**3. Test Results and Analysis**

### **3. Test Results and Analysis**  *3.1. Determination of Compressive Strength*

*3.1. Determination of Compressive Strength*  The cubic compressive strength of CSG material was followed the Test Rules for Hy-The cubic compressive strength of CSG material was followed the Test Rules for Hydraulic Concrete (SL352-2006).

draulic Concrete (SL352-2006). In this test, four specimens were prepared as one group. After testing, the largest discrete data were removed and the other three groups were averaged. The test results In this test, four specimens were prepared as one group. After testing, the largest discrete data were removed and the other three groups were averaged. The test results were in accordance with the Rules.

### were in accordance with the Rules. *3.2. Analysis of the Test Data*

### *3.2. Analysis of the Test Data*  3.2.1. Effect of Fly Ash Content on the Compressive Strength of CSG Material

3.2.1. Effect of Fly Ash Content on the Compressive Strength of CSG Material Fly ash is a type of artificial pozzolanic material made of silica or silica-alumina. It possesses minimal or no cementing value. However, in the presence of water, fly ash pow-Fly ash is a type of artificial pozzolanic material made of silica or silica-alumina. It possesses minimal or no cementing value. However, in the presence of water, fly ash powder will react with Ca(OH)<sup>2</sup> at room temperature to form a compound with cementing properties. The pozzolanic activity of fly ash is reflected by its cementing.

der will react with Ca(OH)2 at room temperature to form a compound with cementing properties. The pozzolanic activity of fly ash is reflected by its cementing. The test results are shown in Figure 2 for the analysis of the relationship between age, fly ash content, and strength.

The test results are shown in Figure 2 for the analysis of the relationship between age, fly ash content, and strength. As detailed in Figure 2, the rules can be found as follows: (1) the compressive strength of CSG increases with age. The compressive strength of CSG at 90 d is generally 10–30% higher than that at 28 d. (2) When the cement content is 50 kg/m<sup>3</sup> and 60 kg/m<sup>3</sup> , respectively, the compressive strength of CSG increases with the addition of fly ash content. When the cement content is 50 kg/m<sup>3</sup> , the increase of compressive strength at 28 d is greater than that at 90 d. When the cement content is 60 kg/m<sup>3</sup> , the increase of compressive strength at 90 d is greater than that at 28 d [35].

**Figure 2.** The relationship between the compressive strength of CSG material and the age / the content of fly ash. **Figure 2.** The relationship between the compressive strength of CSG material and the age/the content of fly ash.

As detailed in Figure 2, the rules can be found as follows: (1) the compressive strength of CSG increases with age. The compressive strength of CSG at 90 d is generally 10–30% higher than that at 28 d. (2) When the cement content is 50 kg/m3 and 60 kg/m3, respectively, the compressive strength of CSG increases with the addition of fly ash content. When the cement content is 50 kg/m3, the increase of compressive strength at 28 d is greater than that at 90 d. When the cement content is 60 kg/m3, the increase of compressive strength at 90 d is greater than that at 28 d [35]. The test results can be explained with two-phase hydration reaction of the fly ashcement system. First, the induction stage, during which the soluble ions on the surface of fly ash particles dissolve, which affects the nucleation of Ca(OH)2 and C-S-H hydrates and retards the initial level of C3A in cement. Meanwhile, the hydration of cement is delayed, as the fine size of fly ash particles leads to their easy adhesion to the surface of cement particles under physical action. In addition, Ca(OH)2 and C-S-H produced by cement hydration wrap the surface of fly ash and prevent the hydration of fly ash particles. Therefore, the fly ash with early age has low self-activity. Second, the acceleration stage, during which Ca(OH)2 and C-S-H begin to nucleate and grow. Fly ash particles provide additional accommodation for the precipitation of C-S phase hydrates in cement through many new surfaces. In this way, fewer C-S phase hydrates will precipitate on the surface of cement particles, and the dissolution of C3S will accelerate. As a result, the hydration of cement is promoted. Therefore, during the second phase, the presence of fly ash facilitates The test results can be explained with two-phase hydration reaction of the fly ashcement system. First, the induction stage, during which the soluble ions on the surface of fly ash particles dissolve, which affects the nucleation of Ca(OH)<sup>2</sup> and C-S-H hydrates and retards the initial level of C3A in cement. Meanwhile, the hydration of cement is delayed, as the fine size of fly ash particles leads to their easy adhesion to the surface of cement particles under physical action. In addition, Ca(OH)<sup>2</sup> and C-S-H produced by cement hydration wrap the surface of fly ash and prevent the hydration of fly ash particles. Therefore, the fly ash with early age has low self-activity. Second, the acceleration stage, during which Ca(OH)<sup>2</sup> and C-S-H begin to nucleate and grow. Fly ash particles provide additional accommodation for the precipitation of C-S phase hydrates in cement through many new surfaces. In this way, fewer C-S phase hydrates will precipitate on the surface of cement particles, and the dissolution of C3S will accelerate. As a result, the hydration of cement is promoted. Therefore, during the second phase, the presence of fly ash facilitates the hydration of cement. Moreover, due to the nucleation of cement hydration products, the permeability of fly ash coating increases and leads to faster hydration of the fly ash. As fly as hydration consumes more Ca(OH)2, the hydration of cement is promoted further. During this stage, cement and fly ash promote and accelerate each other's hydration at the same time. This phenomenon become obvious with the development of age, which is highlighted by the significant increase of strength of CSG material at the later stage. Therefore, considering the gradual development of material strength, it is appropriate to choose 90 d or 180 d strength as the design strength of CSG dam.

