface (Figure 3d–f). All the sliced aggregates were assumed to have identical roughness based on the use of the same cutting method. All specimens were cured at room temperature to create the same environment as the actual track system.

**Figure 2.** Geometry of the interfacial fracture toughness (IFT) specimens [4].

**Figure 3.** Surface of the aggregates used in this study (**a**) F-00-0, (**b**) F-00-50, (**c**) F-00-100, (**d**) F-15-0, (**e**) F-15-50, (**f**) F-15-100.

The QM mixture was prepared using a laboratory planetary mixer with a 20 L capacity. The mixing process for QM can be found in Lee et al. [4]. The digital image correlation (DIC) method was adopted in this research to characterize the interfacial crack. Random speckles were applied on the surface of IFT samples for the DIC analysis, and Figure 4 shows the prepared IFT samples before and after the stone spray application.

**Figure 4.** Specimen preparation for the digital image correlation (DIC) analysis [4]. (**a**) Surface of the fracture toughness test specimen; (**b**) surface of the fracture toughness test specimen with the applied stone spray.

#### *3.2. Experimental Setup and Procedure*

The compressive strength of QTC was measured at the age of 7 d, under a 1.0 mm/min machine displacement rate, using a universal testing machine (UTM) with a 3000 kN capacity. The IFT test was carried out at 7 days of curing, following the same procedure used by Lee et al. [4]. A UTM with a 5 kN capacity was used and the load was applied with a speed of 0.5 mm/min using the displacement control, and the test setup is shown in Figure 5. Images for the DIC analysis were recorded using a high-speed camera and the DIC analysis after testing was performed using commercial DIC software (Tracking Eye Motion Analysis). In both tests, at least three specimens were prepared and tested.

**Figure 5.** Test setup for the IFT test [4].

#### **4. Results**

Table 3 provides the compressive strength of the QM used in this study, while Table 4 provides the strength of QTC that corresponds to different surface conditions of the aggregate. Figure 6 summarizes the influences of contents and of water saturation contents on the IFT. The IFT was calculated using the formula found in Lee et al. [4], which is also given in fracture mechanics by Anderson [23].


**Table 4.** Compressive strength of quick-converting track concrete.

**Figure 6.** Effects of the water saturation contents on the IFT; (**a**) 0.0 wt% abraded fine particle, (**b**) 0.15 wt% abraded fine particle

#### *4.1. Influence of Fine Abrasion Dust Particles*

As the amount of FADPs on the aggregate surface increased from 0.00 to 0.15 wt%, the compressive strength of QTC decreased from 34.8 to 24.6 MPa (Table 4) because the FADPs decreased the IFT between the sliced aggregate and QM. In addition, increasing the amount of FADPs, from 0.00 to 0.15 wt%, resulted in a decrease of IFT, from 0.91 to 0.41 MPa·mm1/2, respectively (Figure 6). Although the effects of FADPs on both QTC strength and IFT were similar, the IFT was more sensitive to the FADPs. In Figure 6, the IFT results corresponding to 50% aggregate water saturation showed a large deviation because the location of evaporation of aggregate water saturation would be different. As can be seen in Figure 3b, it is considered that the water saturation on the aggregate surface is inhomogeneous for each specimen, which would result in a high deviation. However, the specimens with 0 and 100% aggregate water saturation produced consistent values of the IFT with smaller deviation because both aggregates with a water saturation of 0% (Figure 3a,d) and aggregate water saturation of 100% (Figure 3c,f) have the same moisture state on the aggregate surface of each specimen. The IFT of the specimens with the aggregate of abraded fine particle contents over 0.20 wt% could not be successfully tested due to premature failure near the interfaces during the casting process and hardening of the specimens. It was also difficult to measure the amount of FADPs less than 0.15 wt%.

Examples of failed surface of the interfaces between the aggregate and QM after the IFT test are shown in Figure 7. F-00-0 without FADPs on the aggregate surface showed no contaminants on the surface of the interface after the test (Figure 7a). On the other hand, as can be seen in Figure 7b, FADPs remained on the surface of the interface after tests, which is a clear indication of the fact that the reduction of IFT was the result of a decrease in IFT between the aggregate and QM. Moreover, Lee et al. [2] concluded that the strength of concrete decreased with increased FADPs because the FADPs deteriorated the interfacial bonding between the aggregate and QM. During the compression tests, the crack propagated in Mode II and/or III as well unlike the Mode I propagation of interfacial cracking during the IFT tests because the shear resistance based on the friction at the interface between the aggregate and matrix influenced the fracture modes. Thus, FADPs at the interface influenced the interfacial friction and consequently deteriorated the compressive strength of the QTC.

**Figure 7.** Failure surface of the interface between the aggregate and the QM after the IFT test (effects of the amount of FADPs); (**a**) F-00-0, (**b**) F-15-0.

#### *4.2. Influence of Aggregate Water Saturation*

It is worth noting the different effects of aggregate water saturation on the compressive strength of QTC, which corresponded to the FADP content on the surface of the aggregate. For the specimens without any FADPs, the compressive strength of the QTC decreased from 34.8 to 31.4 MPa (10%) as aggregate water saturation increased from 0 to 100%. However, the compressive strength of the QTC (using the aggregate with 0.15 wt% FADPs) increased from 24.6 to 28.1 MPa (14%) as the aggregate water saturation increased from 0 to 100%.

