# Optimized Design of Polyethylene Fiber-Engineered Cementitious Composite Mix Ratio Based on the Analytic Hierarchy Process

Authors: Fengxia Han; Qing Liu; Xin Guo; Yanfeng Niu
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

Finding a method to optimize the design of the polyethylene fiber-engineered cementitious composite (PE-ECC) mix proportion is an urgent endeavor. The analytic hierarchy process (AHP) is an efficient decision-making tool for complicated problems with multiple variables and uncertainties. In this study, initial cracking strength, ultimate tensile strength, tensile displacement, and test age, as influencing factors of the PE-ECC optimum mix design were considered. The weightings of the factors were quantified through the AHP method according to the tensile test results of 14 groups of specimens with different mix proportions. The water to binder ratios (0.25, 0.27, 0.29, 0.31), the mineral admixtures (30%, 40%, 50%, and 60%), and the PE ratio (2%) were the three main test parameters for the factors of the PE-ECC tensile properties. The weight of each influence factor was calculated by constructing a matrix, which confirmed that the judgment matrix satisfies the consistency test. The optimum mixture ratio of 30% fly ash and 0.27 water-binder ratio were obtained. The results demonstrate the applicability and rationality of the AHP theory. The findings from this study can be used as a guideline for the optimized design of PE-ECC mix proportions.


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## Body

## 1. Introduction

Concrete is a widely used engineering material. However, this material reduces the carrying capacity of reinforced concrete due to its weak cracking resistance caused by temperature and shrinkage [1]. Furthermore, some flaws exist in ordinary concrete, including low tensile strength, large weight, and high brittleness. Some concrete structures are subject to damage because of freezing and thaw cycles, water penetration, and steel corrosion, and the flaws eventually increase the labor and cost needed to repair reinforced concrete structures [2]. Thus, the performance of concrete should be improved to alleviate the concrete’s deficiencies. To improve the deformability and crack resistance of concrete under loading, researchers have studied cement-based composites for the past 20 years [3]. The engineered cementitious composite (ECC), a new type of concrete material with high-performance fiber-reinforced cement-based composites, entails many excellent properties and offers potential application in improving the working performance of concrete structures. Numerous research has been conducted on the basic mechanical properties of ECC [4–8]. For instance, the tensile strain capability of ECC has been analyzed; it usually exceeds 3% and can effectively control the corresponding crack widths of less than 100 μm and crack spacing between 1 and 2 mm. Moreover, ECC can maintain much lower crack widths for a long time after cracking. ECC also possesses many other excellent properties, such as high ductility, structural integrity, and super-high toughness, and plasticity [9]. The research regarding ECC has attained great progress [10–13] and subsequently has been applied to practical projects in the United States, Japan, and other countries [14, 15]. Previous results showed that ECC can improve the durability of concrete and can be used as a durable repair material for structures.The composition of an ECC matrix usually includes fine sand, water, cement, fine mineral admixtures, and chemical additives. The proportions and amounts of these components determine the properties of the matrix. Because of obtaining the relatively stable properties of the ECC matrix, the method of ECC mix ratio design should be optimized to ensure its practical application in structures.The mechanical properties of different types of ECC vary. Polyvinyl alcohol (PVA) and polyethylene (PE) fibers are types of fibers used in ECC production, and both types contribute to strong crack resistance and energy absorption capacity. The ultimate tensile strains of PE-ECC and PVA-ECC can exceed 3%. Given the same fiber volume fraction, PE-ECC has a slightly larger strain capacity and higher compressive strength than PVA-ECC. This study focuses on the PE-ECC mix ratio, as it is an important factor affecting the ECC tensile ductility of new composites. The optimized design of the PE-ECC was analyzed using a multicriteria method.The analytic hierarchy process (AHP), a technique applied to multiple-criteria decision analysis, was initially developed by Saaty in the 1970s [16, 17]. AHP is a powerful multi-criteria decision-making method for formulating the most beneficial decisions, which are related to different alternatives according to an established set of criteria. AHP has been applied to a wide range of applications to solve decision-making problems with complex structures and multiple parameters. Reference [18] used AHP to analyze the dangerous locations of roads and consequently minimize the occurrence of accidents. Reference [19] applied AHP to obtain the comprehensive ranking index in the decision-making of pavement maintenance. References [20–22] used various sets of evaluation criteria to analyze the damage to reinforced concrete structures. References [23–26] determine the priority of bridge maintenance by using AHP. Reference [27]used AHP to reduce the fire risk of cultural relics and buildings and subsequently improve the guideline for public fire safety assessment. Furthermore, AHP has been widely used in economic management, scientific research, evaluation, and other fields, but the technique has been rarely used to analyze concrete mix ratios.The optimized design of the PE-ECC mix proportion before was mainly determined by an orthogonal test, which take a long time. However, the authors attempted to propose a method to optimize the design of the mix proportion for PE-ECC. For the optimum design of mixture ratio, the AHP was employed. Fourteen groups of specimens were designed to investigate such effects via a tensile test. Then, a hierarchical structural model established to evaluate the weight vector decision analysis by performing PE-ECC uniaxial tensile tests was discussed. The typical mix was proposed and the AHP method for PE-ECCwas introduced.


## 2. Materials and Methods

### 2.1. Material Properties and Mix Proportion Design

The specimens were cast with P·O 42.5 cement, grade II fly ash, mineral powder, natural washing sand with a particle size of less than 1.18 mm and PE fiber. The physical properties of the cement, grade II fly ash and the mineral powder are shown in Tables1–3 respectively. Table 4 shows the physical and mechanical properties of the PE fiber. The fiber with a ratio of 2% of the total composite volume was added to the mix.Table 1
Basic properties of cement.
Cement stabilityFineness (sieve size: 80μm) (%)Specific surface (m2/kg)Standard consistency water consumption (mL)Setting time (s)Compressive strength (MPa)InitialFinal3 d28 dQualified0.6243027.213519525.153.5Table 2
Physical properties of fly ash.
Fineness (%)Ignition loss (%)Water absorption (%)8.62.898Table 3
Physical properties of mineral powder.
Fineness (%)Ignition loss (%)Water absorption (%)7.80.991Table 4
Properties of the PE fiber.
Diameter (um)Length (mm)Density (g/cm3)Young’s modulus (GPa)Tensile strength (MPa)Fiber elongation (%)24120.9712030005In order to optimize the mix design, the mix was divided into 4 groups to realize the pseudo-strain hardening characteristics of the PE-ECC. The first group was used to represent the change in the water-binder ratio given the same fly ash. The second group was used to represent the change in the water-binder ratio given the same mineral powder. The third group was used to represent the change in fly ash content given the same water-binder ratio. The fourth group was used to represent the change in mineral powder content under the same water-binder ratio. The corresponding parameters are listed in Table5. In PE-FA/KF-A/B/C/D-i, the notation PE means PE fiber, FA means fly ash, KF means granulated blast furnace slag, the letters A, B, C, and D represent 30%, 40%, 50%, and 60% of the mineral admixtures, respectively, and i represents the water to binder ratios, which were 0.25, 0.27, 0.29, and 0.31, respectively.Table 5
Mix proportions of PE-ECC.
Specimen numberCement (g)Mineral admixture (g)Sand (g)Water (g)Fiber (g)Water reducer (g)Thickening agent (g)PE-FA-A-0.25742.2318.1318.1265.114.710.000.25PE-FA-A-0.27721.9309.4309.4278.514.78.250.25PE-FA-A-0.29702.8301.2301.2291.114.75.020.25PE-FA-A-0.31684.6293.4293.4303.214.73.910.25PE-KF-A-0.25742.2318.1318.1265.114.710.000.25PE-KF-A-0.27721.9309.4309.4278.514.78.250.25PE-KF-A-0.29702.8301.2301.2291.114.75.020.25PE-KF-A-0.31684.6293.4293.4303.214.73.910.25PE-FA-B-0.27610.6407.0305.3274.814.78.140.25PE-FA-C-0.27502.1502.1301.3271.114.73.50.25PE-FA-D-0.27396.5594.7297.3267.614.72.970.25PE-KF-B-0.27610.6407.0305.3274.814.78.140.25PE-KF-C-0.27502.1502.1301.3271.114.73.500.25PE-KF-D-0.27396.5594.7297.3267.614.72.970.25


### 2.2. Specimens Design and Test Setup

The dimension of the middle part of the specimens was 80 × 30 × 15 mm3 (Figure 1). The specimens were cured for 7, 28, and 60 days in the same environment (temperature 20±2℃, relative humidity ≥ 95%). All specimens were tested by a displacement-controlled uniaxial tensile test machine (5 kN liquid crystal electronic tension machine; model: LDS-5; Jinan Chuanbai Instrument Equipment Co., Ltd.). The running speed of the testing machine was controlled at 0.5 mm/min during the entire test. The length of 80 mm in the middle part of each specimen was selected for measurement. Two linear variable differential transformers were placed on the left and right sides of each specimen (Figure 2).Figure 1
Geometric dimensions of the specimens.Figure 2
Details of the test setup.


### 2.3. Analysis Methods

#### 2.3.1. Construction of the Hierarchical Model

The AHP provides a multicriteria framework for the efficient formulation of decision problems. The elements are represented and quantified in AHP to relate these elements to the overall goals and the evaluation of the alternative solutions. The hierarchical approach involves the decomposition of the problem into multiple levels of hierarchy, usually in three, four, or five levels. Three levels were used in the current study. A typical hierarchical tree of the AHP model is presented in Figure3. AHP can decompose a problem into multiple levels of hierarchy, thus allowing users to decide based on an evaluation index system. The hierarchical model in Figure 3 is divided into the following three levels: (1) the objective level A representing the specific PE-ECC goals to be achieved, (2) the criteria level B for designating the PE-ECC performance index, and (3) the scheme level C representing the components of the PE-ECC mix proportion.Figure 3
PE-ECC hierarchical model.


