# Minimum Water Requirement Method for High-Performance Sulphoaluminate Cement-Based Materials

Authors: Hong-ping Zhang; Pei-kang Bai; Jian-hong Wang; Yan-li Dong; Yun-shan Han
Journal: Advances in Materials Science and Engineering
 (2019)

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## Abstract

In this work, we propose the use of steel slag instead of slag powder, in addition to fly ash and silica fume, to obtain high-performance sulphoaluminate cement-based materials. According to the closest-packing theory and on the basis of the minimum water requirement test, the influence of mineral admixtures on the minimum water requirement was evaluated for sulphoaluminate composite system paste. The optimal composition of the cementitious materials was thus determined. Orthogonal tests were used to assess the validity of this ratio. The correlation between minimum water requirement and the standard consistence was not only analyzed in the system of the minimum water requirement method decided but also in the complicate system of the orthogonal tests determined. Experimental results show that the influence of steel slag on the minimum water requirement is the largest in composite cement paste; minimum water requirement and standard consistency have a good correlation; the cement paste designed with the optimum composite had the highest strength of all the tested materials, but minimum water requirement and strength have a poor correlation in the orthogonal tests. We demonstrate that standard consistency evaluation can replace the minimum water requirement method to determine the optimum ratio of cement mineral admixtures. The proposed method not only simplifies the process but also makes the method more scientific.


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## Body

## 1. Introduction

Recently, the research and applications of cement-based materials have remarkably progressed. Accordingly, the mechanical properties and durability of modern cement-based materials have been significantly improved. The most common approach to obtain high-performance cement-based materials is to reduce the porosity and increase compactness [1]. These materials have high strength and density because of their low water-cement ratio, which is most of the times lower than 0.2 and also because of the addition of fine particles. The diameter of such particles is small enough to gradually fill the gaps left by larger particles, optimizing the overall composition until the gap between solid particles reaches minimum; thus, a high stacking density is achieved and the water requirement is minimal. Therefore, the properties and the accumulation state of cementitious materials are closely related. To obtain high-performance materials, it is crucial to develop granular mixtures with high compactness and low water requirement [2].There are two important characteristic indexes when evaluating the effect of fine particles on high-performance concrete: stacking density and water to solid volume ratio on the matrix. This ratio represents the volume of unit solid material in a paste with the water requirement for a fixed working consistency. The stacking density of solid particles in the concrete considers the physical contribution of fine particles with a diameter under 0.125 mm (including cement) in relation to the strength and compactness of the structure. When comparing equivalent water-cement ratios, the porosity of paste with the lower water to solid volume ratio is lower and the compressive strength is higher. Also, the water requirement of the fine particles, which depends on the stacking density of particles, can be used to determine the water to solid volume ratio. For a good particle composition, the particles with small diameter fill the spaces between coarser particles, thus reducing both the unfilled voids and the water required to fill pores [2].There are several methods to evaluate the compactness of cement gel material: theoretical calculations, model prediction analysis, paste relative density, standard consistency water requirement ratio, stacking density, Puntke saturation point water requirement, minimum water requirement, and wet process, among others. The last four are direct determination methods [3]. Minimum water requirement is often used especially.Presently, there are three types of widely reported cements: Portland, sulphoaluminate, and aluminate cement [4]. Portland cement is most often used to prepare high-performance concrete; for the sulphoaluminate and aluminate ones, there are only a few related reports. Their limitations for engineering applications rise from their defects, e.g., the reduction in later strength. Therefore, certain issues need to be overcome so that these varieties are further developed and used. A possible solution is the combination with mineral admixtures, which not only reduces cement cost but also promotes the use of waste. The efficient utilization of waste represents an important advantage for the environment and, most importantly, may compensate the reduction in later strength [5]. Zhang et al. [6] proved sulphoaluminate cement had characteristic of higher early strength and steady later strength through compounding slag and fly ash, but they adopted a tentative method to prepare the high-performance concrete, which wasted his much time and lacked theoretical guidance; it is very significant to find a good method to replace the traditional method.As one of the mineral admixtures, in comparison with fly ash and slag, ground steel slag has been utilized less sufficiently because of the rare investigation on its characteristics and its usage as cementing material. Liu [7] studied preparation and application of RPC with steel slag, but steel was not used as active ingredients but as aggregate; the maximum of particle size was 2.5 mm. As a new mineral additive of cement, ground steel slag powder has very high activity and its activity is obviously higher than fly ash and close to slag. Furthermore, its distribution is very wide and its quantity is quite plenty in China. Therefore, it has quite high value [8].In this study, sulphoaluminate cement, steel slag (instead of slag powder), fly ash, and silica fume were used to develop composite cement. According to the closest-packing theory and the method of the minimum water requirement, it will be obtained to the maximum density of composite system. Peng [9] obtained the optimum powder ratio of composition of the cementitious materials through the minimum water requirement method; Peng also only took the method as a means, not in-depth discussions; the character of the method was not mentioned and the existing problem was not analyzed. In addition to this, the test depends on the experimental observations, and the operative determines the critical condition where the mixture transforms from the solid to paste state; thus, it is highly subjective and unscientific. Therefore, it is very necessary to seek a new method to replace the minimum water requirement method.In this work, we propose an alternative method to determine the compactness of cement materials. This method eliminates the errors that rise from the subjective measurements in the minimum water requirement method when estimating the end point of paste preparation based on the status of the mixture. To make this method more convictive, we determined the correlation between minimum basic water requirement and standard consistency. If the correlation of two methods is better, we can utilize standard consistency instead of minimum basic water requirement method to determine the optimum powder ratio of composition of the cementitious materials.


## 2. Materials and Experiment Programs

### 2.1. Materials Used

P42.5 rapid hardening sulphoaluminate cement was produced by Tianlong Cement Factory, Shanxi, China. Its specific surface area is 404.6 g/cm2. II grade fly ash was obtained from Second Thermal Power Plant, Taiyuan, China, with the specific surface area of 305.1 g/cm2. Steel slag was purchased from Taiyuan Iron and Steel Group Co., Ltd., China, with the specific surface area of 370 g/cm2. The specific area of silica fume (Shaanxi Linyuan Micro Silicon Powder Company, China) was close to 20000 g/cm2. The water reducing agent is imported from BASF, Germany. The physical properties of the sulphoaluminate cement are listed in Table 1, while the chemical compositions of the used cement and mineral admixtures are shown in Table 2.Table 1
Physical properties index of cement.
Density (g/cm3)
Specific area (g/cm2)
Stability
Standard consistence
Setting time (min)
Rupture strength (MPa)
Compression strength (MPa)
Initial setting
Final setting
1 d
3 d
1 d
3 d
2.76
410
Qualified
0.282
21
30
7.5
8
40
52Table 2
Chemical compositions (%) of cement and mineral admixtures.
Loss on ignition
SiO2
Al2O3
Fe2O3
CaO
MgO
SO3
Na2O
K2O
R2O
Sulphoaluminate cement
5.33
16.3
27.5
1.23
36.5
2.02
9.78
0.24
0.37
0.57
Steel slag
—
15.48
2.34
25.18
37.52
5.43
—
—
0.12
Fly ash
—
51.28
24.12
5.78
3.12
1.08
0.27
—
—
—
Silica fume
—
88.12
0.24
0.07
0.18
0.26
—
—
0.3
—


### 2.2. Particle Size Analysis

The particle size distribution of cement samples was analyzed using a laser particle size analyzer. The result is obtained in Figure1.Figure 1
Cumulative percentage of particle size distribution of raw materials.


