Study on Mechanical Properties and Microstructure of Basalt Fiber Reactive Powder Concrete

: In order to promote the wide application of reactive powder concrete (RPC) in practical engineering. In this paper, RPC was prepared using conventional and economical natural river sand instead of quartz sand and economical and environmentally friendly basalt ﬁber (BF) instead of steel ﬁber, and the macroscopic properties of basalt ﬁber reactive powder concrete (BFRPC) with different ﬁber content, such as ﬂowability, failure mode, compressive strength and splitting tensile strength were studied, and the strength calculation formula of BFRPC was established based on the mechanical property results. The microscopic morphology and structure of BFRPC were characterized by scanning electron microscope (SEM) and Image Pro Plus (IPP) image processing software. The results show that BF has a small effect on the compressive strength of RPC, while it has a signiﬁcant increase on the splitting tensile strength. When BF content is at 2 kg/m 3 , the 28-day compressive strength reaches 95.2 MPa and splitting tensile strength reaches 7.78 MPa. Compared with the RPC with BF of 0 kg/m 3 , the BFRPC shows an improvement in its 28-day compressive strength by 25.70% and an increase in its splitting tensile strength by 83.92%. According to the microscopic analysis, reasonable ﬁber content can optimize the internal microstructure of BFRPC, but excessive BF content will produce agglomeration and overlap, resulting in strength loss. Based on the gray correlation analysis method, it was concluded that the particle area ratio and pore fraction dimension were the most correlated with the mechanical properties of BFRPC. In addition, the feasibility and applicability of the BFRPC strength calculation formula were summarized. This research results of this paper provides a valuable reference for the further research and promotion of BFRPC.


Introduction
With the emergence of super high-rise, long-span, lightweight structures, the requirements for concrete are constantly increasing and have driven the development of concrete with ultrahigh strength, high toughness, and high reliability. As a new type of building structure material, reactive powder concrete (RPC) can meet and adapt to the development of current building structure towards high strength and high durability [1,2]. It lacks the coarse aggregates and instead contains quartz sand, silica fume, and fly ash to reach maximum filling density inside RPC. Through thermal curing, the reaction between components of the material is accelerated, and the bond strength of the interface is improved. In addition, fine steel fiber is incorporated to improve toughness and ductility [3]. Therefore, RPC has great application prospects in construction engineering.
Quartz sand contains a high content of silicon, which accelerates the ash reaction and improves the filling effect at the interface between aggregates [4,5]. It can also enhance the compactness of RPC matrix and reduce internal porosity. Silica sand contributes negatively to RPC under certain circumstances. However, in some cases, quartz sand reduces RPC strength by filling the internal voids and reducing the pozzolanic reaction between silica have varying effects on concrete strength. Short-sized BF (12 mm) contribute more to the compressive strength of concrete than long-sized BF (25 mm, 37 mm, 50 mm) [40]. Compared with steel fiber, BF has good corrosion resistance and cheap price. In addition, BF is superior to polypropylene fiber in the contribution of concrete compressive strength [41]. Ahmet B showed that BF concrete has better crack resistance and ductility than glass fiber concrete [32] and is cheaper than carbon fiber concrete. In addition, BF can also improve the durability of concrete. Ding [42] showed that BF can effectively improve the anti-carbonation properties of recycled concrete, but the anti-carbonation properties can be reduced by incorporating too much. Lu [43] showed that the addition of BF could inhibit high temperature carbonation of concrete, reduce the thickness of the burnt layer, and significantly improve the chloride ion penetration resistance of concrete. Meanwhile, with the increase in erosion age, the concentration increased rapidly in the initial stage, and the pore structure was optimized in the later stage with the continuous hydration process, and the gradual increase rate of erosion concentration decreased [44,45]. Wang [46] showed that the appropriate amount of BF can improve the resistance of concrete to sulfate attack. Ren [47] showed that erosion became more pronounced with increasing sulfate concentration and time. Fan [48] showed that BF can significantly improve the freeze-thaw resistance of concrete. After 100 freeze-thaw cycles, the dynamic elastic modulus of BF concrete was 1.47 times higher than that of ordinary concrete, and the mass loss was 0.64 times higher than that of ordinary concrete. Therefore, BF has a wide application prospect in the field of construction and can become a suitable substitute for steel fiber, glass fiber, polypropylene fiber, and carbon fiber [49,50]. Researchers have prepared common concrete mixed with BF and obtained a high performance. However, the study of BFRPC is still in the exploratory stage. Therefore, the present work investigated the macro mechanical properties and microstructure of BFRPC to lay the foundation for its practical engineering application.
RPC research still has some deficiencies. The selection of economical and reasonable materials and the preparation of RPC by conventional maintenance methods are the keys to solving the difficulty in popularizing and applying this material in practical engineering. In this paper, BFRPC was prepared by using economical ordinary conventional materials and standard curing methods, and the working performance and macroscopic mechanical properties of RPC with different dosage of BF were studied, so as to find the optimal dosage of BFRPC. The micromorphology of BFRPC was characterized and analyzed by scanning electron microscope (SEM), and the microstructure was quantitatively analyzed by Image Pro Plus (IPP) software. The relationship between macroscopic mechanical properties and microscopic mechanism of BFRPC was clarified. On this basis, a scientific and reasonable mechanical property calculation formula of BFRPC is established, which provides valuable reference basis for the wide application of BFRPC.

