# Study on Mechanical Performance of ECC Reinforced by Polypropylene Fiber Mixed with Manufactured Sand and Carbon Black (CBMSPP-ECC) Based on Response Surface Method

Authors: Nixia Song; Min Song; Yunlong Zhang; Jing Wang
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

In order to study the mechanical performance of Engineered Cementitious Composites (ECCs) mixed with carbon black (CB), manufactured sand (MS), and polypropylene fiber (PPF), response surface methodology (RSM) was used to design the experiment, and three process variables including PPF content, fly ash content (FA), and CB content were selected as factors. The flexural strength, compressive strength, flexural-compressive ratio, and splitting tensile strength were used as four responses to study the mechanical performance. The prediction model indicates that there is a good correlation between the factors and the responses. Multiobjective optimization results show that the optimal content of the three factors is 2.4%, 58.48%, and 1.09%, respectively, for the carbon black, and manufactured sand of polypropylene fiber reinforced ECC development laid a foundation.


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## Body

## 1. Introduction

Traditional concrete has high brittleness [1] and poor toughness [2], which makes them less safe for structures bearing bending loads such as bridge decks and road surfaces. Scholars have adopted a variety of methods to reduce the cracking risk of concrete [3]. Engineered Cementitious Composites (ECCs) are a kind of ultra-high toughness fiber reinforced concrete developed in recent years. Through the internal balance between fiber and matrix, multiple cracks of smaller width can be formed in the loading process, which is one of the most important properties of this material [4]. With the continuous progress of technology, a variety of intelligent materials have emerged. By adding carbon-based materials into concrete, such as carbon fiber (CF) [5] and carbon nanotube (CNT) [6], researchers have achieved self-sensing performance, which helps us monitor the health status of the structure in real time.Since the advent of ECC, people have studied the composition characteristics and mix ratio of materials [7–9] through theoretical design methods [10, 11] to obtain an appropriate strain hardening response [12]. Abdulkadir et al. [13] studied the influence of polyvinyl alcohol fiber (PVAF) content and fly ash (FA) content on the performance of self-compacting ECC, and the results showed that the increase of PVAF content led to the deterioration of the working performance of the mixture, while the increase of FA content had the opposite effect. Cui et al. [7] studied the role of bagasse ash (SCBA) as a partial or complete substitute for silica sand in engineered cementing composites (ECCs). With the addition of SCBA, the compressive strength of ECCs decreased slightly (up to 11%), but the tensile strength, especially the tensile ductility, increased significantly (22.3% and 311%, respectively) due to the volcanic ash and/or filling effect of SCBA. In recent years, research has mainly focused on the realization of self-sensing performance. Ali al-Dahawi et al. [14] studied the ECC self-sensing ability of different carbon-based materials during repeated loading and unloading cycles within the elastic-plastic range. The results show that the self-perception of loading in elastic and plastic range is successful, but the self-perception of unloading in the elastic range is not successful. Compared with other carbon-based materials, CF is the most effective self-sensing method for elastic-plastic cyclic loading and unloading in the production process of ECC. Sahmaran et al. [15] studied the self-sensing behavior of cube and prismatic specimens subjected to monotonic uniaxial compression and cyclic bending loads. The results show that the carbon-based materials CF and CNT prove their value in capturing compression damage changes, and the electrical measurements after unloading are significantly reversible.In order to realize large-scale engineering application of self-sensing ECC, from the perspective of material economy, domestic polypropylene fiber (PPF) was used instead of imported polyvinyl alcohol fiber coated with oil, using manufactured sand (MS) that is rich in raw materials, to explore the possibility of preparing ECC. In order to make the specimen have self-sensing performance, carbon black was added into the concrete. Through the experiment, whether its mechanical properties meet the engineering needs was discussed.


## 2. Experimental Program

### 2.1. Materials and Methods

CB was used as conductive material (as shown in Figure1(a)), apparent specific volume was 17 ml/g, and Portland cement of P. II 42.5 was used. Relevant parameters of cement and FA are shown in Table 1, and related parameters of PPF (as shown in Figure 1(b)) are shown in Table 2. MS (as shown in Figure 1(c)) was a single particle size (40 mesh), and a high-performance polycarboxylic acid water-reducing agent with a water-reducing efficiency of 28% was used.Figure 1
Carbon black (a), polypropylene fiber (b), and manufactured sand (c).
(a)(b)(c)Table 1
Physical properties and chemical composition of cement.
NameFinenessStrength activity index (%)Specific surface area (m2/kg)Ignition loss (%)MgO (%)SO3 (%)Cl−(%)Insoluble (%)Grinding aid (%)Cement3621.720.992.560.0080.90.03Fly ash14.2740.770.1Table 2
The properties of PPF.
Diameter (μm)Length (mm)Density (g/mm3)Breaking strength (MPa)Breaking elongation (%)Melting point (°C)20120.9168018165