#### 2.3.2. Matrix Establishment

The hierarchical model represents the qualitative results of the subjective decision-making produced by the AHP. The relationship between the effects should be quantitatively analyzed with the PE-ECC mixture ratio to ensure the objectivity and accuracy of the results. In this research, the judgment matrix was established using the 1–9 scale method of the study [28] (Table 6).Table 6
Comparison of factor importance.
ScaleMeaning1Two factors are equally important3Two factors are slightly more important than the former5Two factors are more important than the former7Two factors are more important than the former9Comparing the two factors, the former is extremely important2, 4, 6, 8Between the above two levelsThe comparison matrix [A] is shown in equation (1).(1)A=B1B1B1B2B1B3B1B4B2B1B2B2B2B3B2B4B3B1B3B2B3B3B3B4B4B1B4B2B4B3B4B4.The diagonal elements of the matrix are always equal to one. The relative weights of the items (Aij) of the group are evaluated by comparing objective Bi with objective Bj, which can then be used to assign the ratio.The scheme-level comparison matrix [B], as shown in (2), is constructed similarly to that of the comparison matrix [A]. The relative weights of the items (Bij) of the group are evaluated by comparing the objective Ci with objective Cj relative to different criteria.(2)Bi=C1C1C1C2⋯C1C4C2C1C2C2⋯C2C4⋮⋯⋯⋮CiC1CiC2⋯CiC4.


#### 2.3.3. Hierarchical Single Ranking and Consistency Test

In finding the membership values of any hierarchy elements and the total objective, the single-ranking results of all levels should be determined in the hierarchy. Hierarchical single ranking refers to the importance ranking of factors at this level relative to a factor at the previous level. Thus, the eigenvalueλ and eigenvector ω should be obtained. Given the subjectivity of decision-making, a judgment matrix is usually constructed inconsistently. Nonetheless, the degree of inconsistency should be within an acceptable range and needs to pass the consistency test. The consistency index (CI) of the matrix [A] is shown in equation (3)(3)CI=λn−1,Where λ is the eigenvalue of the comparison matrix, and n stands for the number of columns or rows of the matrix.When CI is equal to 0, the matrix is consistent. Moreover, the larger is the CI, the higher is the inconsistency degree of the matrix.Following the work of [29], the consistency ratio (CR) (equation (4) is obtained by dividing CI with the random consistency index (RCI), as shown in Table 7.Table 7
RCI values of different order sets ofn.
n1234567RI000.580.901.121.241.32When CR is less than or equal to 0.10, the judgment matrix is recommended.(4)CR=CIRCI.In the calculation method presented above, the tensile properties of the PE-ECC should include both the water-binder ratio and the fly ash content.


## 2.1. Material Properties and Mix Proportion Design

The specimens were cast with P·O 42.5 cement, grade II fly ash, mineral powder, natural washing sand with a particle size of less than 1.18 mm and PE fiber. The physical properties of the cement, grade II fly ash and the mineral powder are shown in Tables1–3 respectively. Table 4 shows the physical and mechanical properties of the PE fiber. The fiber with a ratio of 2% of the total composite volume was added to the mix.Table 1
Basic properties of cement.
Cement stabilityFineness (sieve size: 80μm) (%)Specific surface (m2/kg)Standard consistency water consumption (mL)Setting time (s)Compressive strength (MPa)InitialFinal3 d28 dQualified0.6243027.213519525.153.5Table 2
Physical properties of fly ash.
Fineness (%)Ignition loss (%)Water absorption (%)8.62.898Table 3
Physical properties of mineral powder.
Fineness (%)Ignition loss (%)Water absorption (%)7.80.991Table 4
Properties of the PE fiber.
Diameter (um)Length (mm)Density (g/cm3)Young’s modulus (GPa)Tensile strength (MPa)Fiber elongation (%)24120.9712030005In order to optimize the mix design, the mix was divided into 4 groups to realize the pseudo-strain hardening characteristics of the PE-ECC. The first group was used to represent the change in the water-binder ratio given the same fly ash. The second group was used to represent the change in the water-binder ratio given the same mineral powder. The third group was used to represent the change in fly ash content given the same water-binder ratio. The fourth group was used to represent the change in mineral powder content under the same water-binder ratio. The corresponding parameters are listed in Table5. In PE-FA/KF-A/B/C/D-i, the notation PE means PE fiber, FA means fly ash, KF means granulated blast furnace slag, the letters A, B, C, and D represent 30%, 40%, 50%, and 60% of the mineral admixtures, respectively, and i represents the water to binder ratios, which were 0.25, 0.27, 0.29, and 0.31, respectively.Table 5
Mix proportions of PE-ECC.
Specimen numberCement (g)Mineral admixture (g)Sand (g)Water (g)Fiber (g)Water reducer (g)Thickening agent (g)PE-FA-A-0.25742.2318.1318.1265.114.710.000.25PE-FA-A-0.27721.9309.4309.4278.514.78.250.25PE-FA-A-0.29702.8301.2301.2291.114.75.020.25PE-FA-A-0.31684.6293.4293.4303.214.73.910.25PE-KF-A-0.25742.2318.1318.1265.114.710.000.25PE-KF-A-0.27721.9309.4309.4278.514.78.250.25PE-KF-A-0.29702.8301.2301.2291.114.75.020.25PE-KF-A-0.31684.6293.4293.4303.214.73.910.25PE-FA-B-0.27610.6407.0305.3274.814.78.140.25PE-FA-C-0.27502.1502.1301.3271.114.73.50.25PE-FA-D-0.27396.5594.7297.3267.614.72.970.25PE-KF-B-0.27610.6407.0305.3274.814.78.140.25PE-KF-C-0.27502.1502.1301.3271.114.73.500.25PE-KF-D-0.27396.5594.7297.3267.614.72.970.25


## 2.2. Specimens Design and Test Setup

The dimension of the middle part of the specimens was 80 × 30 × 15 mm3 (Figure 1). The specimens were cured for 7, 28, and 60 days in the same environment (temperature 20±2℃, relative humidity ≥ 95%). All specimens were tested by a displacement-controlled uniaxial tensile test machine (5 kN liquid crystal electronic tension machine; model: LDS-5; Jinan Chuanbai Instrument Equipment Co., Ltd.). The running speed of the testing machine was controlled at 0.5 mm/min during the entire test. The length of 80 mm in the middle part of each specimen was selected for measurement. Two linear variable differential transformers were placed on the left and right sides of each specimen (Figure 2).Figure 1
Geometric dimensions of the specimens.Figure 2
Details of the test setup.


## 2.3. Analysis Methods

### 2.3.1. Construction of the Hierarchical Model

The AHP provides a multicriteria framework for the efficient formulation of decision problems. The elements are represented and quantified in AHP to relate these elements to the overall goals and the evaluation of the alternative solutions. The hierarchical approach involves the decomposition of the problem into multiple levels of hierarchy, usually in three, four, or five levels. Three levels were used in the current study. A typical hierarchical tree of the AHP model is presented in Figure3. AHP can decompose a problem into multiple levels of hierarchy, thus allowing users to decide based on an evaluation index system. The hierarchical model in Figure 3 is divided into the following three levels: (1) the objective level A representing the specific PE-ECC goals to be achieved, (2) the criteria level B for designating the PE-ECC performance index, and (3) the scheme level C representing the components of the PE-ECC mix proportion.Figure 3
PE-ECC hierarchical model.


### 2.3.2. Matrix Establishment

The hierarchical model represents the qualitative results of the subjective decision-making produced by the AHP. The relationship between the effects should be quantitatively analyzed with the PE-ECC mixture ratio to ensure the objectivity and accuracy of the results. In this research, the judgment matrix was established using the 1–9 scale method of the study [28] (Table 6).Table 6
Comparison of factor importance.
ScaleMeaning1Two factors are equally important3Two factors are slightly more important than the former5Two factors are more important than the former7Two factors are more important than the former9Comparing the two factors, the former is extremely important2, 4, 6, 8Between the above two levelsThe comparison matrix [A] is shown in equation (1).(1)A=B1B1B1B2B1B3B1B4B2B1B2B2B2B3B2B4B3B1B3B2B3B3B3B4B4B1B4B2B4B3B4B4.The diagonal elements of the matrix are always equal to one. The relative weights of the items (Aij) of the group are evaluated by comparing objective Bi with objective Bj, which can then be used to assign the ratio.The scheme-level comparison matrix [B], as shown in (2), is constructed similarly to that of the comparison matrix [A]. The relative weights of the items (Bij) of the group are evaluated by comparing the objective Ci with objective Cj relative to different criteria.(2)Bi=C1C1C1C2⋯C1C4C2C1C2C2⋯C2C4⋮⋯⋯⋮CiC1CiC2⋯CiC4.