Materials
The test uses grade 52.5 cement produced by Yatai Cement Factory, which conforms to the general Portland Cement Inspection Standard (GB175-2007) [51]. Grade I fly ash was obtained from Xiao Haibao Superfine Bead Technology Development Co., Henan, China. Silica fume was obtained from Boken Silicon Material Co., Shandong, China. All of these were in accordance with the technical specifications of the Application of Mineral Admixtures (GB/T51003/2014) [52]. The superplasticizer was obtained from Hongxia Polymer Materials Co., Qingdao, China. Fine aggregate uses natural river sand, and the gradation curve is obtained according to sand particle gradation screening test, as shown in Figure 1. BF of 12 mm length produced by Chenqi Chemical Technology Co., Shanghai, China is selected as the fiber. The basic parameters of BF are shown in Table 1, and a picture is shown in Figure 2. Buildings 2022, 12, x FOR PEER REVIEW China is selected as the fiber. The basic parameters of BF are shown in Ta picture is shown in Figure 2.

Sample Preparation
On the basis of the optimal mix ratio of RPC matrix obtained in the prev mental study, 0, 1, 2, 3, and 4 kg/m 3 BF were added to prepare BFRPC. The R and sample number of different BF content are shown in Table 2. An amount is RMB 35, which increases the cost of BFRPC by RMB 35/m 3 compared to BF   China is selected as the fiber. The basic parameters of BF are show picture is shown in Figure 2.

Sample Preparation
On the basis of the optimal mix ratio of RPC matrix obtained in mental study, 0, 1, 2, 3, and 4 kg/m 3 BF were added to prepare BFRP and sample number of different BF content are shown in Table 2. An a

Sample Preparation
On the basis of the optimal mix ratio of RPC matrix obtained in the previous experimental study, 0, 1, 2, 3, and 4 kg/m 3 BF were added to prepare BFRPC. The RPC fit ratio and sample number of different BF content are shown in Table 2. An amount of 1 kg of BF is RMB 35, which increases the cost of BFRPC by RMB 35/m 3 compared to BF0.
The dispersion uniformity of BF has an important influence on the performance of BFRPC. Therefore, if the fiber can be uniformly dispersed, the properties of the specimens can be effectively improved. It is shown that the friction between sand particles can make the fiber uniformly dispersed [53]. In order to disperse BF more uniformly, most previous studies have used pre-mixing of BF with fine aggregates for dispersion [54][55][56]. The process of sample preparation is shown in Figure 3. (i) BF and natural river sand were mixed and stirred for 120 s so that the BF can be dispersed evenly; (ii) cement, fly ash, and silica fume were then added, and the mixture was stirred for 120 s; (iii) 80% mixture of water reducer and water was added, and the mixture was continuously stirred for 240 s; (iv) the remaining mixture of water reducer and water was added, and the mixture was stirred for 120 s; (v) after stirring and molding, the mixture was transferred to the test mold placed on a vibrating table to vibrate the mixture and make it fully dense; (vi) after forming, the specimens were demolded and then cured to 7 and 28 days under standard curing conditions.

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The dispersion uniformity of BF has an important influence on the performance of BFRPC. Therefore, if the fiber can be uniformly dispersed, the properties of the specimens can be effectively improved. It is shown that the friction between sand particles can make the fiber uniformly dispersed [53]. In order to disperse BF more uniformly, most previous studies have used pre-mixing of BF with fine aggregates for dispersion [54][55][56].
The process of sample preparation is shown in Figure 3. (i) BF and natural river sand were mixed and stirred for 120 s so that the BF can be dispersed evenly; (ii) cement, fly ash, and silica fume were then added, and the mixture was stirred for 120 s; (iii) 80% mixture of water reducer and water was added, and the mixture was continuously stirred for 240 s; (iv) the remaining mixture of water reducer and water was added, and the mixture was stirred for 120 s; (v) after stirring and molding, the mixture was transferred to the test mold placed on a vibrating table to vibrate the mixture and make it fully dense; (vi) after forming, the specimens were demolded and then cured to 7 and 28 days under standard curing conditions.