### 2.2. Mixture Proportioning and Mixing

The Box-Behnken design (BBD) in RSM was used to design 17 groups of mixture ratios with PPF content (1.5%, 2%, and 2.5%), FA content (45%, 60%, and 75%), and CB content (0.3%, 0.7%, and 1.1%) as three technological variables. The flexural strength (R1), compressive strength (R2), flexural ratio (R3), and splitting tensile strength (R4) were taken as four responses.For convenient operation in the project promotion, test all dry materials (cement, FA, MS, CB, and PPF), do stir for 2 minutes, and stir in a mixture of water and high-efficiency water-reducing agent, for 6 to 8 minutesuntil the reunion phenomenon PPF disappears.


### 2.3. Specimen Preparation and Testing

After mixing is finished, the mixture was poured into the molds. The specimen was kept in the mold for 48 hours before demolding and then removed from the mold and cured under normal indoor air conditions. The samples were covered with plastic film, treated with water, and tested at about 28 days of age.The main purpose of this study is to evaluate the mechanical performance of the CBMSPP-ECC. WAW-600 microcomputer-controlled electro-hydraulic servo universal testing machine was used for loading. The loading diagram is shown in Figure2. The test method and specimen size are as follows.Figure 2
Loading diagram of test methods for flexural strength (a) and splitting strength (b).
(a)(b)Flexural strength is measured by the central loading method described in standard GB/T17671-1999 [16]. Three specimens with the size of 40 mm × 40 mm × 160 mm in each group were tested. The loading speed was set at 50 N/s. The average of the three measurements was determined as the flexural strength. Its strength value is calculated according to the following formula:(1)Rf=1.5Ff×Lb3,where Rf is the flexural strength (MPa); Ff is the failure load (N); L is the distance between the two bearings (mm); and b is the side length of the square section of the specimen (40 mm).Compressive strength is measured according to the standard GB/T17671-1999 [16]. The blocks obtained after the bending test (six in each group) were used for the compression test. The loading speed was set at 2.5 KN/s. The average of the six test results was considered to be the compressive strength. Its strength value is calculated according to following formula:(2)Rc=FcA,where Rc is the compressive strength (MPa); Fc is the compressive failure load (N); and A is the compression area of the specimen (40 mm × 40 mm).Splitting tensile strength is referred to GB/T50081-2002 [17]. Three specimens with the size of 100 mm ×  100 mm × 100 mm in each group were tested. Circular arc pads and pads were placed between the upper and lower pressing plates of the press and between the specimens and loaded to failure at the speed of 0.08 MPa/s. The average value of the three test results was taken as the splitting tensile strength.


### 2.4. Box-Behnken Design (BBD)

BBD is a response surface design that can evaluate nonlinear relationships between responses and factors. In the case of the same number of experimental factors, it takes less experimental time and is more economical and effective [18].BBD was established using Design-expert 12® software. Three factors were taken as variables: PPF content (A), FA content (B), and CB content (C). The flexural strength (R1), compressive strength (R2), flexural-compressive ratio (R3), and splitting tensile strength (R4) of the mixture were set as response variables, shown in Tables3 and 4. A response surface model with 17 experimental points, 12 factorial factors, and 5 central points was established.Table 3
The level of experimental factors.
SymbolFactorsActual value (%)Code valueAPPF content1.52%2.5%−101BFA content4060%80%−101CCB content0.30.7%1.1%−101Table 4
Experimental factors and response results of BBD matrix design.
Mix numberVariable code and levelResponse valueStdABCR1: flexural strength (MPa)R2: compressive strength (MPa)R3: flexural-compressive ratio (%)R4: splitting tensile strength (MPa)1−1−108.2458.8914.008.8921−1010.6246.6222.786.433−1107.1637.4919.115.58411011.0532.9533.535.325−10−18.9029.6130.054.73610−110.1338.1026.575.577−10110.7370.7815.159.01810115.4171.7521.488.9990−1−17.0748.0414.726.901001−18.4523.9335.294.41110−1111.7067.8617.2510.181201112.0452.8022.805.921300012.8170.2118.257.051400013.2369.7918.966.851500013.0863.9820.449.301600012.7369.3418.367.641700010.8768.6915.827.23