### the hydration of cement. Moreover, due to the nucleation of cement hydration products, the permeability of fly ash coating increases and leads to faster hydration of the fly ash. 3.2.2. Optimal Fly Ash Content of CSG Material

As fly as hydration consumes more Ca(OH)2, the hydration of cement is promoted further. During this stage, cement and fly ash promote and accelerate each other's hydration at the same time. This phenomenon become obvious with the development of age, which is highlighted by the significant increase of strength of CSG material at the later stage. Therefore, considering the gradual development of material strength, it is appropriate to choose Most hydraulic projects will add fly ash to cementitious materials, and the RCC dam has the highest proportion of fly ash addition (70%) (Jiangya Hydropower Station). Technical Guidelines for Damming with Cemented Granular Materials (SL678-2014) also proposes including fly ash into cement gravel and sand material for dam construction, but without mentioning the most optimal and economical fly ash content.

90 d or 180 d strength as the design strength of CSG dam. 3.2.2. Optimal Fly Ash Content of CSG Material Most hydraulic projects will add fly ash to cementitious materials, and the RCC dam has the highest proportion of fly ash addition (70%) (Jiangya Hydropower Station). Technical Guidelines for Damming with Cemented Granular Materials (SL678-2014) also proposes including fly ash into cement gravel and sand material for dam construction, but During the test, prepared the cement content of 50 kg/m<sup>3</sup> and 60 kg/m<sup>3</sup> , added fly ash of 20 kg/m<sup>3</sup> , 30 kg/m<sup>3</sup> , 40 kg/m<sup>3</sup> , 50 kg/m<sup>3</sup> , 60 kg/m<sup>3</sup> , 80 kg/m<sup>3</sup> , or 100 kg/m<sup>3</sup> , respectively, into the cement and waited for 90 d maintenance to make CSG materials to see the difference of their compressive strengths, with results drawn in the figure below. According to the figure, as the fly ash content increases, the compressive strength reaches a peak before falling down to a level. The CSG material test proves that an optimal content of fly ash could be found. The compressive strength of materials will reach its maximum

without mentioning the most optimal and economical fly ash content.

*Crystals* **2021**, *11*, x FOR PEER REVIEW 6 of 10

when both cement and fly ash contents stand at 50 kg/m<sup>3</sup> or 60 kg/m<sup>3</sup> , as highlighted in Figure 3. falling down to a level. The CSG material test proves that an optimal content of fly ash could be found. The compressive strength of materials will reach its maximum when both cement and fly ash contents stand at 50 kg/m3 or 60 kg/m3, as highlighted in Figure 3.