Flowability
Fluidity was tested according to GBT50080-2016 [57]. Slump test is performed by using slump bucket. The slump bucket shall comply with the provisions of JG/T 248-2009 [58].
The mixture was evenly divided into three layers into the slump barrel, the height of each layer of mixture is about 100 mm. In each layer after loading uniform vibration for 25 times, the top layer was tamped to remove the feeding funnel and wiped along the barrel mouth to obtain a flat, vertical, and smooth lift slump barrel. When sample stops slumping, the cylinder height and backward height difference between high mixture was measured as the BFRPC slump value. The expansion degree of the extended mixture was

Flowability
Fluidity was tested according to GBT50080-2016 [57]. Slump test is performed by using slump bucket. The slump bucket shall comply with the provisions of JG/T 248-2009 [58].
The mixture was evenly divided into three layers into the slump barrel, the height of each layer of mixture is about 100 mm. In each layer after loading uniform vibration for 25 times, the top layer was tamped to remove the feeding funnel and wiped along the barrel mouth to obtain a flat, vertical, and smooth lift slump barrel. When sample stops slumping, the cylinder height and backward height difference between high mixture was measured as the BFRPC slump value. The expansion degree of the extended mixture was measured with a steel ruler.

Mechanical Properties
The mechanical properties include compressive strength and splitting tensile strength. Test specimens with size of 100 mm × 100 mm × 100 mm were prepared according to Reactive Powder Concrete (GB/T31387-2015) [59]. Three specimens were prepared for each group, and the arithmetic average of the test values of the three specimens was taken as the final test value. The compressive test loading rate was maintained between 1.2 and 1.4 MPa/s, and the loading rate of the splitting tensile strength test was maintained between 0.08 and 0.1 MPa/s.

Microstructure
The combination of stereo optical microscope and digital image processing is considered to be an effective method for the characterization of microstructure and has been widely used in studying the microstructure of materials [60][61][62].
SEM samples were selected as the damaged specimens closest to the arithmetic mean value in the compressive strength test, and the sample size was about 10 mm. The sample treatment procedures were as follows: (i) sanding the sample with sandpaper to make the surface smooth and smooth, (ii) vacuum-drying the sample, (iii) gold-plating the surface of the sample, and (iv) observing and capturing images using an environmental scanning electron microscope (XL-30).
IPP has powerful filters and contrast adjustment functions that help enhance the image to obtain accurate data results [60][61][62]. The process of microstructure parameter extraction is as follows. (1) The histeq function of MATLAB is used to process the histogram equalization of the image to make the microstructure clearer and improve the accuracy of data extraction. (2) Using medfilt2 function to carry out median filtering processing on the image. (3) Using fspecial function and Filter2 function to sharpen the image. (4) Image binarization is performed by combining graythresh function and im2bw function. (5) IPP is used to extract pore microscopic parameters from binarized images. (6) The bwdist function and watershed function were used to process the binarized image, and IPP was used to extract particle microscopic parameters from the binarized image after processing.

Macroscopic Performance Analysis of BFRPC
The test results of slump, extension, and mechanical properties of BFRPC are shown in Table 3.

Analysis of Slump and Extension
The slump test is shown in Figure 4. The test results of slump and extension of BFRPC is shown in Figure 5. The incorporation of BFs has a certain influence on the flowability of BFRPC. With the increase in the content of BF, slump, and extension gradually decreased because BF has hydrophilic effect, disperses into a large number of extremely fine flocculent fiber in the mixture, and absorbs part of the free water. BF surface is rough, and its friction coefficient is high. With the increase in the amount added, BF easily coalesced during mixing and absorbed a large amount of cement slurry to wrap. Therefore, the fluidity of BFRPC was weakened. As other studies have shown [63,64], concrete slump decreases with the increase in BF volume fraction. However, the target slump can be achieved by adding an appropriate amount of superplasticizer.

Failure Mode
The compressive failure mode of BFRPC is shown in Figu without BF is brittle failure. When BF was added, the speci slight peeling accompanied by a number of small cracks. This cause the friction between BF and the matrix limits the develo tain integrity after any damaging event.

Failure Mode
The compressive failure mode of BFRPC is shown in Figure 6. The RPC failure form without BF is brittle failure. When BF was added, the specimen surface still exhibited slight peeling accompanied by a number of small cracks. This phenomenon occurred because the friction between BF and the matrix limits the development of cracks and maintain integrity after any damaging event.