### 2.3. Materials Mixes

The cementitious mix proportion was designed by the minimum water requirement method. The process was carried out in [10] to obtain the optimum powder ratio of mix.


### 2.4. Mixing Methods

The method that was used for mixing materials and the curing conditions are in accordance with those given in GB/T1346-2001.


### 2.5. The Optimum Powder Ratio Test

The optimum powder ratio test was determined using the following tests:(i)
Minimum water requirement test(ii)
Standard consistency test: GB/T1346-2001(iii)
Compactness test: GB/T208-1994Minimum water requirement [11, 12] was introduced by LCPC to determine the practical stacking density of powder particles through the measurement of minimum basic water requirement in a paste. According to equation (1), the maximum packing density of the cementing material is(1)∅=11+ρmw/mB,where ρ is the density of the cementing material mixture, g/cm3; mB is the mass of the cementing material, g; and mW is the minimum water requirement of the paste, g.


### 2.6. Orthogonal Test

The tests conducted on the cement paste are as follows:(i)
Compressive strength: GB/T17671-1999(ii)
Minimum water requirement test(iii)
Standard consistency test: GB/T1346-2001Because the main aim of the article is to verify whether the ratio determined by the minimal basic water requirement is optimum, the amount of water reducing agent usually is set to a limit dosage, i.e., saturation point, which is determined by examining the fluidity of cement paste. Herein, the optimum amount of water reducing agent was determined to be 0.6%. The water blinder ratio is determined by the fluidity of cement paste and the mechanical properties of cement. Therefore, it is uncertain whether it is the smallest ratio of water to cement.Three influencing factors are chosen in orthogonal experiments, and each takes three levels. In view of the above discussion, the water-cement ratio is fixed at 0.27. The water reducing agent is fixed as 0.6% of the total quality of composite cementing material. The test ratios of the nine groups of cementitious materials are shown in Table3.Table 3
Mix ratios of compound cement paste.
Dosage (%)
Test No.
Cement
Fly ash
Silica fume
Steel slag
Water binder ratio
Water reducing agent
A1
86.5
4
5
4.5
0.27
0.6
A2
77
4
10
9
0.27
0.6
A3
67.5
4
15
13.5
0.27
0.6
A4
80
6
5
9
0.27
0.6
A5
70.5
6
10
13.5
0.27
0.6
A6
74.5
6
15
4.5
0.27
0.6
A7
67.5
8
5
13.5
0.27
0.6
A8
77.5
8
10
4.5
0.27
0.6
A9
68
8
15
9
0.27
0.6


## 2.1. Materials Used

P42.5 rapid hardening sulphoaluminate cement was produced by Tianlong Cement Factory, Shanxi, China. Its specific surface area is 404.6 g/cm2. II grade fly ash was obtained from Second Thermal Power Plant, Taiyuan, China, with the specific surface area of 305.1 g/cm2. Steel slag was purchased from Taiyuan Iron and Steel Group Co., Ltd., China, with the specific surface area of 370 g/cm2. The specific area of silica fume (Shaanxi Linyuan Micro Silicon Powder Company, China) was close to 20000 g/cm2. The water reducing agent is imported from BASF, Germany. The physical properties of the sulphoaluminate cement are listed in Table 1, while the chemical compositions of the used cement and mineral admixtures are shown in Table 2.Table 1
Physical properties index of cement.
Density (g/cm3)
Specific area (g/cm2)
Stability
Standard consistence
Setting time (min)
Rupture strength (MPa)
Compression strength (MPa)
Initial setting
Final setting
1 d
3 d
1 d
3 d
2.76
410
Qualified
0.282
21
30
7.5
8
40
52Table 2
Chemical compositions (%) of cement and mineral admixtures.
Loss on ignition
SiO2
Al2O3
Fe2O3
CaO
MgO
SO3
Na2O
K2O
R2O
Sulphoaluminate cement
5.33
16.3
27.5
1.23
36.5
2.02
9.78
0.24
0.37
0.57
Steel slag
—
15.48
2.34
25.18
37.52
5.43
—
—
0.12
Fly ash
—
51.28
24.12
5.78
3.12
1.08
0.27
—
—
—
Silica fume
—
88.12
0.24
0.07
0.18
0.26
—
—
0.3
—


## 2.2. Particle Size Analysis

The particle size distribution of cement samples was analyzed using a laser particle size analyzer. The result is obtained in Figure1.Figure 1
Cumulative percentage of particle size distribution of raw materials.


## 2.3. Materials Mixes

The cementitious mix proportion was designed by the minimum water requirement method. The process was carried out in [10] to obtain the optimum powder ratio of mix.


## 2.4. Mixing Methods

The method that was used for mixing materials and the curing conditions are in accordance with those given in GB/T1346-2001.


## 2.5. The Optimum Powder Ratio Test

The optimum powder ratio test was determined using the following tests:(i)
Minimum water requirement test(ii)
Standard consistency test: GB/T1346-2001(iii)
Compactness test: GB/T208-1994Minimum water requirement [11, 12] was introduced by LCPC to determine the practical stacking density of powder particles through the measurement of minimum basic water requirement in a paste. According to equation (1), the maximum packing density of the cementing material is(1)∅=11+ρmw/mB,where ρ is the density of the cementing material mixture, g/cm3; mB is the mass of the cementing material, g; and mW is the minimum water requirement of the paste, g.


## 2.6. Orthogonal Test

The tests conducted on the cement paste are as follows:(i)
Compressive strength: GB/T17671-1999(ii)
Minimum water requirement test(iii)
Standard consistency test: GB/T1346-2001Because the main aim of the article is to verify whether the ratio determined by the minimal basic water requirement is optimum, the amount of water reducing agent usually is set to a limit dosage, i.e., saturation point, which is determined by examining the fluidity of cement paste. Herein, the optimum amount of water reducing agent was determined to be 0.6%. The water blinder ratio is determined by the fluidity of cement paste and the mechanical properties of cement. Therefore, it is uncertain whether it is the smallest ratio of water to cement.Three influencing factors are chosen in orthogonal experiments, and each takes three levels. In view of the above discussion, the water-cement ratio is fixed at 0.27. The water reducing agent is fixed as 0.6% of the total quality of composite cementing material. The test ratios of the nine groups of cementitious materials are shown in Table3.Table 3
Mix ratios of compound cement paste.
Dosage (%)
Test No.
Cement
Fly ash
Silica fume
Steel slag
Water binder ratio
Water reducing agent
A1
86.5
4
5
4.5
0.27
0.6
A2
77
4
10
9
0.27
0.6
A3
67.5
4
15
13.5
0.27
0.6
A4
80
6
5
9
0.27
0.6
A5
70.5
6
10
13.5
0.27
0.6
A6
74.5
6
15
4.5
0.27
0.6
A7
67.5
8
5
13.5
0.27
0.6
A8
77.5
8
10
4.5
0.27
0.6
A9
68
8
15
9
0.27
0.6