### 2.3.3. Hierarchical Single Ranking and Consistency Test

In finding the membership values of any hierarchy elements and the total objective, the single-ranking results of all levels should be determined in the hierarchy. Hierarchical single ranking refers to the importance ranking of factors at this level relative to a factor at the previous level. Thus, the eigenvalueλ and eigenvector ω should be obtained. Given the subjectivity of decision-making, a judgment matrix is usually constructed inconsistently. Nonetheless, the degree of inconsistency should be within an acceptable range and needs to pass the consistency test. The consistency index (CI) of the matrix [A] is shown in equation (3)(3)CI=λn−1,Where λ is the eigenvalue of the comparison matrix, and n stands for the number of columns or rows of the matrix.When CI is equal to 0, the matrix is consistent. Moreover, the larger is the CI, the higher is the inconsistency degree of the matrix.Following the work of [29], the consistency ratio (CR) (equation (4) is obtained by dividing CI with the random consistency index (RCI), as shown in Table 7.Table 7
RCI values of different order sets ofn.
n1234567RI000.580.901.121.241.32When CR is less than or equal to 0.10, the judgment matrix is recommended.(4)CR=CIRCI.In the calculation method presented above, the tensile properties of the PE-ECC should include both the water-binder ratio and the fly ash content.


## 2.3.1. Construction of the Hierarchical Model

The AHP provides a multicriteria framework for the efficient formulation of decision problems. The elements are represented and quantified in AHP to relate these elements to the overall goals and the evaluation of the alternative solutions. The hierarchical approach involves the decomposition of the problem into multiple levels of hierarchy, usually in three, four, or five levels. Three levels were used in the current study. A typical hierarchical tree of the AHP model is presented in Figure3. AHP can decompose a problem into multiple levels of hierarchy, thus allowing users to decide based on an evaluation index system. The hierarchical model in Figure 3 is divided into the following three levels: (1) the objective level A representing the specific PE-ECC goals to be achieved, (2) the criteria level B for designating the PE-ECC performance index, and (3) the scheme level C representing the components of the PE-ECC mix proportion.Figure 3
PE-ECC hierarchical model.


## 2.3.2. Matrix Establishment

The hierarchical model represents the qualitative results of the subjective decision-making produced by the AHP. The relationship between the effects should be quantitatively analyzed with the PE-ECC mixture ratio to ensure the objectivity and accuracy of the results. In this research, the judgment matrix was established using the 1–9 scale method of the study [28] (Table 6).Table 6
Comparison of factor importance.
ScaleMeaning1Two factors are equally important3Two factors are slightly more important than the former5Two factors are more important than the former7Two factors are more important than the former9Comparing the two factors, the former is extremely important2, 4, 6, 8Between the above two levelsThe comparison matrix [A] is shown in equation (1).(1)A=B1B1B1B2B1B3B1B4B2B1B2B2B2B3B2B4B3B1B3B2B3B3B3B4B4B1B4B2B4B3B4B4.The diagonal elements of the matrix are always equal to one. The relative weights of the items (Aij) of the group are evaluated by comparing objective Bi with objective Bj, which can then be used to assign the ratio.The scheme-level comparison matrix [B], as shown in (2), is constructed similarly to that of the comparison matrix [A]. The relative weights of the items (Bij) of the group are evaluated by comparing the objective Ci with objective Cj relative to different criteria.(2)Bi=C1C1C1C2⋯C1C4C2C1C2C2⋯C2C4⋮⋯⋯⋮CiC1CiC2⋯CiC4.


## 2.3.3. Hierarchical Single Ranking and Consistency Test

In finding the membership values of any hierarchy elements and the total objective, the single-ranking results of all levels should be determined in the hierarchy. Hierarchical single ranking refers to the importance ranking of factors at this level relative to a factor at the previous level. Thus, the eigenvalueλ and eigenvector ω should be obtained. Given the subjectivity of decision-making, a judgment matrix is usually constructed inconsistently. Nonetheless, the degree of inconsistency should be within an acceptable range and needs to pass the consistency test. The consistency index (CI) of the matrix [A] is shown in equation (3)(3)CI=λn−1,Where λ is the eigenvalue of the comparison matrix, and n stands for the number of columns or rows of the matrix.When CI is equal to 0, the matrix is consistent. Moreover, the larger is the CI, the higher is the inconsistency degree of the matrix.Following the work of [29], the consistency ratio (CR) (equation (4) is obtained by dividing CI with the random consistency index (RCI), as shown in Table 7.Table 7
RCI values of different order sets ofn.
n1234567RI000.580.901.121.241.32When CR is less than or equal to 0.10, the judgment matrix is recommended.(4)CR=CIRCI.In the calculation method presented above, the tensile properties of the PE-ECC should include both the water-binder ratio and the fly ash content.


## 3. Results and Discussion

Under the formulation presented in the previous section, a case study was developed for PE-ECC mix ratio optimization. The optimal mix proportion of PE-ECC was considered the goal of this study. Subsequently, the initial cracking strength, tensile displacement, ultimate tensile strength, and test age were selected as the evaluation indices, and the judgment matrix was constructed. Finally, the optimal mix proportion was determined after the weight calculation.


### 3.1. Test Failure Phenomenon

The uniaxial tensile test was conducted to achieve the objective of searching for the optimal mix ratio of the PE-ECC. Different mix proportions of fly ash content, mineral powder content, and water-binder ratios were compared to determine the specimens’ failure modes and other property indices (Figures4–7).Figure 4
Failure phenomenon of the PE-ECC with the water-binder ratio of 0.27 and different FA contents and: (a) 7 days, (b) 28 days, (c) 60 days.
(a)(b)(c)Figure 5
Failure phenomenon of PE-ECC with the water-binder ratio of 0.27 and different KF contents: (a) 7 days, (b) 28 days, (c) 60 days.
(a)(b)(c)Figure 6
Failure phenomenon of PE-ECC with different water-binder ratios under fly ash: (a) 7 days, (b) 28 days, (c) 60 days.
(a)(b)(c)Figure 7
Failure phenomenon of PE-ECC with different water-binder ratios under single mineral powder: (a) 7 days, (b) 28 days, (c) 60 days.
(a)(b)(c)Multiple cracks appeared in all specimens at certain lengths (Figures4–7). For the specimens with a water-binder ratio of 0.27, in the early stage of loading, the mixture was restrained by the fibers, and the cracks were small and less visible. In the middle stage of loading, the fibers acted as a bridge and dispersed the cracks evenly, and fine-grained cracks appeared with widths of 0.10–0.35 mm. In the later stage of loading, cracks develop in the weakest part of the specimens, forming the main cracks with a maximum width of 1.3 mm. The details are shown in Figure 4(c).As shown in Figures4–7, with the increase in age, the width and number of surface cracks of the specimens also increase, and the specimens do not burst into pieces after failure because of the bridging interaction between the PE fibers and the cementitious matrix.


### 3.2. Discussion of Test Results for Different Factors

#### 3.2.1. Effect of Water-Binder Ratio on the Tensile Properties of PE-ECC

The average ultimate tensile strength of the specimens basically increased first and then decreased with the increase of age of the specimens at the water-binder ratios of 0.25, 0.27, 0.29, and 0.31 in the two situations of single admixture of fly ash and single mixed mineral powder. A difference of 1.68 MPa was found between the two groups of specimens with water-binder ratios of 0.27 and 0.29 on the situation of a single admixture of fly ash.For the specimens of the same age, the fluctuation range of the average initial cracking strength was between 0.1 and 1 MPa with the increase in the water-binder ratio. For the specimens with the age of 7 days, the fluctuation range of the average initial cracking strength was relatively small with the increase in the water-binder ratio. For the specimens at the age of 28 days, with the increase in the water-binder ratio, the fluctuation range of the average initial cracking strength was the smallest. For the specimens at 60 days of age, the average initial cracking strength fluctuated greatly and reached the maximum value of 0.51 MPa when the water-binder ratio was between 0.25 and 0.29.In the situation of a single admixture of fly ash, the average tensile displacement of 7-day-old specimens changed minimally with the increase in water-binder ratio, and the average tensile displacement of the 28-day-old specimens varied greatly with the increase in water-binder ratio. The average tensile displacement reached the maximum value at 7.34 mm when the water-binder ratio was 0.27. The average tensile displacement was the smallest at 2.85 mm when the water-binder ratio was 0.29. For the specimens aged for 60 days, the maximum tensile displacement was 7.07 mm when the water-binder ratio was 0.25 mm. The average tensile displacement was nearly the same at approximately 4.46 mm when the water-binder ratios were 0.27, 0.29, and 0.31.In the situation of single mixed mineral powder, the average tensile displacement of the 7-day-old specimens decreased with the increase in the water-binder ratio. For the 28-day-old specimens, the average tensile displacement changed minimally with the increase in the water-binder ratio. For the 60-day-old specimens, the average tensile displacement varied greatly with the increase in the water-binder ratio, and the average tensile displacement was the smallest at 3.47 mm when the water-binder ratio was 0.31.From Figure8(a), it can be seen that with the increase in water-binder ratio, the average ultimate tensile strength of the specimens with single fly ash and single mineral powder showed a trend of first decreasing and then increasing, and the average ultimate tensile strength of the specimens with the age of 7 d was the smallest, and the average ultimate tensile strength of the specimen with the age of 28 d was the largest when the water-binder ratio was 0.31.Figure 8
The effect of water-binder ratio: (a) average ultimate tensile strength, (b) average tensile displacement.
(a)(b)From Figure8(b), with single fly ash of the specimens, the average tensile displacement of the specimens with the age of 7 d did not change much with the increase of the water-cement ratio. The average tensile displacement of the specimen with age of 28 d was the largest at the water-cement ratio of 0.27, and the smallest at the water-binder ratio of 0.29, and the data are more volatile. The specimens with the age of 60 d showed the first decrease and then increase with the increase of the water-binder ratio, and the average tensile displacement was the largest at the water-binder ratio of 0.31. The average tensile displacement of the specimen with the increase of the water-binder ratio was not changed much compared with that of the specimen with fly ash, and the average tensile displacement of the specimen with the age of 28 d at the water-binder ratio of 0.31 was the largest.Combining Figures8(a) and 8(b), the ultimate tensile strength and the average tensile displacement of the specimens with an age of 28 d at the water-binder ratio of 0.27 performed the best for the specimens with fly ash alone, For the specimens doped with mineral powder alone, the specimens with an age of 60 d showed the best ultimate tensile strength and average tensile displacement at a water-binder ratio of 0.29.