During the test, prepared the cement content of 50 kg/m3 and 60 kg/m3, added fly ash of 20 kg/m3, 30 kg/m3, 40 kg/m3, 50 kg/m3, 60 kg/m3, 80 kg/m3, or 100 kg/m3, respectively, into the cement and waited for 90 d maintenance to make CSG materials to see the difference of their compressive strengths, with results drawn in the figure below. According to the figure, as the fly ash content increases, the compressive strength reaches a peak before

**Figure 3.** Optimal content of fly ash of CSG material. **Figure 3.** Optimal content of fly ash of CSG material.

According to our analysis, as the design of mixed proportions in this test is based on previous research results, the total water consumption of the mixture is fixed by selecting a water–binder ratio of 1.0 and sand ratio of 20%. [35,36] At the initial stage, the strength of CSG material increases with the increase of fly ash content and the water amount is enough to support the hydration of cement and fly ash. The increase of fly ash facilitates C-S-H cementing; when all the water is consumed during the hydration of cement and fly ash, the fly ash added will only serve as a filler, which fill in the concrete voids or attach to the surface of cement particles. At this stage, more fly ash will affect the formation of Ca(OH)2, C-S-H, which leads to the declining strength of CSG materials. Therefore, there is an optimal fly ash content in CSG material, and it is defined to be 50% of the contentious material (cement + fly ash). According to our analysis, as the design of mixed proportions in this test is based on previous research results, the total water consumption of the mixture is fixed by selecting a water–binder ratio of 1.0 and sand ratio of 20%. [35,36] At the initial stage, the strength of CSG material increases with the increase of fly ash content and the water amount is enough to support the hydration of cement and fly ash. The increase of fly ash facilitates C-S-H cementing; when all the water is consumed during the hydration of cement and fly ash, the fly ash added will only serve as a filler, which fill in the concrete voids or attach to the surface of cement particles. At this stage, more fly ash will affect the formation of Ca(OH)2, C-S-H, which leads to the declining strength of CSG materials. Therefore, there is an optimal fly ash content in CSG material, and it is defined to be 50% of the contentious material (cement + fly ash).

### **4. Numerical Regression Analysis 4. Numerical Regression Analysis**

Regression analysis is an important branch of mathematical statistics and an important statistical tool to study the correlation between variables. It is well applied in Regression analysis is an important branch of mathematical statistics and an important statistical tool to study the correlation between variables. It is well applied in many areas, such as seeking empirical formulas or establishing mathematical models.

many areas, such as seeking empirical formulas or establishing mathematical models. According to the test, fly ash content has significant influence on the compressive strength of CSG material. Based on the theory of linear regression model, Formula (1) is built to reflect the statistical relationship between 90 d compressive strength and fly ash content in CSG material: According to the test, fly ash content has significant influence on the compressive strength of CSG material. Based on the theory of linear regression model, Formula (1) is built to reflect the statistical relationship between 90 d compressive strength and fly ash content in CSG material:

$$X\_F = a\_f x\_f^2 + b\_f x\_f + c\_f \tag{1}$$

<sup>2</sup> *XF ff ff f* = ++ *ax bx c* (1) where *a <sup>f</sup>* , *b<sup>f</sup>* , and *c <sup>f</sup>* are statistical constants.

where *<sup>f</sup> a* , *<sup>f</sup> b* , and *<sup>f</sup> c* are statistical constants. After calculation, the regression equation parameters of fly ash content and compressive strength are obtained and shown in Table 4.

After calculation, the regression equation parameters of fly ash content and compressive strength are obtained and shown in Table 4. As illustrated in Table 4, the fitting correlation coefficients are greater than 0.90 and the standard errors are less than 0.58 in all cases. The fitting strength of each regression As illustrated in Table 4, the fitting correlation coefficients are greater than 0.90 and the standard errors are less than 0.58 in all cases. The fitting strength of each regression equation and measured values have demonstrated excellent correlation with regard to 90 d compressive strength of CSG material, with small deviation of regression values and measured values, and high fitting accuracy. The comprehensive analysis shows that the test results suit the mathematical model of linear regression.

Through numerical analysis, the maximum value of compressive strength under different fly ash content can be obtained, where x represents the optimal fly ash content and y represents the maximum compressive strength of CSG material, as detailed in Table 4.

The numerical analysis shows that when (1) 50 kg/m<sup>3</sup> of cement content is combined with 51 kg/m<sup>3</sup> of fly ash content, or (2) the cement and fly ash contents are 60 kg/m<sup>3</sup> and 59 kg/m<sup>3</sup> , respectively, the compressive strength of CSG material is the highest in 90 d. Therefore, when fly ash content: cement content ≈ 1:1 or when the fly ash content is 50% of cementitious materials (cement + fly ash), the "optimal content" is achieved. The "optimal fly ash content" of CSG material was verified again through numerical analysis.


**Table 4.** Regression analysis parameter table.