## 3. Results and Discussion

### 3.1. The Optimum Powder Ratio Test

#### 3.1.1. The Minimum Water Requirement Test and Compactness Test

In this section, the influence of fly ash dosage on minimum water requirement and density of the binary system, of steel slag’s dosage on the parameters of the ternary system, and of silica fume’s dosage on the parameters of the quaternary system was evaluated, and the results are shown in Figure2–7.Figure 2
Fly ash content effect on standard consistence, minimal water requirement, and stacking density.Figure 3
Steel slag content effect on standard consistence minimal water requirement and stacking density.Figure 4
Silica fume on standard consistence, minimal water requirement, and stacking density.Figure 5
Fly ash (SEM).Figure 6
Steel slag (SEM).Figure 7
Silica fume (SEM).Figure2 shows that the effect of fly ash dosage on the water requirement and density; as fly ash dosage increases, the minimum water requirement of the paste initially decreases and the density first increases and more fine fly ash particles fill the gap between particles, improve the density of composite system, and reduce the water requirement to fill the voids of paste particles; when fly ash dosage is for a 7.5% content, the minimum value of minimum water requirement and the maximum value of maximum density will be obtained; this corresponds to the point where the number of voids between particles is the lowest, and then the amount of water to fill the voids is also minimal. According to equation (1), the stacking density of the system reaches the maximum value at this point. Thereafter, minimum water requirement increases, and compactness decreases when the content of fly ash further increases; at the same time, Figure 1 shows that the particle size of fly ash is less than that of sulphoaluminate cement, the specific surface area of the system becomes greater with more fine particles of fly ash, and the water amount of the surface layer of the powder particles in the paste increases; it leads to minimum water requirement increase, and the density decreases. Figure 2 indicates that there is only a slight effect of fly ash on the water requirement because the curve is slower than that of Figure 3 and the minimum value of minimum water requirement (0.254) is less than that of cement paste (0.267). This small influence may be explained by the fact that in addition to grain diameter and granularity, the shape of the particles is also an important factor. Because of the characteristics of spherical particles and the adequate particle shape of fly ash, the ball bearing and wettability effects are remarkable. Therefore, the mechanical friction between particles is relatively small after particle packing, and the moisture needed to wet the surface is reduced; the amount of water necessary to reach the same humidity is lower (Figure 5) [13, 14]. For the binary system (FA + SAC), the optimum content of fly ash is 7.5%, the minimum basic water requirement of the mixed system is 0.254, and the maximum stacking density is 0.553.According to Figure3, the behavior of minimum water requirement and density after adding steel slag into the binary system is similar to that of adding fly ash into the cement system, that is, the minimum water requirement initially decreases and then increases with increasing steel slag powder dosage. The minimum water requirement is 0.266 at 10% (optimal proportion), and the stacking compactness is 0.548 at this point. Figure 3 shows that compared with the minimum value (0.254) of minimum water requirement of the binary system and the maximum value (0.553) of density, the minimum value (0.266) of the paste increases after adding steel slag, and the maximum (0.548) compactness decreases. This can be explained because the minimum water requirement of the paste involves two factors: the amount of water in the voids and the amount of water on the surface of the particles. After adding steel slag, the amount of water on the surface is greatly affected by the shape of particles; the sphericity coefficient of steel slag particles is small, and they are irregular, so the water requirement is large (Figure 6) [15, 16]. Besides, Figure 1 shows that the particle size of steel slag is larger than the particle size of fly ash, even close to the particle size of sulphoaluminate cement; its ability to fill the gap of paste particles is poorer than fly ash.Similar to the ternary system, the quaternary one is obtained by fixing the proportion of (FA + SAC + SS), which is 0.8325 : 0.0675 : 0.10, and then adding the silica fume in different proportions into the mixed system. Figure4 shows that with the addition of silica fume, the minimum basic water requirement of the paste has a similar behavior that the one described above: it first decreases and then increases with increasing silica fume. The maximum density also initially increases and then decreases. The optimum dosage of silica fume is 10%, where the minimum basic water requirement is 0.24 and the maximum density is 0.573. Comparing Figures 2 and 3, the minimum water requirement of the paste has decreased and the maximum compactness is larger. This also shows that the gradation of particles is closely related to the compactness. For the larger difference of particle size and the wider distribution of it, the large packing density will be easily achieved [17]. Since the particle size of silica fume is small (Figure 7), it fills the voids between particles and improves the particle size distribution compared with the ternary system; thus, the water content is reduced and compactness is enhanced. The minimum water requirement the optimal composition, 0.24, is lower than that of the ternary system, with further increasing the silica fume, because of the larger specific area of silica fume (Figure 1). It will lead to the increase in surface layer of the powder particles, and thus the water requirement of surface layer will increase. In terms of improving the stacking compactness, adding three kinds of particles of different sizes is more efficient than adding only two kinds of particles. The optimum ratio of silica fume is 10%.According to the results obtained from the minimum water requirement method, the optimum ratio of the sulphoaluminate cementitious material is 0.75 : 0.06 : 0.09 : 0.10 for SAC : FA : SF : SS. The test verified again that when the reasonable particle size reaches or be close to the tightest closely packed state, these cement materials have high strength and density because fine particles fill the gap left by larger particles [2].