#### 3.2.2. Effect of Fly Ash Content on the Tensile Properties of PE-ECC

The average ultimate tensile strength of the 7-day-old specimens changed minimally with the increase in fly ash content, whereas that for 28-day-old specimens changed greatly. A difference of 1.75 MPa was observed between the two groups of specimens with fly ash contents of 30% and 40%. For the specimens with the age of 60 days, the average ultimate tensile strength increased first and then became effective with the increase in fly ash content. For the specimens with 30% fly ash content, the average ultimate tensile strength increased first and then decreased with the increase in age. For the specimens with fly ash contents of 40% and 50%, the average ultimate tensile strength increased gradually with the increase in age. For the specimens with 60% fly ash content, the average ultimate tensile strength changed minimally with the increase in age. When the fly ash content was constant, the average tensile displacement fluctuated with the age of the specimens. When the fly ash content was 40%, the range of fluctuation was the smallest.For the specimens of the same age, the initial cracking strength fluctuated from 0.5 to 0.9 MPa with the increase in fly ash content. For the specimens aged for 7 days, the average initial cracking strength increased first and then decreased with the increase in fly ash content. For the specimens aged for 28 days, with the increase in fly ash content, the average initial cracking strength fluctuated greatly and reached 0.8 MPa. For the specimens with the age of 60 days, with the increase in fly ash content, the fluctuation range of the average initial cracking strength was the smallest at approximately 0.4 MPa.For the specimens of the same age, the average ultimate tensile strength fluctuated between 0.3 and 1.6 MPa with the increase in fly ash content. Meanwhile, for the specimens at the age of 7 days, the average ultimate tensile strength fluctuated slightly at approximately 0.5 MPa with the increase in fly ash content. For the 28-day-old specimens with a fly ash content between 30% and 50%, the average ultimate tensile strength fluctuated greatly and reached the maximum value of 1.6 MPa. For the specimens with 60 days of age, the average ultimate tensile strength increased first and then decreased with the increase in fly ash.The average tensile displacements of the specimens with ages of 7 and 60 days showed nearly the same trend with the increase in fly ash content. When the fly ash contents were 30% and 40%, the average tensile displacements at 7 and 60 days were nearly the same at approximately 4.0 and 4.55 mm, respectively. When the fly ash content was 50%, the average tensile displacement was higher than that with 40% fly ash content, and the values increased by 12% at 7 days and 30% at 60 days. When the fly ash content was 60%, the average tensile displacement decreased. When the age was 28 days and the fly ash content was 30%, the maximum average tensile displacement was 7.34 mm.From Figures9(a) and 9(b), the average ultimate tensile strength and average ultimate displacement showed a decreasing trend with the increase of fly ash admixture, and when the fly ash admixture was 50%, the average ultimate tensile strength and average ultimate displacement of the specimens with the age of 7 d and 60 d were the highest at this time, except for the specimens with the age of 28 d. The average ultimate tensile strength and average ultimate displacement of the specimens with the age of 60 d were the highest, but the average ultimate tensile strength and average ultimate displacement of the specimens with the age of 28 d were the highest when the fly ash dosing was 60%. Combining Figures 9(a) and 9(b), it can be seen that the specimens with the age of 60 d showed the best ultimate tensile strength and average tensile displacement at 50% of fly ash admixture.Figure 9
The effect of fly ash content: (a) average ultimate tensile strength, (b) average tensile displacement.
(a)(b)


#### 3.2.3. Effect of Mineral Powder Content on the Tensile Properties of PE-ECC

The average ultimate tensile strength of the 7-day-old specimens changed greatly with the increase in mineral powder content, and the difference value was 1.55 MPa between the two groups of specimens with mineral powder contents of 30% and 60%. For the specimens aged 28 and 60 days, the average ultimate tensile strength changed minimally with the increase in mineral powder content. For the specimens with a mineral powder content of 30%, the average ultimate tensile strength decreased with the increase in age. For the specimens with a mineral powder content of 40%, the average ultimate tensile strength changed greatly with the increase in age. For the specimens with mineral powder contents of 50% and 60%, the average ultimate tensile strength increased gradually with the increase in age. When the amount of mineral powder was constant, the average tensile displacement of the specimens fluctuated with age. When the amount of mineral powder was 50%, the fluctuation was the smallest.For the specimens of the same age, the initial cracking strength fluctuated from 0.6 to 1.7 MPa with the increase in mineral powder content. The average initial cracking strength of the specimens aged for 7 days fluctuated greatly and reached the maximum value of 1.7 MPa with the increase in mineral powder content. For the specimens at 28 days of age, the average initial cracking strength increased first and then decreased with the increase in mineral powder content. The average initial cracking strength of the specimens with 7 days of age fluctuated greatly with the increase in mineral powder content, whereas that of the specimens with 28 days of age increased first and then decreased. For the specimens aged for 60 days, the fluctuation range of the average initial cracking strength was the smallest at approximately 0.6 MPa with the increase in the content of the mineral powder.For the specimens of the same age, the average ultimate tensile strength fluctuated between 0.5 and 1.2 MPa with the increase in mineral powder content. For the specimens aged for 7 days, the average ultimate tensile strength decreased with the increase in mineral powder content. For the specimens aged for 28 days, when the mineral powder content was between 30% and 50%, the average ultimate tensile strength fluctuated greatly and reached 1.2 MPa. For the specimens with the age of 60 days, the average ultimate tensile strength increased with the increase in mineral powder.The average tensile displacement of the specimens aged for 7 days varied greatly with the increase in mineral powder content. When the mineral powder content ranged between 30% and 50%, the average tensile displacement of the specimens was approximately 3 mm. For the specimens aged 28 and 60 days, the average tensile displacements presented an upward trend with the increase in mineral powder content.From Figure10(a), the average ultimate tensile strength of the specimen with age 7 d decreases gradually with the increase of mineral powder admixture, while the age 28 d and 60 d showed a trend of decreasing and then increasing, and the average ultimate tensile strength of the specimen with age 60 d was the largest when the mineral powder admixture was 60%. From Figure 10(b), it can be seen that the average tensile displacement of the specimens with the age of 60 d showed an increasing trend with the increase of mineral powder dosing, and the average tensile displacement of the specimens with the age of 7 d was the largest when the mineral powder dosing was 40%, but with the increase of mineral powder dosing, the average tensile displacement of the specimens with the age of 60 d was the largest when the mineral powder dosing was 60%. Combined with Figures 10(a) and 10(b), the specimens with age 7 d exhibit the best ultimate tensile strength and average tensile displacement at 40% mineral powder doping.Figure 10
The effect of mineral powder content: (a) average ultimate tensile strength, (b) average tensile displacement.
(a)(b)The test results of the PE-FA-A-0.27 (28 days), PE-KF-B-0.27 (7 days), and PE-FA-A-0.25 (60 days) specimens are presented in Table8. These three groups have larger tensile displacement, better ductility, and more apparent strain-hardening characteristics compared with the other groups.Table 8
Uniaxial tensile test results of the specimens.
Mix numberAge(day)Average initial cracking strength (MPa)Standard deviation of initial crack strength (MPa)Average ultimate tensile strength (MPa)Standard deviation of ultimate tensile strength (MPa)Average tensiledisplacement(mm)Standard deviation of tensile displacement (mm)Averageelongation(%)PE-FA-A-0.2572.130.365.630.383.590.553.59282.340.536.340.494.230.254.23602.710.256.750.217.070.727.07PE-FA-A-0.2771.920.304.960.674.030.604.03282.930.586.590.397.341.437.34602.490.515.831.124.552.454.55PE-FA-A-0.2972.320.384.260.383.340.673.34282.130.234.910.972.851.442.85602.330.515.370.393.970.643.97PE-FA-A-0.3171.970.214.450.633.370.603.37281.990.475.790.153.970.993.97601.930.195.560.684.882.154.88PE-FA-B-0.2772.210.484.810.514.011.564.01282.150.644.840.384.361.304.36602.140.155.900.864.552.464.55PE-FA-C-0.2772.560.305.230.624.481.434.48282.210.145.560.334.330.334.33602.180.166.290.615.861.615.86PE-FA-D-0.2772.060.264.530.353.460.793.46282.630.275.460.175.300.445.30601.970.464.930.223.040.103.04PE-KF-A-0.2572.320.506.360.606.161.856.16282.390.796.660.916.462.936.46602.820.516.080.816.001.946.00PE-KF-A-0.2772.000.126.020.086.010.046.01282.500.875.981.165.182.595.18602.160.405.540.964.402.344.40PE-KF-A-0.2972.200.594.670.184.101.784.10282.490.335.600.255.371.275.37602.100.226.030.796.152.556.15PE-KF-A-0.3172.200.314.750.324.040.504.04282.400.635.771.305.721.225.72602.590.655.310.573.470.783.47PE-KF-B-0.2772.270.706.000.187.300.987.30282.640.044.820.933.641.163.64602.530.515.240.244.701.264.70PE-KF-C-0.2772.620.104.930.094.840.544.84282.270.545.090884.352.194.35702.330.175.390.804.941.754.94PE-KF-D-0.2772.390.634.470.695.072.715.07281.720.535.130.483.980.223.98601.900.265.860.156.000.916.00


### 3.3. Analysis Results Based on AHP Method

#### 3.3.1. Calculation of Weight Vector

AHP was used to rank the optimal tensile effects of the three groups of mixtures whose average tensile displacement exceeded 7.0 mm. The results and the scale (Tables6 and 8, respectively) were then used to calculate the scores of the elements (Table 9).Table 9
Assignment score table.
Assign itemsAssign valueIndex level357Initial cracking strength351Ultimate tensile strength432Tensile displacement566Age135Obtaining the ultimate weights for the individual ratings can help to determine the weights for each criterion. According to Table6 and (1), the matrix A can be defined as (5)(5)A=1353735315757375171315171.The weight vectorω can be computed using the matrix A as follows:(6)ω2=0,1875,0.3125,0.4375,0.0625T.From (6), the ranking of the four elements (initial cracking strength, tensile displacement, ultimate tensile strength, and test age) in the criterion level relative to the total objective level can be obtained, which altogether comprise the matrix ω2.