## 2.1. Materials and Methods

CB was used as conductive material (as shown in Figure1(a)), apparent specific volume was 17 ml/g, and Portland cement of P. II 42.5 was used. Relevant parameters of cement and FA are shown in Table 1, and related parameters of PPF (as shown in Figure 1(b)) are shown in Table 2. MS (as shown in Figure 1(c)) was a single particle size (40 mesh), and a high-performance polycarboxylic acid water-reducing agent with a water-reducing efficiency of 28% was used.Figure 1
Carbon black (a), polypropylene fiber (b), and manufactured sand (c).
(a)(b)(c)Table 1
Physical properties and chemical composition of cement.
NameFinenessStrength activity index (%)Specific surface area (m2/kg)Ignition loss (%)MgO (%)SO3 (%)Cl−(%)Insoluble (%)Grinding aid (%)Cement3621.720.992.560.0080.90.03Fly ash14.2740.770.1Table 2
The properties of PPF.
Diameter (μm)Length (mm)Density (g/mm3)Breaking strength (MPa)Breaking elongation (%)Melting point (°C)20120.9168018165


## 2.2. Mixture Proportioning and Mixing

The Box-Behnken design (BBD) in RSM was used to design 17 groups of mixture ratios with PPF content (1.5%, 2%, and 2.5%), FA content (45%, 60%, and 75%), and CB content (0.3%, 0.7%, and 1.1%) as three technological variables. The flexural strength (R1), compressive strength (R2), flexural ratio (R3), and splitting tensile strength (R4) were taken as four responses.For convenient operation in the project promotion, test all dry materials (cement, FA, MS, CB, and PPF), do stir for 2 minutes, and stir in a mixture of water and high-efficiency water-reducing agent, for 6 to 8 minutesuntil the reunion phenomenon PPF disappears.


## 2.3. Specimen Preparation and Testing

After mixing is finished, the mixture was poured into the molds. The specimen was kept in the mold for 48 hours before demolding and then removed from the mold and cured under normal indoor air conditions. The samples were covered with plastic film, treated with water, and tested at about 28 days of age.The main purpose of this study is to evaluate the mechanical performance of the CBMSPP-ECC. WAW-600 microcomputer-controlled electro-hydraulic servo universal testing machine was used for loading. The loading diagram is shown in Figure2. The test method and specimen size are as follows.Figure 2
Loading diagram of test methods for flexural strength (a) and splitting strength (b).
(a)(b)Flexural strength is measured by the central loading method described in standard GB/T17671-1999 [16]. Three specimens with the size of 40 mm × 40 mm × 160 mm in each group were tested. The loading speed was set at 50 N/s. The average of the three measurements was determined as the flexural strength. Its strength value is calculated according to the following formula:(1)Rf=1.5Ff×Lb3,where Rf is the flexural strength (MPa); Ff is the failure load (N); L is the distance between the two bearings (mm); and b is the side length of the square section of the specimen (40 mm).Compressive strength is measured according to the standard GB/T17671-1999 [16]. The blocks obtained after the bending test (six in each group) were used for the compression test. The loading speed was set at 2.5 KN/s. The average of the six test results was considered to be the compressive strength. Its strength value is calculated according to following formula:(2)Rc=FcA,where Rc is the compressive strength (MPa); Fc is the compressive failure load (N); and A is the compression area of the specimen (40 mm × 40 mm).Splitting tensile strength is referred to GB/T50081-2002 [17]. Three specimens with the size of 100 mm ×  100 mm × 100 mm in each group were tested. Circular arc pads and pads were placed between the upper and lower pressing plates of the press and between the specimens and loaded to failure at the speed of 0.08 MPa/s. The average value of the three test results was taken as the splitting tensile strength.


## 2.4. Box-Behnken Design (BBD)

BBD is a response surface design that can evaluate nonlinear relationships between responses and factors. In the case of the same number of experimental factors, it takes less experimental time and is more economical and effective [18].BBD was established using Design-expert 12® software. Three factors were taken as variables: PPF content (A), FA content (B), and CB content (C). The flexural strength (R1), compressive strength (R2), flexural-compressive ratio (R3), and splitting tensile strength (R4) of the mixture were set as response variables, shown in Tables3 and 4. A response surface model with 17 experimental points, 12 factorial factors, and 5 central points was established.Table 3
The level of experimental factors.
SymbolFactorsActual value (%)Code valueAPPF content1.52%2.5%−101BFA content4060%80%−101CCB content0.30.7%1.1%−101Table 4
Experimental factors and response results of BBD matrix design.
Mix numberVariable code and levelResponse valueStdABCR1: flexural strength (MPa)R2: compressive strength (MPa)R3: flexural-compressive ratio (%)R4: splitting tensile strength (MPa)1−1−108.2458.8914.008.8921−1010.6246.6222.786.433−1107.1637.4919.115.58411011.0532.9533.535.325−10−18.9029.6130.054.73610−110.1338.1026.575.577−10110.7370.7815.159.01810115.4171.7521.488.9990−1−17.0748.0414.726.901001−18.4523.9335.294.41110−1111.7067.8617.2510.181201112.0452.8022.805.921300012.8170.2118.257.051400013.2369.7918.966.851500013.0863.9820.449.301600012.7369.3418.367.641700010.8768.6915.827.23