Failure Mode
The compressive failure mode of BFRPC is shown in Figure 6. The RPC failure form without BF is brittle failure. When BF was added, the specimen surface still exhibited slight peeling accompanied by a number of small cracks. This phenomenon occurred because the friction between BF and the matrix limits the development of cracks and maintain integrity after any damaging event. The failure modes of BFRPC splitting tensile strength are shown in Figure 7. The cracks of the RPC without BF gradually developed and penetrated along the middle of the specimen due to the longitudinal splitting failure form. When mixed with BF, the basic crack interface was a flat line because the BF incorporation can have similar "reinforcement" effect. In the event of a micro crack, the BF and matrix under tensile stress showed plastic failure, effectively improving the toughness of BFRPC. The failure modes of BFRPC splitting tensile strength are shown in Figure 7. The cracks of the RPC without BF gradually developed and penetrated along the middle of the specimen due to the longitudinal splitting failure form. When mixed with BF, the basic crack interface was a flat line because the BF incorporation can have similar "reinforcement" effect. In the event of a micro crack, the BF and matrix under tensile stress showed plastic failure, effectively improving the toughness of BFRPC. B. Ramesh [64] and Zhang [65] obtained similar results. When BF was not doped, with the gradual increase in load, the cracks expanded rapidly, and a loud cracking sound was made when the compressive strength test was damaged, and the damage was in the form of quadrangular cone damage, and the splitting tensile strength test was suddenly split into two halves when the ultimate load was reached. After the incorporation of BF, due to the bridging effect of fiber on the cracks effectively limiting the expansion of cracks, the specimens show good plasticity. Therefore, BF can improve the crack resistance of B. Ramesh [64] and Zhang [65] obtained similar results. When BF was not doped, with the gradual increase in load, the cracks expanded rapidly, and a loud cracking sound was made when the compressive strength test was damaged, and the damage was in the form of quadrangular cone damage, and the splitting tensile strength test was suddenly split into two halves when the ultimate load was reached. After the incorporation of BF, due to the bridging effect of fiber on the cracks effectively limiting the expansion of cracks, the specimens show good plasticity. Therefore, BF can improve the crack resistance of concrete.

Analysis of Mechanical Properties
The test results of 7-and 28-day compressive strength and splitting tensile strength of BFRPC are shown in Figures 8 and 9. When the amount of BF is 2 kg/m 3 , it is the best amount. The maximum compressive strength at 28-day reaches 95.2 MPa and the maximum splitting tensile strength reaches 7.78 MPa. With the increase in the amount of BF, the mechanical properties of BFRPC gradually decreases. When the content of BF is low, it can be evenly distributed in the mixture, forming a dense spatial network structure with the aggregate, optimizing the internal structure, reducing the internal porosity, and creating a homogeneous and complete structural system. When cracks occur, BF can play a bridging role and effectively prevent the development of cracks. However, when the content of BF exceeds the optimum content, the BF clumps in the matrix, affects the overall uniformity of the mixture, forms many weak surfaces, and fails to generate a space grid with integrity, resulting in the declining trend of the strength of BFRPC.  The effect of BF on the improvement of compressive strength of RPC was not significant. When the dosage was 2 kg/m 3 , the compressive strength increased the most, and the maximum increase percentage was 6.84% and 25.70% at 7 and 28 days, respectively. The splitting tensile strength of RPC increased by BF was large. When the dosage was 2 kg/m 3 , the maximum increase in splitting tensile strength was 74.21% and 83.92% for 7 and 28 days, respectively. BF can improve the strength of RPC because BF has excellent material properties. Hence, a complete bearing system is formed between the aggregates. When the BFRPC is loaded, the BF at the stress concentration point acts as a bridge, thus, effectively limiting the initiation and expansion of the crack and improving the mechanical properties of BFRPC.
As found in earlier studies, the addition of BF can improve the compressive strength  The effect of BF on the improvement of compressive strength of RPC was not significant. When the dosage was 2 kg/m 3 , the compressive strength increased the most, and the maximum increase percentage was 6.84% and 25.70% at 7 and 28 days, respectively. The splitting tensile strength of RPC increased by BF was large. When the dosage was 2 kg/m 3 , the maximum increase in splitting tensile strength was 74.21% and 83.92% for 7 and 28 days, respectively. BF can improve the strength of RPC because BF has excellent material properties. Hence, a complete bearing system is formed between the aggregates. When the BFRPC is loaded, the BF at the stress concentration point acts as a bridge, thus, effectively limiting the initiation and expansion of the crack and improving the mechanical properties of BFRPC. The effect of BF on the improvement of compressive strength of RPC was not significant. When the dosage was 2 kg/m 3 , the compressive strength increased the most, and the maximum increase percentage was 6.84% and 25.70% at 7 and 28 days, respectively. The splitting tensile strength of RPC increased by BF was large. When the dosage was 2 kg/m 3 , the maximum increase in splitting tensile strength was 74.21% and 83.92% for 7 and 28 days, respectively. BF can improve the strength of RPC because BF has excellent material properties. Hence, a complete bearing system is formed between the aggregates. When the BFRPC is loaded, the BF at the stress concentration point acts as a bridge, thus, effectively limiting the initiation and expansion of the crack and improving the mechanical properties of BFRPC.
As found in earlier studies, the addition of BF can improve the compressive strength [55] and splitting tensile strength [66] of concrete, but the improvement of compressive strength is not obvious [67]. Zhang [68] also showed that BF added to concrete was more effective in enhancing tensile and flexural strengths than compressive strength. Liu [56] pointed out that uniformly distributed BF can inhibit crack sprouting and bear part of the load, thus, increasing the compressive strength. Sha [67] pointed out that BF effectively inhibited the extension of microcracks, mainly due to the bridging effect of randomly distributed discrete fiber on the cracks. After bending cracking, the stress is transferred to the bridging fiber, which retards the crack development and increases the cracking tensile strength. The conclusions of these studies are the same as the results of this study.