#### 3.3.2. Determination of Optimal Mixture Proportion

The judgment matrix was established based on the evaluation indices of the first crack strength, ultimate tensile strength, elongation rate, and test age. The matrix is 3 × 4 matrix, in which each column of the matrix represents the order of scheme levelC corresponding to criterion level B, as demonstrated in (7).(7)U3=0.330.450.2940.110.560.330.3530.330.110.220.3530.56.The order of elements of the scheme levelC concerning the objective level A can be expressed as(8)ω3=u3ω2ω3.The global weight vector was calculated using (8). Each element in the weight vector was used to represent the final weight (equation (9)) for the three sampled groups’ mix ratios. The maximum weight of 0.383 was determined as the second scheme’s weight. Thus, the optimal mix ratio was the PE-FA-A-0.27 scheme.(9)ω3=0.3380.3830.279.The load-displacement curves of the three groups’ specimens were plotted to further prove the result (Figure8).The test implemented in this study was divided into the following three stages: initial crack formation stage, stage of stable development of cracks, and failure stage. Based on Figure11, the crack load of PE-FA-A-0.27 is 1.32 kN with an ultimate load is 2.97 kN; the crack load of PE-KF-B-0.27 is 1.02 kN with an ultimate load of 2.70 kN, and the crack load of PE-FA-A-0.25 is 1.22 kN with an ultimate load of 3.04 kN. The initial crack strength and curve slope of PE-FA-A-0.27 are at the maximum in the elastic stage. At the yield stage, the microcrack has likely reduced the specimens’ capacity by transferring the internal forces, hence the nonlinear trend. The curve slopes of the three sampled groups’ mix ratios begin to decrease, indicating that the stiffness of the specimens has degenerated. The stiffness degradation of PE-FA-A-0.27 is the slowest. However, the ultimate crack strength of PE-FA-A-0.27 is slightly lower than that of PE-FA-A-0.25, its elongation rate upon failure is the largest, and its strain-hardening characteristics are the most obvious. Therefore, the performance of the PE-FA-A-0.27 scheme is better than those of the other two groups.Figure 11
The uniaxial tensile load-displacement curve of PE-ECC.


## 3.1. Test Failure Phenomenon

The uniaxial tensile test was conducted to achieve the objective of searching for the optimal mix ratio of the PE-ECC. Different mix proportions of fly ash content, mineral powder content, and water-binder ratios were compared to determine the specimens’ failure modes and other property indices (Figures4–7).Figure 4
Failure phenomenon of the PE-ECC with the water-binder ratio of 0.27 and different FA contents and: (a) 7 days, (b) 28 days, (c) 60 days.
(a)(b)(c)Figure 5
Failure phenomenon of PE-ECC with the water-binder ratio of 0.27 and different KF contents: (a) 7 days, (b) 28 days, (c) 60 days.
(a)(b)(c)Figure 6
Failure phenomenon of PE-ECC with different water-binder ratios under fly ash: (a) 7 days, (b) 28 days, (c) 60 days.
(a)(b)(c)Figure 7
Failure phenomenon of PE-ECC with different water-binder ratios under single mineral powder: (a) 7 days, (b) 28 days, (c) 60 days.
(a)(b)(c)Multiple cracks appeared in all specimens at certain lengths (Figures4–7). For the specimens with a water-binder ratio of 0.27, in the early stage of loading, the mixture was restrained by the fibers, and the cracks were small and less visible. In the middle stage of loading, the fibers acted as a bridge and dispersed the cracks evenly, and fine-grained cracks appeared with widths of 0.10–0.35 mm. In the later stage of loading, cracks develop in the weakest part of the specimens, forming the main cracks with a maximum width of 1.3 mm. The details are shown in Figure 4(c).As shown in Figures4–7, with the increase in age, the width and number of surface cracks of the specimens also increase, and the specimens do not burst into pieces after failure because of the bridging interaction between the PE fibers and the cementitious matrix.


## 3.2. Discussion of Test Results for Different Factors

### 3.2.1. Effect of Water-Binder Ratio on the Tensile Properties of PE-ECC

The average ultimate tensile strength of the specimens basically increased first and then decreased with the increase of age of the specimens at the water-binder ratios of 0.25, 0.27, 0.29, and 0.31 in the two situations of single admixture of fly ash and single mixed mineral powder. A difference of 1.68 MPa was found between the two groups of specimens with water-binder ratios of 0.27 and 0.29 on the situation of a single admixture of fly ash.For the specimens of the same age, the fluctuation range of the average initial cracking strength was between 0.1 and 1 MPa with the increase in the water-binder ratio. For the specimens with the age of 7 days, the fluctuation range of the average initial cracking strength was relatively small with the increase in the water-binder ratio. For the specimens at the age of 28 days, with the increase in the water-binder ratio, the fluctuation range of the average initial cracking strength was the smallest. For the specimens at 60 days of age, the average initial cracking strength fluctuated greatly and reached the maximum value of 0.51 MPa when the water-binder ratio was between 0.25 and 0.29.In the situation of a single admixture of fly ash, the average tensile displacement of 7-day-old specimens changed minimally with the increase in water-binder ratio, and the average tensile displacement of the 28-day-old specimens varied greatly with the increase in water-binder ratio. The average tensile displacement reached the maximum value at 7.34 mm when the water-binder ratio was 0.27. The average tensile displacement was the smallest at 2.85 mm when the water-binder ratio was 0.29. For the specimens aged for 60 days, the maximum tensile displacement was 7.07 mm when the water-binder ratio was 0.25 mm. The average tensile displacement was nearly the same at approximately 4.46 mm when the water-binder ratios were 0.27, 0.29, and 0.31.In the situation of single mixed mineral powder, the average tensile displacement of the 7-day-old specimens decreased with the increase in the water-binder ratio. For the 28-day-old specimens, the average tensile displacement changed minimally with the increase in the water-binder ratio. For the 60-day-old specimens, the average tensile displacement varied greatly with the increase in the water-binder ratio, and the average tensile displacement was the smallest at 3.47 mm when the water-binder ratio was 0.31.From Figure8(a), it can be seen that with the increase in water-binder ratio, the average ultimate tensile strength of the specimens with single fly ash and single mineral powder showed a trend of first decreasing and then increasing, and the average ultimate tensile strength of the specimens with the age of 7 d was the smallest, and the average ultimate tensile strength of the specimen with the age of 28 d was the largest when the water-binder ratio was 0.31.Figure 8
The effect of water-binder ratio: (a) average ultimate tensile strength, (b) average tensile displacement.
(a)(b)From Figure8(b), with single fly ash of the specimens, the average tensile displacement of the specimens with the age of 7 d did not change much with the increase of the water-cement ratio. The average tensile displacement of the specimen with age of 28 d was the largest at the water-cement ratio of 0.27, and the smallest at the water-binder ratio of 0.29, and the data are more volatile. The specimens with the age of 60 d showed the first decrease and then increase with the increase of the water-binder ratio, and the average tensile displacement was the largest at the water-binder ratio of 0.31. The average tensile displacement of the specimen with the increase of the water-binder ratio was not changed much compared with that of the specimen with fly ash, and the average tensile displacement of the specimen with the age of 28 d at the water-binder ratio of 0.31 was the largest.Combining Figures8(a) and 8(b), the ultimate tensile strength and the average tensile displacement of the specimens with an age of 28 d at the water-binder ratio of 0.27 performed the best for the specimens with fly ash alone, For the specimens doped with mineral powder alone, the specimens with an age of 60 d showed the best ultimate tensile strength and average tensile displacement at a water-binder ratio of 0.29.