#### 3.1.2. Standard Consistency Test

The influence of three kinds of mineral admixtures dosage on standard consistency of respective system was evaluated, and the results also are shown in Figures2–4. The influence of them on the standard consistency of the paste is similar to that on the minimum basic water requirement. That is, the variation trends of the two curves in every graph are same; the minimum value of standard consistency and the minimum value of minimum water requirement are acquired in the same dosage of mineral admixture. As previously mentioned, the stacking density and water to solid volume ratio are two important indexes to evaluate the influence of fine particles on high-performance concrete. Volume ratio is defined for a certain work consistency; thus, different work consistencies have different water requirement. The minimum basic water requirement is needed when changing from solid powder to forming spheration particle (Figure 8) into paste state (Figure 9). The standard consistency corresponds to the water requirement when the test rod sinks into the grout and sinks to 6 mm ± 1 mm away from the floor (Figure 10). These are different states of same property corresponding to the conditions of the solid powder when adding different amounts of water. This former depends on the experimental observations to determine the critical condition where the mixture transforms from the solid to paste state; thus, it is highly subjective and lacks scientificity, but the latter acquires the concrete value to determine the state through Vicat apparatus.Figure 8
Solid particle.Figure 9
Paste state.Figure 10
Cement standard consistency.For this composition according to the results obtained from the minimum water requirement method, the minimum water requirement and standard consistency are the smallest and the density is largest. The result is in agreement with Zhang’s conclusion; Zhang and Zhang [18] pointed out that slag cement would have higher density and strength and lower standard consistency when the particle size distribution of slag cement was close to the closest-packing theory; though Zhang did not discuss the relation between the minimum water requirement and the density of slag cement, we all know that the theory basis of the minimum water requirement method is the closest-packing theory, so the two results are consistent. In addition to this, the composition system determined by the minimum water requirement and the one obtained by Zhang are also binary systems and more simple, though the system for the minimum water requirement is not a genuine binary system (Zhang’s test cement system is genuine binary system that has two kinds of materials). The scope of application for the minimum basic water requirement method to evaluate the compactness is generally considered for binary powder materials. The two corresponding systems determined by the Aim-Goff model and by the Toufar model to analyze different stacking densities of mixed powder materials are also generally for binary systems [19]. The ternary system in this work is obtained from an initial cement and fly ash mixture in a fixed proportion (0.925 : 0.075) mixed with steel slag. Then, the quaternary system is based on a cement, fly ash, and steel slag mixture in a fixed proportion (0.8325 : 0.0675 : 0.10), to which silica fume is added. Therefore, in essence, they can be considered as binary systems, initial mixture plus the additional mineral.In the binary system, as previously discussed, we demonstrate that standard consistency evaluation can replace the minimum water requirement method to determine the optimum ratio of cement mineral admixtures.How is the relation between standard consistency of paste and the minimum water consistent when the composite system is the genuine ternary system (three mineral admixtures) or the genuine quaternary (four mineral admixtures) system? In order to verify the strength obtained from optimum ratio is the largest and to discuss the correlation of them in the complicated system, in the following section, the design of an orthogonal experiment to evaluate this ratio is presented.


### 3.2. Orthogonal Test

The test results of the nine groups of cementitious materials are shown in Tables4 and 5.Table 4
Compressive strength, standard consistency, and minimal water requirement.
Dosage (%)
Test number
Cement
Fly ash
Silica fume
Steel slag
Water binder ratio
Water reducing agent
Standard consistence
Minimal water requirement
28 d compress strength (MPa)
A1
86.5
4
5
4.5
0.27
0.6
0.312
0.243
85.1
A2
77
4
10
9
0.27
0.6
0.36
0.263
85.2
A3
67.5
4
15
13.5
0.27
0.6
0.468
0.315
59.6
A4
80
6
5
9
0.27
0.6
0.358
0.266
88.4
A5
70.5
6
10
13.5
0.27
0.6
0.407
0.291
79.4
A6
74.5
6
15
4.5
0.27
0.6
0.363
0.268
71.5
A7
67.5
8
5
13.5
0.27
0.6
0.392
0.277
65.1
A8
77.5
8
10
4.5
0.27
0.6
0.352
0.251
71.4
A9
68
8
15
9
0.27
0.6
0.420
0.280
66.0Table 5
Orthogonal test analysis.
Function
Dosage (%)
FF
SS
SF
Standard consistency
K1
1.172
1.049
1.027
K2
1.128
1.151
1.17
K3
1.151
1.251
1.254
R
0.044
0.202
0.227
Strength after 28 d
K1
229.9
238.6
228
K2
239.3
236.0
239.6
K3
202.5
197.1
204.1
R
36.55
41.44
35.64


#### 3.2.1. Standard Consistency Test

Table5 shows the analysis of the orthogonal test results. The influence of the factors affecting the material standard consistency is as follows: slag steel power > silica fume > fly ash. The result is consistent with the influence of mineral admixture on the standard consistency of the paste through analyzing optimum powder ratio test. Range analysis shows that steel slag is the most important factor affecting the standard consistency; its K value is 0.227. For silica fume, the K value is 0.202. These two values are very similar. The relationship between average standard consistency of paste and contents of slag steel power, silica fume, and fly ash is shown in Figure 11. With increasing mineral admixtures content, the two curves from fly ash and silica fume have same trend that initially decreases, reaches the minimum value, and then increases; the result is consistent with the optimum powder ratio test, but the behavior of steel slag is different from them; the lowest point does not appear, and standard consistency seems always increasing with steel slag content; the reason is steel slag is too sensitive to water, and many factors are considered in the orthogonal test. For steel slag, no matter how large the particle size is, they are irregular, so a large amount of water is necessary; therefore, it has a more notorious influence than that of silica fume. From K value, the difference between these two factors is not very significant; the mechanism by which they affect the consistence is not the same. Large specific surface area and large SiO2 content were observed for silica fume with small particle size (Figure 7). In addition, silica fume has high pozzolanic activity during the early hydration process, and it may react with the Ca(OH)2 produced due to cement hydration in a very short time to generate a low calcium C-S-H gel. Thus, the early strength of cementitious material can be increased. However, the addition of silica fume requires a larger amount of water because of the elevated heat release [19, 20]. The effect of fly ash is the smallest among the three factors, possibly because of its spherical particles. The advantages of adequate particle morphology, ball bearing, and wetting effect are significant. Therefore, the mechanical friction between particles is relatively small after particle accumulation, and the moisture required to damp the surface is reduced; less water is needed to achieve the same moisture.Figure 11
The relationship between the standard consistency average and the added mineral content.


#### 3.2.2. Compressive Strength Test and the Optimum Ratio Determined

According to Table5, the effect on later strength is as follows: silica fume > fly ash > steel slag powder. The different relationship between the average 28 day compressive strength of the cement paste and the silica fume, slag steel, and fly ash content is shown in Figure 12. Range analysis shows the effect of steel slag powder and fly ash is very similar. K value of former is 35.64; the latter is 36.55. These two values are very similar. But for silica fume, K value is 41.44. Since the increase in silica fume reduces the later strength, it is necessary to consider its role for cementing materials. The influence of steel slag and fly ash on the later strength does not show remarkable differences. With the increase in curing period, the mineral phase of steel slag gradually hydrated, promoting the strength increase of the composite system, but to find whether it is steel slag, fly ash, or silica fume, there exists an optimum value; it is consistent with the result of optimum powder ratio determined by the minimum basic water requirement test. For the functional effect of fly ash, the volcano ash, filling densification, and micro aggregate effects may occur with the increase in curing period [21].Figure 12
The relationship curve between the 28-day compression average and added mineral content.According to theK value analysis results (Table 5), the best level should be 5% for the silica fume dosage because the difference between the K values at 5 and 10% dosage is not very large (238.6 MPa and 236.0 MPa). To take full advantage of the waste resources without a great sacrifice in later strength, the level of silica fume may be adjusted to 10%. The optimum levels of fly ash and steel slag are 6% and 9%. Orthogonal test results show that the strength of the ratio determined by the minimal water requirement method is the highest. In addition to the optimum ratio, ratios A2 and A4 listed in Table 4 may be selected. Moreover, as seen in Table 4, the 28 d strength determined by the ratios close to the optimum is high. The result also is consistent with Zhang’s conclusion [18].