## 3. Results and Discussion

### 3.1. Analysis of Mechanical Properties

#### 3.1.1. Flexural Strength of Different Mixing Ratios

The flexural strength values of 17 groups of CBMSPP-ECC with different proportions are shown in Table4. It can be seen that the 28 d flexural strength is between 7.07–15.41 MPa.As can be seen from the histogram of Figure3, the increase of PPF content leads to an increase of the flexural strength of the specimen. This is because when the load reaches the cracking load of the concrete matrix, the ultimate load of specimens increases with the increase of internal PPF. As mentioned above, the increase of FA content will lead to a decrease of specimen strength. With the increase of CB and FA content, the fluidity becomes better, the internal pores are reduced [19], the bond between fiber and matrix is enhanced, and the flexural strength of the specimen increases.Figure 3
Flexural strength of CBMSPP-ECC with different proportions.Figure4 shows the appearance of the specimen after flexural failure. After reaching flexural strength, no brittle fracture occurs and the specimen has a complete appearance, which can greatly protect the integrity of the structure.Figure 4
Appearance of the specimen with flexural failure resistance.Starting after loading, the load increases linearly. After reaching the initial crack load of the specimen, the first crack was produced. Then, the load began to grow slowly. Then, fiber transferred the load to the sides. The surface of the specimen produced the phenomenon of multiple cracks.


#### 3.1.2. Compressive Strength of Different Mixing Ratios

As can be seen in Table4, the 28-d compressive strength of CBMSPP-ECC prepared by the test is 23.93–71.75 MPa.As can be seen from the histogram of Figure5, the compressive strength of specimens decreases with the increase of PPF content. This is because the addition of fibers introduces pores into the concrete matrix, which leads to reduction of specimen strength. With the increase of FA content, the compressive strength also shows a decreasing trend. This is because the reaction of FA volcanic ash is slow, FA has not yet fully reacted. As a result, the higher the FA content, the lower the compressive strength at 28 d. When the content of CB increases, the compressive strength of the specimen tends to increase, which may be because CB dissolved in water makes the matrix oily and has better fluidity, which reduces the internal pores, and the compressive strength of the specimen increases.Figure 5
Compressive strength of specimens with different mixing ratios.Figure6 shows the appearance of the specimen under compression failure of CBMSPP-ECC. It is found that no obvious cracks appear on the surface of the specimen even after the failure load is reached. In addition, in the test process, it was found that several groups of specimens showed the phenomenon of “Continuous compression without obvious failure load” in the loading process, as shown in Figures 7(a) and 7(b). In other words, under the action of continuous pressure, the specimen height continues to be compressed and the load continues to rise, but there is no final failure load, which has never been seen in the literature. It also reflected the good toughness and flexibility of the specimens. When calculating the strength, the load value corresponding to the platform stage on the failure process curve is taken as the failure load to calculate the compressive strength of the specimen.Figure 6
Appearance and curves of specimens under compressive failure in normal experimental group.Figure 7
Specimen appearance and curve of the experimental group of “Continuous compression without obvious failure load.”
(a)(b)


#### 3.1.3. Flexural-Compression Ratio of Different Mixing Ratio

According to the above values of flexural strength and compressive strength, the flexural pressure is calculated as shown in Table4. The flexural ratio of this test is 14–35.29%, which is expressed as a histogram as shown in Figure 8. The variation trend is consistent with the flexural strength.Figure 8
Flexural-compression ratio of different mixing ratios.


#### 3.1.4. Splitting Tensile Strength of Different Mixing Ratios

The splitting tensile strength test results of 17 groups of mix ratio are shown in Table4, and the histogram is drawn as shown in Figure 9. The splitting tensile strength of the CBMSPP-ECC prepared by the test is between 4.41–10.18 MPa, and its failure mode is shown in Figure 10. After the specimens reach the failure load, there is no obvious failure of the specimens, only a few small cracks on the surface of the specimens, which benefits from a good bond between the fiber and the matrix [20]. It is conducive to the safety of the structure.Figure 9
Splitting tensile strength of different mixing ratios.Figure 10
Appearance of split tensile failure specimen.