### 3.2.2. Effect of Fly Ash Content on the Tensile Properties of PE-ECC

The average ultimate tensile strength of the 7-day-old specimens changed minimally with the increase in fly ash content, whereas that for 28-day-old specimens changed greatly. A difference of 1.75 MPa was observed between the two groups of specimens with fly ash contents of 30% and 40%. For the specimens with the age of 60 days, the average ultimate tensile strength increased first and then became effective with the increase in fly ash content. For the specimens with 30% fly ash content, the average ultimate tensile strength increased first and then decreased with the increase in age. For the specimens with fly ash contents of 40% and 50%, the average ultimate tensile strength increased gradually with the increase in age. For the specimens with 60% fly ash content, the average ultimate tensile strength changed minimally with the increase in age. When the fly ash content was constant, the average tensile displacement fluctuated with the age of the specimens. When the fly ash content was 40%, the range of fluctuation was the smallest.For the specimens of the same age, the initial cracking strength fluctuated from 0.5 to 0.9 MPa with the increase in fly ash content. For the specimens aged for 7 days, the average initial cracking strength increased first and then decreased with the increase in fly ash content. For the specimens aged for 28 days, with the increase in fly ash content, the average initial cracking strength fluctuated greatly and reached 0.8 MPa. For the specimens with the age of 60 days, with the increase in fly ash content, the fluctuation range of the average initial cracking strength was the smallest at approximately 0.4 MPa.For the specimens of the same age, the average ultimate tensile strength fluctuated between 0.3 and 1.6 MPa with the increase in fly ash content. Meanwhile, for the specimens at the age of 7 days, the average ultimate tensile strength fluctuated slightly at approximately 0.5 MPa with the increase in fly ash content. For the 28-day-old specimens with a fly ash content between 30% and 50%, the average ultimate tensile strength fluctuated greatly and reached the maximum value of 1.6 MPa. For the specimens with 60 days of age, the average ultimate tensile strength increased first and then decreased with the increase in fly ash.The average tensile displacements of the specimens with ages of 7 and 60 days showed nearly the same trend with the increase in fly ash content. When the fly ash contents were 30% and 40%, the average tensile displacements at 7 and 60 days were nearly the same at approximately 4.0 and 4.55 mm, respectively. When the fly ash content was 50%, the average tensile displacement was higher than that with 40% fly ash content, and the values increased by 12% at 7 days and 30% at 60 days. When the fly ash content was 60%, the average tensile displacement decreased. When the age was 28 days and the fly ash content was 30%, the maximum average tensile displacement was 7.34 mm.From Figures9(a) and 9(b), the average ultimate tensile strength and average ultimate displacement showed a decreasing trend with the increase of fly ash admixture, and when the fly ash admixture was 50%, the average ultimate tensile strength and average ultimate displacement of the specimens with the age of 7 d and 60 d were the highest at this time, except for the specimens with the age of 28 d. The average ultimate tensile strength and average ultimate displacement of the specimens with the age of 60 d were the highest, but the average ultimate tensile strength and average ultimate displacement of the specimens with the age of 28 d were the highest when the fly ash dosing was 60%. Combining Figures 9(a) and 9(b), it can be seen that the specimens with the age of 60 d showed the best ultimate tensile strength and average tensile displacement at 50% of fly ash admixture.Figure 9
The effect of fly ash content: (a) average ultimate tensile strength, (b) average tensile displacement.
(a)(b)


### 3.2.3. Effect of Mineral Powder Content on the Tensile Properties of PE-ECC

The average ultimate tensile strength of the 7-day-old specimens changed greatly with the increase in mineral powder content, and the difference value was 1.55 MPa between the two groups of specimens with mineral powder contents of 30% and 60%. For the specimens aged 28 and 60 days, the average ultimate tensile strength changed minimally with the increase in mineral powder content. For the specimens with a mineral powder content of 30%, the average ultimate tensile strength decreased with the increase in age. For the specimens with a mineral powder content of 40%, the average ultimate tensile strength changed greatly with the increase in age. For the specimens with mineral powder contents of 50% and 60%, the average ultimate tensile strength increased gradually with the increase in age. When the amount of mineral powder was constant, the average tensile displacement of the specimens fluctuated with age. When the amount of mineral powder was 50%, the fluctuation was the smallest.For the specimens of the same age, the initial cracking strength fluctuated from 0.6 to 1.7 MPa with the increase in mineral powder content. The average initial cracking strength of the specimens aged for 7 days fluctuated greatly and reached the maximum value of 1.7 MPa with the increase in mineral powder content. For the specimens at 28 days of age, the average initial cracking strength increased first and then decreased with the increase in mineral powder content. The average initial cracking strength of the specimens with 7 days of age fluctuated greatly with the increase in mineral powder content, whereas that of the specimens with 28 days of age increased first and then decreased. For the specimens aged for 60 days, the fluctuation range of the average initial cracking strength was the smallest at approximately 0.6 MPa with the increase in the content of the mineral powder.For the specimens of the same age, the average ultimate tensile strength fluctuated between 0.5 and 1.2 MPa with the increase in mineral powder content. For the specimens aged for 7 days, the average ultimate tensile strength decreased with the increase in mineral powder content. For the specimens aged for 28 days, when the mineral powder content was between 30% and 50%, the average ultimate tensile strength fluctuated greatly and reached 1.2 MPa. For the specimens with the age of 60 days, the average ultimate tensile strength increased with the increase in mineral powder.The average tensile displacement of the specimens aged for 7 days varied greatly with the increase in mineral powder content. When the mineral powder content ranged between 30% and 50%, the average tensile displacement of the specimens was approximately 3 mm. For the specimens aged 28 and 60 days, the average tensile displacements presented an upward trend with the increase in mineral powder content.From Figure10(a), the average ultimate tensile strength of the specimen with age 7 d decreases gradually with the increase of mineral powder admixture, while the age 28 d and 60 d showed a trend of decreasing and then increasing, and the average ultimate tensile strength of the specimen with age 60 d was the largest when the mineral powder admixture was 60%. From Figure 10(b), it can be seen that the average tensile displacement of the specimens with the age of 60 d showed an increasing trend with the increase of mineral powder dosing, and the average tensile displacement of the specimens with the age of 7 d was the largest when the mineral powder dosing was 40%, but with the increase of mineral powder dosing, the average tensile displacement of the specimens with the age of 60 d was the largest when the mineral powder dosing was 60%. Combined with Figures 10(a) and 10(b), the specimens with age 7 d exhibit the best ultimate tensile strength and average tensile displacement at 40% mineral powder doping.Figure 10
The effect of mineral powder content: (a) average ultimate tensile strength, (b) average tensile displacement.
(a)(b)The test results of the PE-FA-A-0.27 (28 days), PE-KF-B-0.27 (7 days), and PE-FA-A-0.25 (60 days) specimens are presented in Table8. These three groups have larger tensile displacement, better ductility, and more apparent strain-hardening characteristics compared with the other groups.Table 8
Uniaxial tensile test results of the specimens.
Mix numberAge(day)Average initial cracking strength (MPa)Standard deviation of initial crack strength (MPa)Average ultimate tensile strength (MPa)Standard deviation of ultimate tensile strength (MPa)Average tensiledisplacement(mm)Standard deviation of tensile displacement (mm)Averageelongation(%)PE-FA-A-0.2572.130.365.630.383.590.553.59282.340.536.340.494.230.254.23602.710.256.750.217.070.727.07PE-FA-A-0.2771.920.304.960.674.030.604.03282.930.586.590.397.341.437.34602.490.515.831.124.552.454.55PE-FA-A-0.2972.320.384.260.383.340.673.34282.130.234.910.972.851.442.85602.330.515.370.393.970.643.97PE-FA-A-0.3171.970.214.450.633.370.603.37281.990.475.790.153.970.993.97601.930.195.560.684.882.154.88PE-FA-B-0.2772.210.484.810.514.011.564.01282.150.644.840.384.361.304.36602.140.155.900.864.552.464.55PE-FA-C-0.2772.560.305.230.624.481.434.48282.210.145.560.334.330.334.33602.180.166.290.615.861.615.86PE-FA-D-0.2772.060.264.530.353.460.793.46282.630.275.460.175.300.445.30601.970.464.930.223.040.103.04PE-KF-A-0.2572.320.506.360.606.161.856.16282.390.796.660.916.462.936.46602.820.516.080.816.001.946.00PE-KF-A-0.2772.000.126.020.086.010.046.01282.500.875.981.165.182.595.18602.160.405.540.964.402.344.40PE-KF-A-0.2972.200.594.670.184.101.784.10282.490.335.600.255.371.275.37602.100.226.030.796.152.556.15PE-KF-A-0.3172.200.314.750.324.040.504.04282.400.635.771.305.721.225.72602.590.655.310.573.470.783.47PE-KF-B-0.2772.270.706.000.187.300.987.30282.640.044.820.933.641.163.64602.530.515.240.244.701.264.70PE-KF-C-0.2772.620.104.930.094.840.544.84282.270.545.090884.352.194.35702.330.175.390.804.941.754.94PE-KF-D-0.2772.390.634.470.695.072.715.07281.720.535.130.483.980.223.98601.900.265.860.156.000.916.00