The influence of water saturation content on the IFT between the aggregate and QM is summarized in Figure 6. The influence of aggregate water saturation on the IFT was similar to the influence on the compressive strength of the QTC. For the samples without any FADPs on the surface of the aggregate, the IFT decreased from 0.91 to 0.58 MPa·mm1/<sup>2</sup> (36%) as aggregate water saturation increased from 0 to 100%. However, the increase of aggregate water saturation, from 0 to 100%, resulted in an increase of IFT (using the aggregate with 0.15 wt% FADPs) from 0.41 to 0.88 MPa·mm1/<sup>2</sup> (115%).

Figure 8 shows the fractured interface, after IFT tests, between the aggregate and QM, which corresponds to different water saturations of the aggregate. In the figure, the red boxes indicate the area where pores occurred at the interface. For the specimens without any FADPs on the aggregate surfaces, aggregate water saturation caused an increment of the water/cement ratio of the concrete [5], and consequently, the porosity in the concrete increased [24]. However, for the specimens using the aggregate with 0.15 wt% FADPs, the water/cement ratio at the interface was reduced because of the water absorption by the FADPs on the surface of the aggregates and the cleaning effects of the aggregate surface.

Figure 9 shows photos of the specimens after compressive tests. As shown in Figure 9c, the C-15-0 specimen had a large number of FADPs on the aggregate surface, and thus, porosity occurred at the interface between the coarse aggregate and QM. However, the C-15-100 specimen did not have many FADPs on the aggregate surface, similar to the C-0-100 specimen. All the specimens, except C-15-0, showed similar surface conditions. For the C-15-0 specimen, the interface between aggregate and mortar was clearly separated in comparison with other specimens. Figure 10 illustrates the correlation between the IFT and compressive strength, which indicates that the concrete strength was proportional to the IFT. As the compressive strength of concrete increases, the IFT increases. It is considered that the compressive strength of concrete and IFT are related. However, F(C)-15-100 shows a different tendency. The reason is the moisture and FADPs were removed from interfacial transition zone (ITZ), so that the interfacial bonding was strengthened, but it is considered that the strength of the mortar decreased because the moisture moved to the mortar.

**Figure 8.** Fractured interface between the aggregate and the QM after the IFT test (effects of the aggregate water saturation content); (**a**) F-0-50, (**b**) F-0-100, (**c**) F-15-50, (**d**) F-15-100.

Figure 11 shows the transverse strain contour during IFT tests. The first set of images shows the state of the specimen under the peak load and the second set of images shows the interfacial crack propagation, taking 0.3 s after peak loads. The last set of images shows the state of the fracture. In the first set of images (peak load), all specimens were unchanged in transverse strain contour. As shown in the second set of images, DIC analysis indicates that the initial crack quickly propagates with decreasing IFT. For the specimens without any FADPs, the crack propagated faster as the contents of aggregate water saturation increased from 0 to 100% (Figure 11a–c). This phenomenon can be explained by the reduced interfacial adhesion due to the increased W/C ratio in ITZ as the aggregate water saturation increased. However, the crack propagation (using the sliced aggregate with 0.15 wt% FADPs) decreased as the content of aggregate water saturation was increased from 0 to 100% (Figure 11d–f). The reduction in the W/C ratio at the interface resulted from the absorption of water by the FADPs on the surface of the aggregate and the cleaning effects of the aggregate surface. It should be noted that crack propagation of the whole series occurred exactly at the interface between the aggregate and QM because the IFT value is significantly low. If it had a high IFT, the adhesion between the aggregate and mortar would have been strengthened, and the crack would have propagated into the mortar. Lee et al. [4] also reported that the higher IFT specimens show that the cracks propagate through the QM.

**Figure 9.** Failure surface of concrete specimens after compressive tests; (**a**) C-0-0, (**b**) C-0-100, (**c**) C-15-0, (**d**) C-15-100.

**Figure 10.** Correlation between the compressive strength and the IFT.

**Figure 11.** Transverse strain contour of IFT specimens; (**a**) F-00-0, (**b**) F-00-50, (**c**) F-00-100, (**d**) F-15-0, (e) F-15-50, (**f**) F-15-100.

#### **5. Conclusions**

The compressive strength of QTC and IFT between the aggregates and QM was investigated by changing the amount of FADPs on the surface of the aggregate and the content of aggregate water saturation. The key conclusions can be summarized as:


The results obtained in this study provide fundamental knowledge of the importance of the aggregate surface conditions for the strength development of QTC. Therefore, in order to efficiently apply the quick-converting method, further research is required to improve interfacial bond strength according to aggregate surface conditions. Therefore, research with additional variables is essential. The effects of precipitation on the strength of QTC during the curing period in the actual track system should be investigated in addition to the effects of aggregate water saturation.

**Author Contributions:** Experiments, Formal analysis, Visualization, Writing original draft, R.H.; I.-W.L.: Supervision, Writing-review and editing, I.-W.L.; Supervision, Formal analysis, Writing-review and editing, S.P.; Supervision, Formal analysis, Writing-review and editing, D.J.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research described herein was sponsored by a grant from the R&D Program of the Korea Railroad Research Institute, Korea. This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2019R1F1A1060906). The opinions expressed in this paper are those of the authors and do not necessarily reflect the views of the sponsors.

**Conflicts of Interest:** The authors declare no conflicts of interest.

#### **References**


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#### *Article*