### 3.2. Establishment and Analysis of Response Surface Model

#### 3.2.1. Influence of Various Factors on the Mechanical Properties of CBMSPP-ECC

The response surface models were established by multiple regression analysis in Design-Expert 12® software. The final equation is determined based on four practical factors of response:(3)InR1=−2.74+1.12A+0.12B+0.58C+0.006AB+0.29AC−0.006BC−0.35A2−0.001B2−0.24C2,InR2=−2.54+3.04A+0.11B+1.56C+0.003AB−0.298AC+0.019BC−0.77A2−0.001B2−0.89C2,SqrtR3=2.44−0.99A+0.05B+0.11C+0.01AB+1.37AC−0.06BC,InR4=0.44+0.55A+0.025B+1.59C+0.009AB−0.205AC−0.004BC−0.25A2+0.000451B2−0.28C2.Figure11(a) shows the contour plot of flexural strength (R1). FA content (B) is denser than PPF content (A), which is steeper in the 3D graph (Figure 11(b)), indicating that the B factor has a greater influence on R1. Flexural strength increased with the increase of the content of FA to reduce after. This is because FA makes the matrix better fluidity and internal porosity decreases [21]. This makes the fiber bond better with the concrete. However, the excessive reaction of FA due to its slow ash makes concrete strength reduced, so within the scope of the test, there exists an optimal content of FA.Figure 11
Contour plot of flexural strength. (a) R1. (b) 3D graph of R1.
(a)(b)Figure12(a) shows the contour plot of the compressive strength (R2). FA content (B) is denser than PPF content (A), showing a steeper 3D graph (Figure 12(b)), indicating that factor B has a greater influence on R2. Compressive strength increased with the increase of the content of fly ash to reduce after; this is because FA improves the fluidity of the matrix, reduces the internal pores, and improves the compressive strength. Due to the slow pozzolanic reaction, a large amount of unreflected FA exists in the mixture that makes concrete strength reduced.Figure 12
Contour plot of compressive strength. (a) R2. (b) 3D graph of R2.
(a)(b)Figure13(a) shows the contour plot of the flexural-compressive ratio (R3). FA content (B) is denser than PPF content (A), which is steeper in the 3D graph (as shown in Figure 13(b)), indicating that the B factor has a greater influence on R3. The flexural-compressive ratio is a parameter related to flexural strength and compressive strength, so its change and mechanism are consistent with the latter two.Figure 13
Contour plot of flexural-compressive ratio. (a) R3 and (b) 3D graph of R3.
(a)(b)Figure14(a) shows the contour plot of splitting tensile strength (R4). FA content (B) is denser than PPF content (A), which is steeper in the 3D graph (Figure 14(b)), indicating that the B factor has a greater influence on R4. It can be seen that with the increase of PPF content, the splitting tensile strength decreases because the addition of excessive PPF leads to the existence of a large number of pores in the matrix, which weaken the bond between the fiber and the matrix and affect the function of the fiber. In other words, excessive PPF is not conducive to splitting tensile strength.Figure 14
Contour plot of splitting tensile strength. (a) R4 and (b) 3D graph of R4.
(a)(b)


## 3.1. Analysis of Mechanical Properties

### 3.1.1. Flexural Strength of Different Mixing Ratios

The flexural strength values of 17 groups of CBMSPP-ECC with different proportions are shown in Table4. It can be seen that the 28 d flexural strength is between 7.07–15.41 MPa.As can be seen from the histogram of Figure3, the increase of PPF content leads to an increase of the flexural strength of the specimen. This is because when the load reaches the cracking load of the concrete matrix, the ultimate load of specimens increases with the increase of internal PPF. As mentioned above, the increase of FA content will lead to a decrease of specimen strength. With the increase of CB and FA content, the fluidity becomes better, the internal pores are reduced [19], the bond between fiber and matrix is enhanced, and the flexural strength of the specimen increases.Figure 3
Flexural strength of CBMSPP-ECC with different proportions.Figure4 shows the appearance of the specimen after flexural failure. After reaching flexural strength, no brittle fracture occurs and the specimen has a complete appearance, which can greatly protect the integrity of the structure.Figure 4
Appearance of the specimen with flexural failure resistance.Starting after loading, the load increases linearly. After reaching the initial crack load of the specimen, the first crack was produced. Then, the load began to grow slowly. Then, fiber transferred the load to the sides. The surface of the specimen produced the phenomenon of multiple cracks.