## 3.2.1. Effect of Water-Binder Ratio on the Tensile Properties of PE-ECC

The average ultimate tensile strength of the specimens basically increased first and then decreased with the increase of age of the specimens at the water-binder ratios of 0.25, 0.27, 0.29, and 0.31 in the two situations of single admixture of fly ash and single mixed mineral powder. A difference of 1.68 MPa was found between the two groups of specimens with water-binder ratios of 0.27 and 0.29 on the situation of a single admixture of fly ash.For the specimens of the same age, the fluctuation range of the average initial cracking strength was between 0.1 and 1 MPa with the increase in the water-binder ratio. For the specimens with the age of 7 days, the fluctuation range of the average initial cracking strength was relatively small with the increase in the water-binder ratio. For the specimens at the age of 28 days, with the increase in the water-binder ratio, the fluctuation range of the average initial cracking strength was the smallest. For the specimens at 60 days of age, the average initial cracking strength fluctuated greatly and reached the maximum value of 0.51 MPa when the water-binder ratio was between 0.25 and 0.29.In the situation of a single admixture of fly ash, the average tensile displacement of 7-day-old specimens changed minimally with the increase in water-binder ratio, and the average tensile displacement of the 28-day-old specimens varied greatly with the increase in water-binder ratio. The average tensile displacement reached the maximum value at 7.34 mm when the water-binder ratio was 0.27. The average tensile displacement was the smallest at 2.85 mm when the water-binder ratio was 0.29. For the specimens aged for 60 days, the maximum tensile displacement was 7.07 mm when the water-binder ratio was 0.25 mm. The average tensile displacement was nearly the same at approximately 4.46 mm when the water-binder ratios were 0.27, 0.29, and 0.31.In the situation of single mixed mineral powder, the average tensile displacement of the 7-day-old specimens decreased with the increase in the water-binder ratio. For the 28-day-old specimens, the average tensile displacement changed minimally with the increase in the water-binder ratio. For the 60-day-old specimens, the average tensile displacement varied greatly with the increase in the water-binder ratio, and the average tensile displacement was the smallest at 3.47 mm when the water-binder ratio was 0.31.From Figure8(a), it can be seen that with the increase in water-binder ratio, the average ultimate tensile strength of the specimens with single fly ash and single mineral powder showed a trend of first decreasing and then increasing, and the average ultimate tensile strength of the specimens with the age of 7 d was the smallest, and the average ultimate tensile strength of the specimen with the age of 28 d was the largest when the water-binder ratio was 0.31.Figure 8
The effect of water-binder ratio: (a) average ultimate tensile strength, (b) average tensile displacement.
(a)(b)From Figure8(b), with single fly ash of the specimens, the average tensile displacement of the specimens with the age of 7 d did not change much with the increase of the water-cement ratio. The average tensile displacement of the specimen with age of 28 d was the largest at the water-cement ratio of 0.27, and the smallest at the water-binder ratio of 0.29, and the data are more volatile. The specimens with the age of 60 d showed the first decrease and then increase with the increase of the water-binder ratio, and the average tensile displacement was the largest at the water-binder ratio of 0.31. The average tensile displacement of the specimen with the increase of the water-binder ratio was not changed much compared with that of the specimen with fly ash, and the average tensile displacement of the specimen with the age of 28 d at the water-binder ratio of 0.31 was the largest.Combining Figures8(a) and 8(b), the ultimate tensile strength and the average tensile displacement of the specimens with an age of 28 d at the water-binder ratio of 0.27 performed the best for the specimens with fly ash alone, For the specimens doped with mineral powder alone, the specimens with an age of 60 d showed the best ultimate tensile strength and average tensile displacement at a water-binder ratio of 0.29.


## 3.2.2. Effect of Fly Ash Content on the Tensile Properties of PE-ECC

The average ultimate tensile strength of the 7-day-old specimens changed minimally with the increase in fly ash content, whereas that for 28-day-old specimens changed greatly. A difference of 1.75 MPa was observed between the two groups of specimens with fly ash contents of 30% and 40%. For the specimens with the age of 60 days, the average ultimate tensile strength increased first and then became effective with the increase in fly ash content. For the specimens with 30% fly ash content, the average ultimate tensile strength increased first and then decreased with the increase in age. For the specimens with fly ash contents of 40% and 50%, the average ultimate tensile strength increased gradually with the increase in age. For the specimens with 60% fly ash content, the average ultimate tensile strength changed minimally with the increase in age. When the fly ash content was constant, the average tensile displacement fluctuated with the age of the specimens. When the fly ash content was 40%, the range of fluctuation was the smallest.For the specimens of the same age, the initial cracking strength fluctuated from 0.5 to 0.9 MPa with the increase in fly ash content. For the specimens aged for 7 days, the average initial cracking strength increased first and then decreased with the increase in fly ash content. For the specimens aged for 28 days, with the increase in fly ash content, the average initial cracking strength fluctuated greatly and reached 0.8 MPa. For the specimens with the age of 60 days, with the increase in fly ash content, the fluctuation range of the average initial cracking strength was the smallest at approximately 0.4 MPa.For the specimens of the same age, the average ultimate tensile strength fluctuated between 0.3 and 1.6 MPa with the increase in fly ash content. Meanwhile, for the specimens at the age of 7 days, the average ultimate tensile strength fluctuated slightly at approximately 0.5 MPa with the increase in fly ash content. For the 28-day-old specimens with a fly ash content between 30% and 50%, the average ultimate tensile strength fluctuated greatly and reached the maximum value of 1.6 MPa. For the specimens with 60 days of age, the average ultimate tensile strength increased first and then decreased with the increase in fly ash.The average tensile displacements of the specimens with ages of 7 and 60 days showed nearly the same trend with the increase in fly ash content. When the fly ash contents were 30% and 40%, the average tensile displacements at 7 and 60 days were nearly the same at approximately 4.0 and 4.55 mm, respectively. When the fly ash content was 50%, the average tensile displacement was higher than that with 40% fly ash content, and the values increased by 12% at 7 days and 30% at 60 days. When the fly ash content was 60%, the average tensile displacement decreased. When the age was 28 days and the fly ash content was 30%, the maximum average tensile displacement was 7.34 mm.From Figures9(a) and 9(b), the average ultimate tensile strength and average ultimate displacement showed a decreasing trend with the increase of fly ash admixture, and when the fly ash admixture was 50%, the average ultimate tensile strength and average ultimate displacement of the specimens with the age of 7 d and 60 d were the highest at this time, except for the specimens with the age of 28 d. The average ultimate tensile strength and average ultimate displacement of the specimens with the age of 60 d were the highest, but the average ultimate tensile strength and average ultimate displacement of the specimens with the age of 28 d were the highest when the fly ash dosing was 60%. Combining Figures 9(a) and 9(b), it can be seen that the specimens with the age of 60 d showed the best ultimate tensile strength and average tensile displacement at 50% of fly ash admixture.Figure 9
The effect of fly ash content: (a) average ultimate tensile strength, (b) average tensile displacement.
(a)(b)


## 3.2.3. Effect of Mineral Powder Content on the Tensile Properties of PE-ECC

The average ultimate tensile strength of the 7-day-old specimens changed greatly with the increase in mineral powder content, and the difference value was 1.55 MPa between the two groups of specimens with mineral powder contents of 30% and 60%. For the specimens aged 28 and 60 days, the average ultimate tensile strength changed minimally with the increase in mineral powder content. For the specimens with a mineral powder content of 30%, the average ultimate tensile strength decreased with the increase in age. For the specimens with a mineral powder content of 40%, the average ultimate tensile strength changed greatly with the increase in age. For the specimens with mineral powder contents of 50% and 60%, the average ultimate tensile strength increased gradually with the increase in age. When the amount of mineral powder was constant, the average tensile displacement of the specimens fluctuated with age. When the amount of mineral powder was 50%, the fluctuation was the smallest.For the specimens of the same age, the initial cracking strength fluctuated from 0.6 to 1.7 MPa with the increase in mineral powder content. The average initial cracking strength of the specimens aged for 7 days fluctuated greatly and reached the maximum value of 1.7 MPa with the increase in mineral powder content. For the specimens at 28 days of age, the average initial cracking strength increased first and then decreased with the increase in mineral powder content. The average initial cracking strength of the specimens with 7 days of age fluctuated greatly with the increase in mineral powder content, whereas that of the specimens with 28 days of age increased first and then decreased. For the specimens aged for 60 days, the fluctuation range of the average initial cracking strength was the smallest at approximately 0.6 MPa with the increase in the content of the mineral powder.For the specimens of the same age, the average ultimate tensile strength fluctuated between 0.5 and 1.2 MPa with the increase in mineral powder content. For the specimens aged for 7 days, the average ultimate tensile strength decreased with the increase in mineral powder content. For the specimens aged for 28 days, when the mineral powder content was between 30% and 50%, the average ultimate tensile strength fluctuated greatly and reached 1.2 MPa. For the specimens with the age of 60 days, the average ultimate tensile strength increased with the increase in mineral powder.The average tensile displacement of the specimens aged for 7 days varied greatly with the increase in mineral powder content. When the mineral powder content ranged between 30% and 50%, the average tensile displacement of the specimens was approximately 3 mm. For the specimens aged 28 and 60 days, the average tensile displacements presented an upward trend with the increase in mineral powder content.From Figure10(a), the average ultimate tensile strength of the specimen with age 7 d decreases gradually with the increase of mineral powder admixture, while the age 28 d and 60 d showed a trend of decreasing and then increasing, and the average ultimate tensile strength of the specimen with age 60 d was the largest when the mineral powder admixture was 60%. From Figure 10(b), it can be seen that the average tensile displacement of the specimens with the age of 60 d showed an increasing trend with the increase of mineral powder dosing, and the average tensile displacement of the specimens with the age of 7 d was the largest when the mineral powder dosing was 40%, but with the increase of mineral powder dosing, the average tensile displacement of the specimens with the age of 60 d was the largest when the mineral powder dosing was 60%. Combined with Figures 10(a) and 10(b), the specimens with age 7 d exhibit the best ultimate tensile strength and average tensile displacement at 40% mineral powder doping.Figure 10
The effect of mineral powder content: (a) average ultimate tensile strength, (b) average tensile displacement.
(a)(b)The test results of the PE-FA-A-0.27 (28 days), PE-KF-B-0.27 (7 days), and PE-FA-A-0.25 (60 days) specimens are presented in Table8. These three groups have larger tensile displacement, better ductility, and more apparent strain-hardening characteristics compared with the other groups.Table 8
Uniaxial tensile test results of the specimens.
Mix numberAge(day)Average initial cracking strength (MPa)Standard deviation of initial crack strength (MPa)Average ultimate tensile strength (MPa)Standard deviation of ultimate tensile strength (MPa)Average tensiledisplacement(mm)Standard deviation of tensile displacement (mm)Averageelongation(%)PE-FA-A-0.2572.130.365.630.383.590.553.59282.340.536.340.494.230.254.23602.710.256.750.217.070.727.07PE-FA-A-0.2771.920.304.960.674.030.604.03282.930.586.590.397.341.437.34602.490.515.831.124.552.454.55PE-FA-A-0.2972.320.384.260.383.340.673.34282.130.234.910.972.851.442.85602.330.515.370.393.970.643.97PE-FA-A-0.3171.970.214.450.633.370.603.37281.990.475.790.153.970.993.97601.930.195.560.684.882.154.88PE-FA-B-0.2772.210.484.810.514.011.564.01282.150.644.840.384.361.304.36602.140.155.900.864.552.464.55PE-FA-C-0.2772.560.305.230.624.481.434.48282.210.145.560.334.330.334.33602.180.166.290.615.861.615.86PE-FA-D-0.2772.060.264.530.353.460.793.46282.630.275.460.175.300.445.30601.970.464.930.223.040.103.04PE-KF-A-0.2572.320.506.360.606.161.856.16282.390.796.660.916.462.936.46602.820.516.080.816.001.946.00PE-KF-A-0.2772.000.126.020.086.010.046.01282.500.875.981.165.182.595.18602.160.405.540.964.402.344.40PE-KF-A-0.2972.200.594.670.184.101.784.10282.490.335.600.255.371.275.37602.100.226.030.796.152.556.15PE-KF-A-0.3172.200.314.750.324.040.504.04282.400.635.771.305.721.225.72602.590.655.310.573.470.783.47PE-KF-B-0.2772.270.706.000.187.300.987.30282.640.044.820.933.641.163.64602.530.515.240.244.701.264.70PE-KF-C-0.2772.620.104.930.094.840.544.84282.270.545.090884.352.194.35702.330.175.390.804.941.754.94PE-KF-D-0.2772.390.634.470.695.072.715.07281.720.535.130.483.980.223.98601.900.265.860.156.000.916.00