SEM Characterization Analysis
The microscopic morphology and fiber distribution of BFRPC were analyzed by SEM, and the BF reinforcement mechanism was further analyzed through the microstructure.
From the microstructure, the BF is tightly bonded to the substrate and no interfacial transition zone is observed. When BFRPC is under the action of external load, BF is closely connected to the substrate and shares the stress with the substrate. The two use their own strength and good interfacial adhesion to absorb the energy of crack development, which effectively inhibits the development of cracks and achieves the purpose of toughening and blocking the crack of concrete, so that the microstructure of concrete can be improved and eventually be pulled out or fractured. Figure 10a shows the smooth hole left after the fiber is pulled out from the matrix, and Figure 10b shows the cross section of the broken fiber. As demonstrated in the Zhang [65] study, when the BF content is small, most of the BF distributed along the crack is pulled out or broken, and when the BF content is sufficient, the fiber can withstand most of the transverse tensile force, slowing down the stress concentration and effectively preventing the crack expansion and development. However, as shown in Figure 10a, when BF is added in excess, the fiber will agglomerate and overlap due to the uneven distribution of BF, which affects the degree of bonding between the cementitious base and the interfacial transition zone, leading to a decrease in the contribution of BF to the improvement of mechanical properties. Sha [67] also pointed out in his study that when the volume fraction of BF is too high it will agglomerate, leading to a decrease in compressive strength.

SEM Characterization Analysis
The microscopic morphology and fiber distribution of BFRPC were analyzed by SEM, and the BF reinforcement mechanism was further analyzed through the microstructure.
From the microstructure, the BF is tightly bonded to the substrate and no interfacial transition zone is observed. When BFRPC is under the action of external load, BF is closely connected to the substrate and shares the stress with the substrate. The two use their own strength and good interfacial adhesion to absorb the energy of crack development, which effectively inhibits the development of cracks and achieves the purpose of toughening and blocking the crack of concrete, so that the microstructure of concrete can be improved and eventually be pulled out or fractured. Figure 10a shows the smooth hole left after the fiber is pulled out from the matrix, and Figure 10b shows the cross section of the broken fiber. As demonstrated in the Zhang [65] study, when the BF content is small, most of the BF distributed along the crack is pulled out or broken, and when the BF content is sufficient, the fiber can withstand most of the transverse tensile force, slowing down the stress concentration and effectively preventing the crack expansion and development. However, as shown in Figure 10a, when BF is added in excess, the fiber will agglomerate and overlap due to the uneven distribution of BF, which affects the degree of bonding between the cementitious base and the interfacial transition zone, leading to a decrease in the contribution of BF to the improvement of mechanical properties. Sha [67] also pointed out in his study that when the volume fraction of BF is too high it will agglomerate, leading to a decrease in compressive strength.

Quantitative Analysis of Microstructure
Concrete is a porous composite material. As an important part of the microstructure, aggregate particles and pore structure characteristics have a significant impact on the macroscopic mechanical properties of concrete [69,70]. Therefore, Image-Pro Plus image