### 3.1.2. Compressive Strength of Different Mixing Ratios

As can be seen in Table4, the 28-d compressive strength of CBMSPP-ECC prepared by the test is 23.93–71.75 MPa.As can be seen from the histogram of Figure5, the compressive strength of specimens decreases with the increase of PPF content. This is because the addition of fibers introduces pores into the concrete matrix, which leads to reduction of specimen strength. With the increase of FA content, the compressive strength also shows a decreasing trend. This is because the reaction of FA volcanic ash is slow, FA has not yet fully reacted. As a result, the higher the FA content, the lower the compressive strength at 28 d. When the content of CB increases, the compressive strength of the specimen tends to increase, which may be because CB dissolved in water makes the matrix oily and has better fluidity, which reduces the internal pores, and the compressive strength of the specimen increases.Figure 5
Compressive strength of specimens with different mixing ratios.Figure6 shows the appearance of the specimen under compression failure of CBMSPP-ECC. It is found that no obvious cracks appear on the surface of the specimen even after the failure load is reached. In addition, in the test process, it was found that several groups of specimens showed the phenomenon of “Continuous compression without obvious failure load” in the loading process, as shown in Figures 7(a) and 7(b). In other words, under the action of continuous pressure, the specimen height continues to be compressed and the load continues to rise, but there is no final failure load, which has never been seen in the literature. It also reflected the good toughness and flexibility of the specimens. When calculating the strength, the load value corresponding to the platform stage on the failure process curve is taken as the failure load to calculate the compressive strength of the specimen.Figure 6
Appearance and curves of specimens under compressive failure in normal experimental group.Figure 7
Specimen appearance and curve of the experimental group of “Continuous compression without obvious failure load.”
(a)(b)


### 3.1.3. Flexural-Compression Ratio of Different Mixing Ratio

According to the above values of flexural strength and compressive strength, the flexural pressure is calculated as shown in Table4. The flexural ratio of this test is 14–35.29%, which is expressed as a histogram as shown in Figure 8. The variation trend is consistent with the flexural strength.Figure 8
Flexural-compression ratio of different mixing ratios.


### 3.1.4. Splitting Tensile Strength of Different Mixing Ratios

The splitting tensile strength test results of 17 groups of mix ratio are shown in Table4, and the histogram is drawn as shown in Figure 9. The splitting tensile strength of the CBMSPP-ECC prepared by the test is between 4.41–10.18 MPa, and its failure mode is shown in Figure 10. After the specimens reach the failure load, there is no obvious failure of the specimens, only a few small cracks on the surface of the specimens, which benefits from a good bond between the fiber and the matrix [20]. It is conducive to the safety of the structure.Figure 9
Splitting tensile strength of different mixing ratios.Figure 10
Appearance of split tensile failure specimen.


## 3.1.1. Flexural Strength of Different Mixing Ratios

The flexural strength values of 17 groups of CBMSPP-ECC with different proportions are shown in Table4. It can be seen that the 28 d flexural strength is between 7.07–15.41 MPa.As can be seen from the histogram of Figure3, the increase of PPF content leads to an increase of the flexural strength of the specimen. This is because when the load reaches the cracking load of the concrete matrix, the ultimate load of specimens increases with the increase of internal PPF. As mentioned above, the increase of FA content will lead to a decrease of specimen strength. With the increase of CB and FA content, the fluidity becomes better, the internal pores are reduced [19], the bond between fiber and matrix is enhanced, and the flexural strength of the specimen increases.Figure 3
Flexural strength of CBMSPP-ECC with different proportions.Figure4 shows the appearance of the specimen after flexural failure. After reaching flexural strength, no brittle fracture occurs and the specimen has a complete appearance, which can greatly protect the integrity of the structure.Figure 4
Appearance of the specimen with flexural failure resistance.Starting after loading, the load increases linearly. After reaching the initial crack load of the specimen, the first crack was produced. Then, the load began to grow slowly. Then, fiber transferred the load to the sides. The surface of the specimen produced the phenomenon of multiple cracks.


## 3.1.2. Compressive Strength of Different Mixing Ratios

As can be seen in Table4, the 28-d compressive strength of CBMSPP-ECC prepared by the test is 23.93–71.75 MPa.As can be seen from the histogram of Figure5, the compressive strength of specimens decreases with the increase of PPF content. This is because the addition of fibers introduces pores into the concrete matrix, which leads to reduction of specimen strength. With the increase of FA content, the compressive strength also shows a decreasing trend. This is because the reaction of FA volcanic ash is slow, FA has not yet fully reacted. As a result, the higher the FA content, the lower the compressive strength at 28 d. When the content of CB increases, the compressive strength of the specimen tends to increase, which may be because CB dissolved in water makes the matrix oily and has better fluidity, which reduces the internal pores, and the compressive strength of the specimen increases.Figure 5
Compressive strength of specimens with different mixing ratios.Figure6 shows the appearance of the specimen under compression failure of CBMSPP-ECC. It is found that no obvious cracks appear on the surface of the specimen even after the failure load is reached. In addition, in the test process, it was found that several groups of specimens showed the phenomenon of “Continuous compression without obvious failure load” in the loading process, as shown in Figures 7(a) and 7(b). In other words, under the action of continuous pressure, the specimen height continues to be compressed and the load continues to rise, but there is no final failure load, which has never been seen in the literature. It also reflected the good toughness and flexibility of the specimens. When calculating the strength, the load value corresponding to the platform stage on the failure process curve is taken as the failure load to calculate the compressive strength of the specimen.Figure 6
Appearance and curves of specimens under compressive failure in normal experimental group.Figure 7
Specimen appearance and curve of the experimental group of “Continuous compression without obvious failure load.”
(a)(b)


## 3.1.3. Flexural-Compression Ratio of Different Mixing Ratio

According to the above values of flexural strength and compressive strength, the flexural pressure is calculated as shown in Table4. The flexural ratio of this test is 14–35.29%, which is expressed as a histogram as shown in Figure 8. The variation trend is consistent with the flexural strength.Figure 8
Flexural-compression ratio of different mixing ratios.