#### 3.2.3. Correlation between Minimum Basic Water Requirement and Standard Consistency

In the system determined by minimum water requirement method, we have drawn a conclusion that standard consistency evaluation can replace the minimum water requirement method to evaluate the preparation of high-density composite cement. If in the complicated system, the correlation of standard consistency and minimal water is higher; the minimum water requirement method can be really replaced by standard consistency evaluation method. To further understand the relationship between these parameters, the orthogonal test results are presented in Figure13. The plot clearly shows that the two curves have the same behavior. For a quantitative analysis, the correlation coefficient of the two curves from nine groups of ratio of the orthogonal test was determined. The correlation coefficient is 0.948, which indicates that there is a good correlation between them because they are different states of same property of composite system paste even though the quaternary system is more complicated. To determine the optimum proportion of mineral admixture for high-performance cementitious materials, the standard consistency of the mixing system could be measured to indirectly obtain information about the minimum basic water requirement. If only the optimum proportion of the cementitious material is required and not the compactness, it is only necessary to measure standard consistency. If, in addition to the optimum proportion, it is necessary to know the maximum density of the paste, the minimum basic water requirement could be measured only for the already determined optimum proportion and the density would be obtained using equation (1). In this manner, it is possible to eliminate the errors that rise from the subjective determination of the mixture state in the minimum basic water requirement tests. The proposed method not only simplifies the process but also makes the method more scientific.Figure 13
Water requirement and standard consistence as a function of the test number.


#### 3.2.4. Correlation between Minimum Basic Water Requirement (Standard Consistency) and Strength

The correlations between strength (compactness) and minimum basic water requirement and strength and standard consistency are not good; they are all negative correlations as shown in Figure14. The former is −0.714 and the latter is −0.767. However, it can be seen that the paste with lower minimum basic water requirement or standard consistency has an overall higher strength, while the strength of the pastes with high water requirement is generally lower.Figure 14
Water requirement, standard consistence, and compression strength as a function of the test number.The main reason for such poor correlation is that many factors are considered in the orthogonal test. The genuine quaternary powder materials are more complicated than the binary for the minimum basic water requirement method to evaluate the compactness generally considered. Additionally, the minimum basic water requirement and compressive strength are two different properties; the influence of more factors on two properties is different though they have good consistency in binary powder because there is less influencing factors. In addition to these, the poor correlation between water requirement and strength may be due to the particle shape, which is an important factor along with size and granularity. The level of understanding for the relationship between particle shape and compactness of nonspherical particles is very limited. Some reports [20, 21] attempt to predict the compactness of nonspherical particles by considering the parameter of the sphericity, but the results show that the prediction is not accurate. In fact, minimum water requirement includes the water of particle gaps and on the surface, but the shape of the particles has a greater influence on the latter. The sphericity coefficient of steel slag particles is small and the water requirement is large, so this is also an important factor causing the poor correlation between them.The correlation between minimum basic water requirement and strength (density) and standard consistency and strength is poor in the orthogonal test, but it is higher in the binary system. The conclusion is consistent with Wang et al. [22]. Wang et al. pointed that there was a certain correlation between water absorption ratio and strength of cement-fly ash paste. The more the composition of cement paste was, the more complex the interaction between the components was and the worse the correlation between the water absorption and the strength was, but it was more effective to evaluate the correlation of the simple components of cement paste.


## 3.1. The Optimum Powder Ratio Test

### 3.1.1. The Minimum Water Requirement Test and Compactness Test

In this section, the influence of fly ash dosage on minimum water requirement and density of the binary system, of steel slag’s dosage on the parameters of the ternary system, and of silica fume’s dosage on the parameters of the quaternary system was evaluated, and the results are shown in Figure2–7.Figure 2
Fly ash content effect on standard consistence, minimal water requirement, and stacking density.Figure 3
Steel slag content effect on standard consistence minimal water requirement and stacking density.Figure 4
Silica fume on standard consistence, minimal water requirement, and stacking density.Figure 5
Fly ash (SEM).Figure 6
Steel slag (SEM).Figure 7
Silica fume (SEM).Figure2 shows that the effect of fly ash dosage on the water requirement and density; as fly ash dosage increases, the minimum water requirement of the paste initially decreases and the density first increases and more fine fly ash particles fill the gap between particles, improve the density of composite system, and reduce the water requirement to fill the voids of paste particles; when fly ash dosage is for a 7.5% content, the minimum value of minimum water requirement and the maximum value of maximum density will be obtained; this corresponds to the point where the number of voids between particles is the lowest, and then the amount of water to fill the voids is also minimal. According to equation (1), the stacking density of the system reaches the maximum value at this point. Thereafter, minimum water requirement increases, and compactness decreases when the content of fly ash further increases; at the same time, Figure 1 shows that the particle size of fly ash is less than that of sulphoaluminate cement, the specific surface area of the system becomes greater with more fine particles of fly ash, and the water amount of the surface layer of the powder particles in the paste increases; it leads to minimum water requirement increase, and the density decreases. Figure 2 indicates that there is only a slight effect of fly ash on the water requirement because the curve is slower than that of Figure 3 and the minimum value of minimum water requirement (0.254) is less than that of cement paste (0.267). This small influence may be explained by the fact that in addition to grain diameter and granularity, the shape of the particles is also an important factor. Because of the characteristics of spherical particles and the adequate particle shape of fly ash, the ball bearing and wettability effects are remarkable. Therefore, the mechanical friction between particles is relatively small after particle packing, and the moisture needed to wet the surface is reduced; the amount of water necessary to reach the same humidity is lower (Figure 5) [13, 14]. For the binary system (FA + SAC), the optimum content of fly ash is 7.5%, the minimum basic water requirement of the mixed system is 0.254, and the maximum stacking density is 0.553.According to Figure3, the behavior of minimum water requirement and density after adding steel slag into the binary system is similar to that of adding fly ash into the cement system, that is, the minimum water requirement initially decreases and then increases with increasing steel slag powder dosage. The minimum water requirement is 0.266 at 10% (optimal proportion), and the stacking compactness is 0.548 at this point. Figure 3 shows that compared with the minimum value (0.254) of minimum water requirement of the binary system and the maximum value (0.553) of density, the minimum value (0.266) of the paste increases after adding steel slag, and the maximum (0.548) compactness decreases. This can be explained because the minimum water requirement of the paste involves two factors: the amount of water in the voids and the amount of water on the surface of the particles. After adding steel slag, the amount of water on the surface is greatly affected by the shape of particles; the sphericity coefficient of steel slag particles is small, and they are irregular, so the water requirement is large (Figure 6) [15, 16]. Besides, Figure 1 shows that the particle size of steel slag is larger than the particle size of fly ash, even close to the particle size of sulphoaluminate cement; its ability to fill the gap of paste particles is poorer than fly ash.Similar to the ternary system, the quaternary one is obtained by fixing the proportion of (FA + SAC + SS), which is 0.8325 : 0.0675 : 0.10, and then adding the silica fume in different proportions into the mixed system. Figure4 shows that with the addition of silica fume, the minimum basic water requirement of the paste has a similar behavior that the one described above: it first decreases and then increases with increasing silica fume. The maximum density also initially increases and then decreases. The optimum dosage of silica fume is 10%, where the minimum basic water requirement is 0.24 and the maximum density is 0.573. Comparing Figures 2 and 3, the minimum water requirement of the paste has decreased and the maximum compactness is larger. This also shows that the gradation of particles is closely related to the compactness. For the larger difference of particle size and the wider distribution of it, the large packing density will be easily achieved [17]. Since the particle size of silica fume is small (Figure 7), it fills the voids between particles and improves the particle size distribution compared with the ternary system; thus, the water content is reduced and compactness is enhanced. The minimum water requirement the optimal composition, 0.24, is lower than that of the ternary system, with further increasing the silica fume, because of the larger specific area of silica fume (Figure 1). It will lead to the increase in surface layer of the powder particles, and thus the water requirement of surface layer will increase. In terms of improving the stacking compactness, adding three kinds of particles of different sizes is more efficient than adding only two kinds of particles. The optimum ratio of silica fume is 10%.According to the results obtained from the minimum water requirement method, the optimum ratio of the sulphoaluminate cementitious material is 0.75 : 0.06 : 0.09 : 0.10 for SAC : FA : SF : SS. The test verified again that when the reasonable particle size reaches or be close to the tightest closely packed state, these cement materials have high strength and density because fine particles fill the gap left by larger particles [2].