Quantitative Analysis of Microstructure
Concrete is a porous composite material. As an important part of the microstructure, aggregate particles and pore structure characteristics have a significant impact on the macroscopic mechanical properties of concrete [69,70]. Therefore, Image-Pro Plus image processing software was used for quantitative analysis of the microstructure parameters of BFRPC. The fractal dimension reflects the effectiveness of the space occupied by the complex shape, and it is a measure of the irregularity of the complex shape. Abundance refers to the ratio of the short axis to the long axis of the particle or pore, which indicates the geometric shape characteristics of the particle or pore, with the value of abundance tending to 0, the particle or pore is similar to a long strip; with the value of abundance tending to 1, the particle or pore tends to be equiaxed. Roundness characterizes the degree of particle or pore approximating to standard circle; the larger the value of roundness, the more the particle or pore approximates to the circle. The distribution results of particle size and pore size are shown in Figures 11 and 12, and the microscopic parameter results of particle and pore are shown in Figures 13 and 14. 2022, 12, x FOR PEER REVIEW size and pore size are shown in Figures 11 and 12, and the microsco of particle and pore are shown in Figures 13 and 14.    Figures 11 and 12, and the microsco of particle and pore are shown in Figures 13 and 14.      Figure 11 shows that in BFRPC, the particle size was mostly 0-2 μm. The content of particles larger than 20 μm was small. With the increase in the content of BF, the content of 0-2 μm particles gradually increased, that of 2-5 μm particles increased first and then decreased, and that of 5-20 μm and >20 μm particles gradually decreased when the content of BF was 2 kg/m 3 .
As shown in Figure 12, the content of 0-4 μm pores in BFRPC was high, and that of >16 μm pores was less. With the increase in BF addition, the content of 0-4 μm pores first increased, then decreased, and was maximized when the BF addition was 2 kg/m 3 . When the content of BF is small, it can be distributed evenly in the RPC, effectively improving the generation of pores and cracks in RPC and reducing the porosity in BFRPC. The pore size larger than 4μm tends to decrease first and then increase, and it is the smallest, with a content of 2 kg/m 3 . This is due to the high content of BF, which leads to uneven distribution of BF, resulting in the agglomeration and increased internal porosity of BFRPC.
The particle microparameters are shown in Figure 13. With the increase in BF content, the particle area ratio did not change but was the largest when the content was 2 kg/m 3 . The average particle size and fractal dimension of particle size gradually decrease when the fiber content is 0-2 kg/m 3 and gradually increase when the fiber content is 2-4 kg/m 3 . The average abundance of particles basically increased first and then decreased, and the average circularity of particles showed no change. As can be seen in Figure 14, with the increase in BF content, the pore area ratio and average pore abundance gradually decrease when the fiber content is 0-2 kg/m 3 , and gradually increase when the fiber content is 2-4  Figure 11 shows that in BFRPC, the particle size was mostly 0-2 µm. The content of particles larger than 20 µm was small. With the increase in the content of BF, the content of 0-2 µm particles gradually increased, that of 2-5 µm particles increased first and then decreased, and that of 5-20 µm and >20 µm particles gradually decreased when the content of BF was 2 kg/m 3 .
As shown in Figure 12, the content of 0-4 µm pores in BFRPC was high, and that of >16 µm pores was less. With the increase in BF addition, the content of 0-4 µm pores first increased, then decreased, and was maximized when the BF addition was 2 kg/m 3 . When the content of BF is small, it can be distributed evenly in the RPC, effectively improving the generation of pores and cracks in RPC and reducing the porosity in BFRPC. The pore size larger than 4µm tends to decrease first and then increase, and it is the smallest, with a content of 2 kg/m 3 . This is due to the high content of BF, which leads to uneven distribution of BF, resulting in the agglomeration and increased internal porosity of BFRPC.
The particle microparameters are shown in Figure 13. With the increase in BF content, the particle area ratio did not change but was the largest when the content was 2 kg/m 3 . The average particle size and fractal dimension of particle size gradually decrease when the fiber content is 0-2 kg/m 3 and gradually increase when the fiber content is 2-4 kg/m 3 . The average abundance of particles basically increased first and then decreased, and the average circularity of particles showed no change. As can be seen in Figure 14, with the increase in BF content, the pore area ratio and average pore abundance gradually decrease when the fiber content is 0-2 kg/m 3 , and gradually increase when the fiber content is 2-4 kg/m 3 . The average pore size and average pore roundness showed no change, and the fractal dimension of pores basically increased first and then decreased. The fractal dimension of BFRPC pores is the same and maximum at the dosing of 1 kg/m 3 and 2 kg/m 3 .
Xu [54] pointed out through the analysis of the microstructure of concrete that the incorporation of fiber can effectively improve the internal structure of concrete, making the particles and pores smaller, uniform, complex, and full. BF achieves an enhanced toughening effect by connecting the matrix into a whole, mainly through its own strength and good interfacial adhesion.

Gray Correlation Analysis
Gray correlation analysis method can not only solve the conventional and irregular sample size but also reduce the calculation amount, which is a convenient and efficient analysis method [71]. Some scholars studied the strength prediction of recycled aggregate concrete and factors affecting properties of cement-based composites by using gray correlation analysis and achieved good results [72,73].
Gray correlation analysis was used to analyze the BFRPC macro mechanical properties and microstructure parameters, calculate the correlation values between macroscopic mechanical properties and microscopic parameters, and determine the main factors influencing the mechanical properties BFRPC. The gray correlation calculation results are shown in Tables 4 and 5.  Table 4 shows that the correlation between particle microscopic parameters and BFRPC compressive strength was in the order of primary and secondary: particle area ratio > average abundance > average particle size > fractal dimension > average roundness. However, only the correlation between particle area ratio and average particle abundance and compressive strength exceeded 0.6, indicating that the particle area ratio and average particle abundance have a significant effect on BFRPC. In addition, the order of correlation between particle microscopic parameters and the splitting tensile strength of BFRPC was as follows: particle area ratio > average abundance > particle fractal dimension > average roundness > average particle size. The correlation values between particle area ratio, particle average abundance, particle fractal dimension, particle roundness, and splitting tensile strength were all greater than 0.6, and the correlation value between average particle size and splitting tensile strength was 0.599, which was close to 0.6. This finding indicates that the microcosmic parameters of particles are closely related to the splitting tensile strength of BFRPC. Table 5 shows the primary and secondary relationship between pore microscopic parameters and BFRPC compressive strength is as follows: pore fractal dimension > average porosity roundness > average porosity abundance > average pore size > pore area ratio, but only the correlation between pore fractal dimension and average porosity roundness and compressive strength is more than 0.6, indicating that the fractal dimension and average porosity roundness have a significant effect on BFRPC. In addition, the primary and secondary relationship between pore microscopic parameters and the splitting tensile strength of BFRPC is as follows: pore fractal dimension > average roundness > average pore size > pore area ratio > average abundance, and the correlation values of all pore microscopic parameters and splitting tensile strength are greater than 0.6, indicating that the pore microscopic parameters are closely related to the splitting tensile strength of BFRPC.
As Xu [54] showed by analyzing the micro parameters and macro strength of concrete through gray correlation, compared with compressive strength, micro parameters have a closer correlation with splitting tensile strength.