## 3.1.4. Splitting Tensile Strength of Different Mixing Ratios

The splitting tensile strength test results of 17 groups of mix ratio are shown in Table4, and the histogram is drawn as shown in Figure 9. The splitting tensile strength of the CBMSPP-ECC prepared by the test is between 4.41–10.18 MPa, and its failure mode is shown in Figure 10. After the specimens reach the failure load, there is no obvious failure of the specimens, only a few small cracks on the surface of the specimens, which benefits from a good bond between the fiber and the matrix [20]. It is conducive to the safety of the structure.Figure 9
Splitting tensile strength of different mixing ratios.Figure 10
Appearance of split tensile failure specimen.


## 3.2. Establishment and Analysis of Response Surface Model

### 3.2.1. Influence of Various Factors on the Mechanical Properties of CBMSPP-ECC

The response surface models were established by multiple regression analysis in Design-Expert 12® software. The final equation is determined based on four practical factors of response:(3)InR1=−2.74+1.12A+0.12B+0.58C+0.006AB+0.29AC−0.006BC−0.35A2−0.001B2−0.24C2,InR2=−2.54+3.04A+0.11B+1.56C+0.003AB−0.298AC+0.019BC−0.77A2−0.001B2−0.89C2,SqrtR3=2.44−0.99A+0.05B+0.11C+0.01AB+1.37AC−0.06BC,InR4=0.44+0.55A+0.025B+1.59C+0.009AB−0.205AC−0.004BC−0.25A2+0.000451B2−0.28C2.Figure11(a) shows the contour plot of flexural strength (R1). FA content (B) is denser than PPF content (A), which is steeper in the 3D graph (Figure 11(b)), indicating that the B factor has a greater influence on R1. Flexural strength increased with the increase of the content of FA to reduce after. This is because FA makes the matrix better fluidity and internal porosity decreases [21]. This makes the fiber bond better with the concrete. However, the excessive reaction of FA due to its slow ash makes concrete strength reduced, so within the scope of the test, there exists an optimal content of FA.Figure 11
Contour plot of flexural strength. (a) R1. (b) 3D graph of R1.
(a)(b)Figure12(a) shows the contour plot of the compressive strength (R2). FA content (B) is denser than PPF content (A), showing a steeper 3D graph (Figure 12(b)), indicating that factor B has a greater influence on R2. Compressive strength increased with the increase of the content of fly ash to reduce after; this is because FA improves the fluidity of the matrix, reduces the internal pores, and improves the compressive strength. Due to the slow pozzolanic reaction, a large amount of unreflected FA exists in the mixture that makes concrete strength reduced.Figure 12
Contour plot of compressive strength. (a) R2. (b) 3D graph of R2.
(a)(b)Figure13(a) shows the contour plot of the flexural-compressive ratio (R3). FA content (B) is denser than PPF content (A), which is steeper in the 3D graph (as shown in Figure 13(b)), indicating that the B factor has a greater influence on R3. The flexural-compressive ratio is a parameter related to flexural strength and compressive strength, so its change and mechanism are consistent with the latter two.Figure 13
Contour plot of flexural-compressive ratio. (a) R3 and (b) 3D graph of R3.
(a)(b)Figure14(a) shows the contour plot of splitting tensile strength (R4). FA content (B) is denser than PPF content (A), which is steeper in the 3D graph (Figure 14(b)), indicating that the B factor has a greater influence on R4. It can be seen that with the increase of PPF content, the splitting tensile strength decreases because the addition of excessive PPF leads to the existence of a large number of pores in the matrix, which weaken the bond between the fiber and the matrix and affect the function of the fiber. In other words, excessive PPF is not conducive to splitting tensile strength.Figure 14
Contour plot of splitting tensile strength. (a) R4 and (b) 3D graph of R4.
(a)(b)