### 3.1.2. Standard Consistency Test

The influence of three kinds of mineral admixtures dosage on standard consistency of respective system was evaluated, and the results also are shown in Figures2–4. The influence of them on the standard consistency of the paste is similar to that on the minimum basic water requirement. That is, the variation trends of the two curves in every graph are same; the minimum value of standard consistency and the minimum value of minimum water requirement are acquired in the same dosage of mineral admixture. As previously mentioned, the stacking density and water to solid volume ratio are two important indexes to evaluate the influence of fine particles on high-performance concrete. Volume ratio is defined for a certain work consistency; thus, different work consistencies have different water requirement. The minimum basic water requirement is needed when changing from solid powder to forming spheration particle (Figure 8) into paste state (Figure 9). The standard consistency corresponds to the water requirement when the test rod sinks into the grout and sinks to 6 mm ± 1 mm away from the floor (Figure 10). These are different states of same property corresponding to the conditions of the solid powder when adding different amounts of water. This former depends on the experimental observations to determine the critical condition where the mixture transforms from the solid to paste state; thus, it is highly subjective and lacks scientificity, but the latter acquires the concrete value to determine the state through Vicat apparatus.Figure 8
Solid particle.Figure 9
Paste state.Figure 10
Cement standard consistency.For this composition according to the results obtained from the minimum water requirement method, the minimum water requirement and standard consistency are the smallest and the density is largest. The result is in agreement with Zhang’s conclusion; Zhang and Zhang [18] pointed out that slag cement would have higher density and strength and lower standard consistency when the particle size distribution of slag cement was close to the closest-packing theory; though Zhang did not discuss the relation between the minimum water requirement and the density of slag cement, we all know that the theory basis of the minimum water requirement method is the closest-packing theory, so the two results are consistent. In addition to this, the composition system determined by the minimum water requirement and the one obtained by Zhang are also binary systems and more simple, though the system for the minimum water requirement is not a genuine binary system (Zhang’s test cement system is genuine binary system that has two kinds of materials). The scope of application for the minimum basic water requirement method to evaluate the compactness is generally considered for binary powder materials. The two corresponding systems determined by the Aim-Goff model and by the Toufar model to analyze different stacking densities of mixed powder materials are also generally for binary systems [19]. The ternary system in this work is obtained from an initial cement and fly ash mixture in a fixed proportion (0.925 : 0.075) mixed with steel slag. Then, the quaternary system is based on a cement, fly ash, and steel slag mixture in a fixed proportion (0.8325 : 0.0675 : 0.10), to which silica fume is added. Therefore, in essence, they can be considered as binary systems, initial mixture plus the additional mineral.In the binary system, as previously discussed, we demonstrate that standard consistency evaluation can replace the minimum water requirement method to determine the optimum ratio of cement mineral admixtures.How is the relation between standard consistency of paste and the minimum water consistent when the composite system is the genuine ternary system (three mineral admixtures) or the genuine quaternary (four mineral admixtures) system? In order to verify the strength obtained from optimum ratio is the largest and to discuss the correlation of them in the complicated system, in the following section, the design of an orthogonal experiment to evaluate this ratio is presented.


## 3.1.1. The Minimum Water Requirement Test and Compactness Test

In this section, the influence of fly ash dosage on minimum water requirement and density of the binary system, of steel slag’s dosage on the parameters of the ternary system, and of silica fume’s dosage on the parameters of the quaternary system was evaluated, and the results are shown in Figure2–7.Figure 2
Fly ash content effect on standard consistence, minimal water requirement, and stacking density.Figure 3
Steel slag content effect on standard consistence minimal water requirement and stacking density.Figure 4
Silica fume on standard consistence, minimal water requirement, and stacking density.Figure 5
Fly ash (SEM).Figure 6
Steel slag (SEM).Figure 7
Silica fume (SEM).Figure2 shows that the effect of fly ash dosage on the water requirement and density; as fly ash dosage increases, the minimum water requirement of the paste initially decreases and the density first increases and more fine fly ash particles fill the gap between particles, improve the density of composite system, and reduce the water requirement to fill the voids of paste particles; when fly ash dosage is for a 7.5% content, the minimum value of minimum water requirement and the maximum value of maximum density will be obtained; this corresponds to the point where the number of voids between particles is the lowest, and then the amount of water to fill the voids is also minimal. According to equation (1), the stacking density of the system reaches the maximum value at this point. Thereafter, minimum water requirement increases, and compactness decreases when the content of fly ash further increases; at the same time, Figure 1 shows that the particle size of fly ash is less than that of sulphoaluminate cement, the specific surface area of the system becomes greater with more fine particles of fly ash, and the water amount of the surface layer of the powder particles in the paste increases; it leads to minimum water requirement increase, and the density decreases. Figure 2 indicates that there is only a slight effect of fly ash on the water requirement because the curve is slower than that of Figure 3 and the minimum value of minimum water requirement (0.254) is less than that of cement paste (0.267). This small influence may be explained by the fact that in addition to grain diameter and granularity, the shape of the particles is also an important factor. Because of the characteristics of spherical particles and the adequate particle shape of fly ash, the ball bearing and wettability effects are remarkable. Therefore, the mechanical friction between particles is relatively small after particle packing, and the moisture needed to wet the surface is reduced; the amount of water necessary to reach the same humidity is lower (Figure 5) [13, 14]. For the binary system (FA + SAC), the optimum content of fly ash is 7.5%, the minimum basic water requirement of the mixed system is 0.254, and the maximum stacking density is 0.553.According to Figure3, the behavior of minimum water requirement and density after adding steel slag into the binary system is similar to that of adding fly ash into the cement system, that is, the minimum water requirement initially decreases and then increases with increasing steel slag powder dosage. The minimum water requirement is 0.266 at 10% (optimal proportion), and the stacking compactness is 0.548 at this point. Figure 3 shows that compared with the minimum value (0.254) of minimum water requirement of the binary system and the maximum value (0.553) of density, the minimum value (0.266) of the paste increases after adding steel slag, and the maximum (0.548) compactness decreases. This can be explained because the minimum water requirement of the paste involves two factors: the amount of water in the voids and the amount of water on the surface of the particles. After adding steel slag, the amount of water on the surface is greatly affected by the shape of particles; the sphericity coefficient of steel slag particles is small, and they are irregular, so the water requirement is large (Figure 6) [15, 16]. Besides, Figure 1 shows that the particle size of steel slag is larger than the particle size of fly ash, even close to the particle size of sulphoaluminate cement; its ability to fill the gap of paste particles is poorer than fly ash.Similar to the ternary system, the quaternary one is obtained by fixing the proportion of (FA + SAC + SS), which is 0.8325 : 0.0675 : 0.10, and then adding the silica fume in different proportions into the mixed system. Figure4 shows that with the addition of silica fume, the minimum basic water requirement of the paste has a similar behavior that the one described above: it first decreases and then increases with increasing silica fume. The maximum density also initially increases and then decreases. The optimum dosage of silica fume is 10%, where the minimum basic water requirement is 0.24 and the maximum density is 0.573. Comparing Figures 2 and 3, the minimum water requirement of the paste has decreased and the maximum compactness is larger. This also shows that the gradation of particles is closely related to the compactness. For the larger difference of particle size and the wider distribution of it, the large packing density will be easily achieved [17]. Since the particle size of silica fume is small (Figure 7), it fills the voids between particles and improves the particle size distribution compared with the ternary system; thus, the water content is reduced and compactness is enhanced. The minimum water requirement the optimal composition, 0.24, is lower than that of the ternary system, with further increasing the silica fume, because of the larger specific area of silica fume (Figure 1). It will lead to the increase in surface layer of the powder particles, and thus the water requirement of surface layer will increase. In terms of improving the stacking compactness, adding three kinds of particles of different sizes is more efficient than adding only two kinds of particles. The optimum ratio of silica fume is 10%.According to the results obtained from the minimum water requirement method, the optimum ratio of the sulphoaluminate cementitious material is 0.75 : 0.06 : 0.09 : 0.10 for SAC : FA : SF : SS. The test verified again that when the reasonable particle size reaches or be close to the tightest closely packed state, these cement materials have high strength and density because fine particles fill the gap left by larger particles [2].