BFRPC Strength Calculation Formula
Statistical and mathematical models have been applied to the study of cementitious composites. An increasing number of scholars have investigated concrete strength prediction models, of which regression analysis is the most widely used method. Gao [74] developed regression formula for compressive strength and critical strain for steel fiber reinforced recycled coarse aggregate concrete. Zhong [26] proposed formulas for calculating the manufactured sand RPC compressive strength and splitting tensile strength using regression analysis, and the applicability of the formulas was verified and discussed. Kazmi [75] proposed an empirical formula between fiber admixture and post-peak behavior. In these studies, correlations between performance indicators and factors were investigated using linear or nonlinear regression models.
The strength calculation formula of BFRPC is obtained by fitting the test results of mechanical properties of BFRPC. The contribution of BF to compressive strength λ c and splitting tensile strength λ t were obtained by fitting the percentage increase in compressive strength and percentage increase in splitting tensile strength of BFRPC in 28 days, respectively. The calculation formula is shown in Figure 15. Since BF has a negative effect on BFRPC when it exceeds 2 kg/m 3 , according to the percentage of improvement of mechanical properties of BFRPC by the content of BF between 0 and 4 kg/m 3 . The strength calculation formula of BFRPC with BF content of 0-4 kg/m 3 is proposed:

BFRPC Strength Calculation Formula
Statistical and mathematical models have been applied to the study of cementitious composites. An increasing number of scholars have investigated concrete strength prediction models, of which regression analysis is the most widely used method. Gao [74] developed regression formula for compressive strength and critical strain for steel fiber reinforced recycled coarse aggregate concrete. Zhong [26] proposed formulas for calculating the manufactured sand RPC compressive strength and splitting tensile strength using regression analysis, and the applicability of the formulas was verified and discussed. Kazmi [75] proposed an empirical formula between fiber admixture and postpeak behavior. In these studies, correlations between performance indicators and factors were investigated using linear or nonlinear regression models.
The strength calculation formula of BFRPC is obtained by fitting the test results of mechanical properties of BFRPC. The contribution of BF to compressive strength λ and splitting tensile strength λ were obtained by fitting the percentage increase in compressive strength and percentage increase in splitting tensile strength of BFRPC in 28 days, respectively. The calculation formula is shown in Figure 15. Since BF has a negative effect on BFRPC when it exceeds 2 kg/m 3 , according to the percentage of improvement of mechanical properties of BFRPC by the content of BF between 0 and 4 kg/m 3 . The strength calculation formula of BFRPC with BF content of 0-4 kg/m 3 is proposed:

1
(1) In the formula: is 28-day compressive strength (MPa), λ is contribution rate of compressive strength with different BF content, is compressive strength when BF content is 0 kg/m 3 (MPa).

1
(2) In the formula: is 28-day splitting tensile strength (MPa), λ is contribution rate of splitting tensile strength with different BF content, is splitting tensile strength when BF content is 0 kg/m 3 (MPa).  In order to make the BFRPC strength calculation formula widely used, the prediction formula is used to calculate the strength of BFRPC with different BF content in this study. The calculation results and errors are shown in Table 6, and the comparison between the calculated value and the test value is shown in Figure 16. The maximum error between the calculated value of compressive strength and the test value is 2.59%, and the maximum error between the calculated value of splitting tensile strength and the test value is 6.95%, In the formula: f c is 28-day compressive strength (MPa), λ c is contribution rate of compressive strength with different BF content, f c0 is compressive strength when BF content is 0 kg/m 3 (MPa).
In the formula: f t is 28-day splitting tensile strength (MPa), λ t is contribution rate of splitting tensile strength with different BF content, f t0 is splitting tensile strength when BF content is 0 kg/m 3 (MPa).
In order to make the BFRPC strength calculation formula widely used, the prediction formula is used to calculate the strength of BFRPC with different BF content in this study. The calculation results and errors are shown in Table 6, and the comparison between the calculated value and the test value is shown in Figure 16. The maximum error between the calculated value of compressive strength and the test value is 2.59%, and the maximum error between the calculated value of splitting tensile strength and the test value is 6.95%, and the errors are all within 10%. Therefore, this calculation formula has certain reference value. and the errors are all within 10%. Therefore, this calculation formula has certain reference value.
(a) Compressive strength (b) Splitting tensile strength   [76,77]. The test results of Dong [76] and Shen [77] were encoded into Formula (1) for calculation to further verify the feasibility and applicability of the strength calculation formula. The comparison of calculated and experimental values is shown in Table 7. Only a few reports are available on the splitting tensile strength of BFRPC, and different BF sizes have a great impact on the splitting tensile strength. Therefore, other research results cannot be better used to verify the calculation formula.  [76] and Shen [77] were compared with those calculated by the calculation formula.  [76,77]. The test results of Dong [76] and Shen [77] were encoded into Formula (1) for calculation to further verify the feasibility and applicability of the strength calculation formula. The comparison of calculated and experimental values is shown in Table 7. Only a few reports are available on the splitting tensile strength of BFRPC, and different BF sizes have a great impact on the splitting tensile strength. Therefore, other research results cannot be better used to verify the calculation formula.
As shown in Figure 17, the calculation results obtained by using the BFRPC strength calculation formula are very close to the actual test results, and the error is very small, all within 15%, and the maximum error is 14.65%. Therefore, this model can better predict the mechanical properties of 28-day BFRPC, with BF content between 0-4 kg/m 3 and predict the strength of BFRPC in advance, according to the fiber content, which has a guiding role for the further research and application of BFRPC. predict the strength of BFRPC in advance, according to the fiber content, which has a guiding role for the further research and application of BFRPC.
(a) (b) Figure 17. The experimental results of (a) Dong [76] and (b) Shen [77] were compared with those calculated by the calculation formula.