## 3.3. Analysis Results Based on AHP Method

### 3.3.1. Calculation of Weight Vector

AHP was used to rank the optimal tensile effects of the three groups of mixtures whose average tensile displacement exceeded 7.0 mm. The results and the scale (Tables6 and 8, respectively) were then used to calculate the scores of the elements (Table 9).Table 9
Assignment score table.
Assign itemsAssign valueIndex level357Initial cracking strength351Ultimate tensile strength432Tensile displacement566Age135Obtaining the ultimate weights for the individual ratings can help to determine the weights for each criterion. According to Table6 and (1), the matrix A can be defined as (5)(5)A=1353735315757375171315171.The weight vectorω can be computed using the matrix A as follows:(6)ω2=0,1875,0.3125,0.4375,0.0625T.From (6), the ranking of the four elements (initial cracking strength, tensile displacement, ultimate tensile strength, and test age) in the criterion level relative to the total objective level can be obtained, which altogether comprise the matrix ω2.


### 3.3.2. Determination of Optimal Mixture Proportion

The judgment matrix was established based on the evaluation indices of the first crack strength, ultimate tensile strength, elongation rate, and test age. The matrix is 3 × 4 matrix, in which each column of the matrix represents the order of scheme levelC corresponding to criterion level B, as demonstrated in (7).(7)U3=0.330.450.2940.110.560.330.3530.330.110.220.3530.56.The order of elements of the scheme levelC concerning the objective level A can be expressed as(8)ω3=u3ω2ω3.The global weight vector was calculated using (8). Each element in the weight vector was used to represent the final weight (equation (9)) for the three sampled groups’ mix ratios. The maximum weight of 0.383 was determined as the second scheme’s weight. Thus, the optimal mix ratio was the PE-FA-A-0.27 scheme.(9)ω3=0.3380.3830.279.The load-displacement curves of the three groups’ specimens were plotted to further prove the result (Figure8).The test implemented in this study was divided into the following three stages: initial crack formation stage, stage of stable development of cracks, and failure stage. Based on Figure11, the crack load of PE-FA-A-0.27 is 1.32 kN with an ultimate load is 2.97 kN; the crack load of PE-KF-B-0.27 is 1.02 kN with an ultimate load of 2.70 kN, and the crack load of PE-FA-A-0.25 is 1.22 kN with an ultimate load of 3.04 kN. The initial crack strength and curve slope of PE-FA-A-0.27 are at the maximum in the elastic stage. At the yield stage, the microcrack has likely reduced the specimens’ capacity by transferring the internal forces, hence the nonlinear trend. The curve slopes of the three sampled groups’ mix ratios begin to decrease, indicating that the stiffness of the specimens has degenerated. The stiffness degradation of PE-FA-A-0.27 is the slowest. However, the ultimate crack strength of PE-FA-A-0.27 is slightly lower than that of PE-FA-A-0.25, its elongation rate upon failure is the largest, and its strain-hardening characteristics are the most obvious. Therefore, the performance of the PE-FA-A-0.27 scheme is better than those of the other two groups.Figure 11
The uniaxial tensile load-displacement curve of PE-ECC.


## 3.3.1. Calculation of Weight Vector

AHP was used to rank the optimal tensile effects of the three groups of mixtures whose average tensile displacement exceeded 7.0 mm. The results and the scale (Tables6 and 8, respectively) were then used to calculate the scores of the elements (Table 9).Table 9
Assignment score table.
Assign itemsAssign valueIndex level357Initial cracking strength351Ultimate tensile strength432Tensile displacement566Age135Obtaining the ultimate weights for the individual ratings can help to determine the weights for each criterion. According to Table6 and (1), the matrix A can be defined as (5)(5)A=1353735315757375171315171.The weight vectorω can be computed using the matrix A as follows:(6)ω2=0,1875,0.3125,0.4375,0.0625T.From (6), the ranking of the four elements (initial cracking strength, tensile displacement, ultimate tensile strength, and test age) in the criterion level relative to the total objective level can be obtained, which altogether comprise the matrix ω2.


## 3.3.2. Determination of Optimal Mixture Proportion

The judgment matrix was established based on the evaluation indices of the first crack strength, ultimate tensile strength, elongation rate, and test age. The matrix is 3 × 4 matrix, in which each column of the matrix represents the order of scheme levelC corresponding to criterion level B, as demonstrated in (7).(7)U3=0.330.450.2940.110.560.330.3530.330.110.220.3530.56.The order of elements of the scheme levelC concerning the objective level A can be expressed as(8)ω3=u3ω2ω3.The global weight vector was calculated using (8). Each element in the weight vector was used to represent the final weight (equation (9)) for the three sampled groups’ mix ratios. The maximum weight of 0.383 was determined as the second scheme’s weight. Thus, the optimal mix ratio was the PE-FA-A-0.27 scheme.(9)ω3=0.3380.3830.279.The load-displacement curves of the three groups’ specimens were plotted to further prove the result (Figure8).The test implemented in this study was divided into the following three stages: initial crack formation stage, stage of stable development of cracks, and failure stage. Based on Figure11, the crack load of PE-FA-A-0.27 is 1.32 kN with an ultimate load is 2.97 kN; the crack load of PE-KF-B-0.27 is 1.02 kN with an ultimate load of 2.70 kN, and the crack load of PE-FA-A-0.25 is 1.22 kN with an ultimate load of 3.04 kN. The initial crack strength and curve slope of PE-FA-A-0.27 are at the maximum in the elastic stage. At the yield stage, the microcrack has likely reduced the specimens’ capacity by transferring the internal forces, hence the nonlinear trend. The curve slopes of the three sampled groups’ mix ratios begin to decrease, indicating that the stiffness of the specimens has degenerated. The stiffness degradation of PE-FA-A-0.27 is the slowest. However, the ultimate crack strength of PE-FA-A-0.27 is slightly lower than that of PE-FA-A-0.25, its elongation rate upon failure is the largest, and its strain-hardening characteristics are the most obvious. Therefore, the performance of the PE-FA-A-0.27 scheme is better than those of the other two groups.Figure 11
The uniaxial tensile load-displacement curve of PE-ECC.


## 4. Conclusions

In this work, we present a method based on the AHP for solving the optimized design of the PE-ECC mix ratio. Through the PE-ECC mix ratio design and tensile test and in consideration of the initial cracking strength, ultimate tensile strength, tensile displacement, and service life concerning the mix proportion, a reasonable and scientific layered structure were established. The weight of each influence factor was calculated by constructing a matrix, and the judgment matrix was determined to validate the consistency of the results. The main conclusions are as follows:(1)
Through the uniaxial tensile test of the specimens applied with different water-binder ratios and mineral contents, the ultimate tensile strength and tensile displacement of the specimens basically decreased with the increase of the water-binder ratios. When the water-binder ratios were 0.25 and 0.27, the corresponding mixtures were better when the mineral contents were 30% and 40% by comparison and analysis of the test results;(2)
The AHP was used in this study to analyze the weights of the three groups of specimens (PE-FA-0.25, PE-FA-A-0.27, and PE-KF-B-0.27). The weight indices have consisted of the initial cracking strength, tensile displacement, ultimate tensile strength, and test age. Then, the judgment matrix was established with these weight indices. The order of the three mix proportions was obtained by matrix calculation. However, ultimately it was found that the optimal mix proportion was determined to be PE-FA-A-0.27 (i.e., fly ash content of 30% and the water-binder ratio of 0.27);(3)
This research provides a reference for the design of mixed proportion and evaluation index of ECC. This work is also relevant for the design of mix proportion and evaluation systems of high-performance fiber-reinforced concrete.



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*Source: 7876056-2022-09-14.xml*