## 3.1.2. Standard Consistency Test

The influence of three kinds of mineral admixtures dosage on standard consistency of respective system was evaluated, and the results also are shown in Figures2–4. The influence of them on the standard consistency of the paste is similar to that on the minimum basic water requirement. That is, the variation trends of the two curves in every graph are same; the minimum value of standard consistency and the minimum value of minimum water requirement are acquired in the same dosage of mineral admixture. As previously mentioned, the stacking density and water to solid volume ratio are two important indexes to evaluate the influence of fine particles on high-performance concrete. Volume ratio is defined for a certain work consistency; thus, different work consistencies have different water requirement. The minimum basic water requirement is needed when changing from solid powder to forming spheration particle (Figure 8) into paste state (Figure 9). The standard consistency corresponds to the water requirement when the test rod sinks into the grout and sinks to 6 mm ± 1 mm away from the floor (Figure 10). These are different states of same property corresponding to the conditions of the solid powder when adding different amounts of water. This former depends on the experimental observations to determine the critical condition where the mixture transforms from the solid to paste state; thus, it is highly subjective and lacks scientificity, but the latter acquires the concrete value to determine the state through Vicat apparatus.Figure 8
Solid particle.Figure 9
Paste state.Figure 10
Cement standard consistency.For this composition according to the results obtained from the minimum water requirement method, the minimum water requirement and standard consistency are the smallest and the density is largest. The result is in agreement with Zhang’s conclusion; Zhang and Zhang [18] pointed out that slag cement would have higher density and strength and lower standard consistency when the particle size distribution of slag cement was close to the closest-packing theory; though Zhang did not discuss the relation between the minimum water requirement and the density of slag cement, we all know that the theory basis of the minimum water requirement method is the closest-packing theory, so the two results are consistent. In addition to this, the composition system determined by the minimum water requirement and the one obtained by Zhang are also binary systems and more simple, though the system for the minimum water requirement is not a genuine binary system (Zhang’s test cement system is genuine binary system that has two kinds of materials). The scope of application for the minimum basic water requirement method to evaluate the compactness is generally considered for binary powder materials. The two corresponding systems determined by the Aim-Goff model and by the Toufar model to analyze different stacking densities of mixed powder materials are also generally for binary systems [19]. The ternary system in this work is obtained from an initial cement and fly ash mixture in a fixed proportion (0.925 : 0.075) mixed with steel slag. Then, the quaternary system is based on a cement, fly ash, and steel slag mixture in a fixed proportion (0.8325 : 0.0675 : 0.10), to which silica fume is added. Therefore, in essence, they can be considered as binary systems, initial mixture plus the additional mineral.In the binary system, as previously discussed, we demonstrate that standard consistency evaluation can replace the minimum water requirement method to determine the optimum ratio of cement mineral admixtures.How is the relation between standard consistency of paste and the minimum water consistent when the composite system is the genuine ternary system (three mineral admixtures) or the genuine quaternary (four mineral admixtures) system? In order to verify the strength obtained from optimum ratio is the largest and to discuss the correlation of them in the complicated system, in the following section, the design of an orthogonal experiment to evaluate this ratio is presented.


## 3.2. Orthogonal Test

The test results of the nine groups of cementitious materials are shown in Tables4 and 5.Table 4
Compressive strength, standard consistency, and minimal water requirement.
Dosage (%)
Test number
Cement
Fly ash
Silica fume
Steel slag
Water binder ratio
Water reducing agent
Standard consistence
Minimal water requirement
28 d compress strength (MPa)
A1
86.5
4
5
4.5
0.27
0.6
0.312
0.243
85.1
A2
77
4
10
9
0.27
0.6
0.36
0.263
85.2
A3
67.5
4
15
13.5
0.27
0.6
0.468
0.315
59.6
A4
80
6
5
9
0.27
0.6
0.358
0.266
88.4
A5
70.5
6
10
13.5
0.27
0.6
0.407
0.291
79.4
A6
74.5
6
15
4.5
0.27
0.6
0.363
0.268
71.5
A7
67.5
8
5
13.5
0.27
0.6
0.392
0.277
65.1
A8
77.5
8
10
4.5
0.27
0.6
0.352
0.251
71.4
A9
68
8
15
9
0.27
0.6
0.420
0.280
66.0Table 5
Orthogonal test analysis.
Function
Dosage (%)
FF
SS
SF
Standard consistency
K1
1.172
1.049
1.027
K2
1.128
1.151
1.17
K3
1.151
1.251
1.254
R
0.044
0.202
0.227
Strength after 28 d
K1
229.9
238.6
228
K2
239.3
236.0
239.6
K3
202.5
197.1
204.1
R
36.55
41.44
35.64