## 3.2.1. Influence of Various Factors on the Mechanical Properties of CBMSPP-ECC

The response surface models were established by multiple regression analysis in Design-Expert 12® software. The final equation is determined based on four practical factors of response:(3)InR1=−2.74+1.12A+0.12B+0.58C+0.006AB+0.29AC−0.006BC−0.35A2−0.001B2−0.24C2,InR2=−2.54+3.04A+0.11B+1.56C+0.003AB−0.298AC+0.019BC−0.77A2−0.001B2−0.89C2,SqrtR3=2.44−0.99A+0.05B+0.11C+0.01AB+1.37AC−0.06BC,InR4=0.44+0.55A+0.025B+1.59C+0.009AB−0.205AC−0.004BC−0.25A2+0.000451B2−0.28C2.Figure11(a) shows the contour plot of flexural strength (R1). FA content (B) is denser than PPF content (A), which is steeper in the 3D graph (Figure 11(b)), indicating that the B factor has a greater influence on R1. Flexural strength increased with the increase of the content of FA to reduce after. This is because FA makes the matrix better fluidity and internal porosity decreases [21]. This makes the fiber bond better with the concrete. However, the excessive reaction of FA due to its slow ash makes concrete strength reduced, so within the scope of the test, there exists an optimal content of FA.Figure 11
Contour plot of flexural strength. (a) R1. (b) 3D graph of R1.
(a)(b)Figure12(a) shows the contour plot of the compressive strength (R2). FA content (B) is denser than PPF content (A), showing a steeper 3D graph (Figure 12(b)), indicating that factor B has a greater influence on R2. Compressive strength increased with the increase of the content of fly ash to reduce after; this is because FA improves the fluidity of the matrix, reduces the internal pores, and improves the compressive strength. Due to the slow pozzolanic reaction, a large amount of unreflected FA exists in the mixture that makes concrete strength reduced.Figure 12
Contour plot of compressive strength. (a) R2. (b) 3D graph of R2.
(a)(b)Figure13(a) shows the contour plot of the flexural-compressive ratio (R3). FA content (B) is denser than PPF content (A), which is steeper in the 3D graph (as shown in Figure 13(b)), indicating that the B factor has a greater influence on R3. The flexural-compressive ratio is a parameter related to flexural strength and compressive strength, so its change and mechanism are consistent with the latter two.Figure 13
Contour plot of flexural-compressive ratio. (a) R3 and (b) 3D graph of R3.
(a)(b)Figure14(a) shows the contour plot of splitting tensile strength (R4). FA content (B) is denser than PPF content (A), which is steeper in the 3D graph (Figure 14(b)), indicating that the B factor has a greater influence on R4. It can be seen that with the increase of PPF content, the splitting tensile strength decreases because the addition of excessive PPF leads to the existence of a large number of pores in the matrix, which weaken the bond between the fiber and the matrix and affect the function of the fiber. In other words, excessive PPF is not conducive to splitting tensile strength.Figure 14
Contour plot of splitting tensile strength. (a) R4 and (b) 3D graph of R4.
(a)(b)


## 4. Optimization of the Content of the Three Factors

In this study, compromise optimization was carried out for the four responses, and multiobjective optimization technology of RSM was used to find the optimal content of the three factors to maximize the response value. The definition of factors and responses in the optimization process is shown in Table5. Based on the multiobjective optimization process, relatively close solutions satisfying predetermined upper and lower limits are obtained as shown in Figure 15.Table 5
Definition of factors and responses in the process of multiobjective optimization.
Factors and responsesGoalLower limitUpper limitImportancePPF content (%)In the range1.52.5FA content (%)In the range4575CB content (%)In the range0.31.1Flexural strength (MPa)Maximum7.0715.415Compressive strength (MPa)Maximum23.9371.745Flexural-compressive strength (%)Maximum13.9935.295Splitting tensile strength (MPa)Maximum4.4110.185Figure 15
Change of expected value function based on the multiobjective optimization process.


## 5. Conclusion

Based on BBD in RSM, the mechanical performance of ECC mixed with CB, MS, and PPF was tested in this paper, and the following conclusions were drawn:(1)
It is feasible to prepare ECC by MS instead of natural sand. The addition of CB has no obvious adverse effect on mechanical performance, and the material is flexible according to the failure form of the compression test. Increasing fly ash content has adverse effects on compressive strength and has positive effects on flexural strength and flexural ratio.(2)
Four response models were established, and the accuracy of four models was verified by analysis of variance. In addition, the relation equation between response and factors is obtained. This is conducive to the construction according to the actual requirements of the project.(3)
Based on RSM multiobjective optimization technology, the optimal PPF content (A), FA content (B), and CB content are 2.4%, 58.48%, and 1.09%, respectively. The predicted flexural strength (R1), compressive strength (R2), flexural ratio (R3), and split tensile strength (R4) were 16.09 MPa, 68.88 MPa, 22.08%, and 8.38 MPa, respectively.



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*Source: 8228228-2022-04-20.xml*