Conclusions 
The strength of BFRPC tends to decrease when the BF content exceeds 2 kg/m 3 . When BF content is at 2 kg/m 3 , the 28-day compressive strength reaches 95.2 MPa and splitting tensile strength reaches 7.78 MPa.  BF can closely bond to the matrix without forming a transition zone. The energy of crack development is absorbed by the bridging and interfacial bond force, thus, effectively inhibiting the development of crack and improving the mechanical properties of BFRPC. However, when BF is added in excess, agglomeration and overlapping will occur and reduce the mechanical properties of BFRPC.  The incorporation of BF can improve the microstructure of BFRPC, reduce the size of particles and pores, and provide a uniform and plump morphology of particles and pores. When the BF content is 2 kg/m 3 , the particle area ratio and pore area ratio are the lowest. When the content of BF is too high, the internal porosity is increased due to the uneven mixing of the fiber. Based on the gray correlation analysis method, it was concluded that the particle area ratio and pore fraction dimension were the most correlated with the mechanical properties of BFRPC.  The strength calculation formula can be used to effectively obtain RPC compressive strength and splitting tensile strength with different BF content, so as to check whether the design fiber content can meet the target actual engineering requirements, and the fiber content can be flexibly selected, according to the required strength. This work serves as a reliable reference for the engineering application of BFRPC.  Limitation: Different fiber types, sizes, and curing methods have different effects on the mechanical properties of RPC. Therefore, the strength calculation formula proposed in this paper is only applicable when the raw materials and curing methods are the same as this study, and the calculated values for different materials and curing methods will have different degrees of deviation from the actual values, and the use of this method is not recommended.  Future direction: On the basis of this study, further research on the durability performance and damage mechanism of BFRPC is proposed to be carried out in the future to provide valuable references for improving structural safety and extending service life. Figure 17. The experimental results of (a) Dong [76] and (b) Shen [77] were compared with those calculated by the calculation formula.

Conclusions
• The strength of BFRPC tends to decrease when the BF content exceeds 2 kg/m 3 . When BF content is at 2 kg/m 3 , the 28-day compressive strength reaches 95.2 MPa and splitting tensile strength reaches 7.78 MPa. • BF can closely bond to the matrix without forming a transition zone. The energy of crack development is absorbed by the bridging and interfacial bond force, thus, effectively inhibiting the development of crack and improving the mechanical properties of BFRPC. However, when BF is added in excess, agglomeration and overlapping will occur and reduce the mechanical properties of BFRPC.

•
The incorporation of BF can improve the microstructure of BFRPC, reduce the size of particles and pores, and provide a uniform and plump morphology of particles and pores. When the BF content is 2 kg/m 3 , the particle area ratio and pore area ratio are the lowest. When the content of BF is too high, the internal porosity is increased due to the uneven mixing of the fiber. Based on the gray correlation analysis method, it was concluded that the particle area ratio and pore fraction dimension were the most correlated with the mechanical properties of BFRPC.

•
The strength calculation formula can be used to effectively obtain RPC compressive strength and splitting tensile strength with different BF content, so as to check whether the design fiber content can meet the target actual engineering requirements, and the fiber content can be flexibly selected, according to the required strength. This work serves as a reliable reference for the engineering application of BFRPC. • Limitation: Different fiber types, sizes, and curing methods have different effects on the mechanical properties of RPC. Therefore, the strength calculation formula proposed in this paper is only applicable when the raw materials and curing methods are the same as this study, and the calculated values for different materials and curing methods will have different degrees of deviation from the actual values, and the use of this method is not recommended.
• Future direction: On the basis of this study, further research on the durability performance and damage mechanism of BFRPC is proposed to be carried out in the future to provide valuable references for improving structural safety and extending service life.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author. The data are proprietary or confidential in nature and may only be provided with restrictions.