### 3.2.1. Standard Consistency Test

Table5 shows the analysis of the orthogonal test results. The influence of the factors affecting the material standard consistency is as follows: slag steel power > silica fume > fly ash. The result is consistent with the influence of mineral admixture on the standard consistency of the paste through analyzing optimum powder ratio test. Range analysis shows that steel slag is the most important factor affecting the standard consistency; its K value is 0.227. For silica fume, the K value is 0.202. These two values are very similar. The relationship between average standard consistency of paste and contents of slag steel power, silica fume, and fly ash is shown in Figure 11. With increasing mineral admixtures content, the two curves from fly ash and silica fume have same trend that initially decreases, reaches the minimum value, and then increases; the result is consistent with the optimum powder ratio test, but the behavior of steel slag is different from them; the lowest point does not appear, and standard consistency seems always increasing with steel slag content; the reason is steel slag is too sensitive to water, and many factors are considered in the orthogonal test. For steel slag, no matter how large the particle size is, they are irregular, so a large amount of water is necessary; therefore, it has a more notorious influence than that of silica fume. From K value, the difference between these two factors is not very significant; the mechanism by which they affect the consistence is not the same. Large specific surface area and large SiO2 content were observed for silica fume with small particle size (Figure 7). In addition, silica fume has high pozzolanic activity during the early hydration process, and it may react with the Ca(OH)2 produced due to cement hydration in a very short time to generate a low calcium C-S-H gel. Thus, the early strength of cementitious material can be increased. However, the addition of silica fume requires a larger amount of water because of the elevated heat release [19, 20]. The effect of fly ash is the smallest among the three factors, possibly because of its spherical particles. The advantages of adequate particle morphology, ball bearing, and wetting effect are significant. Therefore, the mechanical friction between particles is relatively small after particle accumulation, and the moisture required to damp the surface is reduced; less water is needed to achieve the same moisture.Figure 11
The relationship between the standard consistency average and the added mineral content.


### 3.2.2. Compressive Strength Test and the Optimum Ratio Determined

According to Table5, the effect on later strength is as follows: silica fume > fly ash > steel slag powder. The different relationship between the average 28 day compressive strength of the cement paste and the silica fume, slag steel, and fly ash content is shown in Figure 12. Range analysis shows the effect of steel slag powder and fly ash is very similar. K value of former is 35.64; the latter is 36.55. These two values are very similar. But for silica fume, K value is 41.44. Since the increase in silica fume reduces the later strength, it is necessary to consider its role for cementing materials. The influence of steel slag and fly ash on the later strength does not show remarkable differences. With the increase in curing period, the mineral phase of steel slag gradually hydrated, promoting the strength increase of the composite system, but to find whether it is steel slag, fly ash, or silica fume, there exists an optimum value; it is consistent with the result of optimum powder ratio determined by the minimum basic water requirement test. For the functional effect of fly ash, the volcano ash, filling densification, and micro aggregate effects may occur with the increase in curing period [21].Figure 12
The relationship curve between the 28-day compression average and added mineral content.According to theK value analysis results (Table 5), the best level should be 5% for the silica fume dosage because the difference between the K values at 5 and 10% dosage is not very large (238.6 MPa and 236.0 MPa). To take full advantage of the waste resources without a great sacrifice in later strength, the level of silica fume may be adjusted to 10%. The optimum levels of fly ash and steel slag are 6% and 9%. Orthogonal test results show that the strength of the ratio determined by the minimal water requirement method is the highest. In addition to the optimum ratio, ratios A2 and A4 listed in Table 4 may be selected. Moreover, as seen in Table 4, the 28 d strength determined by the ratios close to the optimum is high. The result also is consistent with Zhang’s conclusion [18].


### 3.2.3. Correlation between Minimum Basic Water Requirement and Standard Consistency

In the system determined by minimum water requirement method, we have drawn a conclusion that standard consistency evaluation can replace the minimum water requirement method to evaluate the preparation of high-density composite cement. If in the complicated system, the correlation of standard consistency and minimal water is higher; the minimum water requirement method can be really replaced by standard consistency evaluation method. To further understand the relationship between these parameters, the orthogonal test results are presented in Figure13. The plot clearly shows that the two curves have the same behavior. For a quantitative analysis, the correlation coefficient of the two curves from nine groups of ratio of the orthogonal test was determined. The correlation coefficient is 0.948, which indicates that there is a good correlation between them because they are different states of same property of composite system paste even though the quaternary system is more complicated. To determine the optimum proportion of mineral admixture for high-performance cementitious materials, the standard consistency of the mixing system could be measured to indirectly obtain information about the minimum basic water requirement. If only the optimum proportion of the cementitious material is required and not the compactness, it is only necessary to measure standard consistency. If, in addition to the optimum proportion, it is necessary to know the maximum density of the paste, the minimum basic water requirement could be measured only for the already determined optimum proportion and the density would be obtained using equation (1). In this manner, it is possible to eliminate the errors that rise from the subjective determination of the mixture state in the minimum basic water requirement tests. The proposed method not only simplifies the process but also makes the method more scientific.Figure 13
Water requirement and standard consistence as a function of the test number.


### 3.2.4. Correlation between Minimum Basic Water Requirement (Standard Consistency) and Strength

The correlations between strength (compactness) and minimum basic water requirement and strength and standard consistency are not good; they are all negative correlations as shown in Figure14. The former is −0.714 and the latter is −0.767. However, it can be seen that the paste with lower minimum basic water requirement or standard consistency has an overall higher strength, while the strength of the pastes with high water requirement is generally lower.Figure 14
Water requirement, standard consistence, and compression strength as a function of the test number.The main reason for such poor correlation is that many factors are considered in the orthogonal test. The genuine quaternary powder materials are more complicated than the binary for the minimum basic water requirement method to evaluate the compactness generally considered. Additionally, the minimum basic water requirement and compressive strength are two different properties; the influence of more factors on two properties is different though they have good consistency in binary powder because there is less influencing factors. In addition to these, the poor correlation between water requirement and strength may be due to the particle shape, which is an important factor along with size and granularity. The level of understanding for the relationship between particle shape and compactness of nonspherical particles is very limited. Some reports [20, 21] attempt to predict the compactness of nonspherical particles by considering the parameter of the sphericity, but the results show that the prediction is not accurate. In fact, minimum water requirement includes the water of particle gaps and on the surface, but the shape of the particles has a greater influence on the latter. The sphericity coefficient of steel slag particles is small and the water requirement is large, so this is also an important factor causing the poor correlation between them.The correlation between minimum basic water requirement and strength (density) and standard consistency and strength is poor in the orthogonal test, but it is higher in the binary system. The conclusion is consistent with Wang et al. [22]. Wang et al. pointed that there was a certain correlation between water absorption ratio and strength of cement-fly ash paste. The more the composition of cement paste was, the more complex the interaction between the components was and the worse the correlation between the water absorption and the strength was, but it was more effective to evaluate the correlation of the simple components of cement paste.


## 3.2.1. Standard Consistency Test

Table5 shows the analysis of the orthogonal test results. The influence of the factors affecting the material standard consistency is as follows: slag steel power > silica fume > fly ash. The result is consistent with the influence of mineral admixture on the standard consistency of the paste through analyzing optimum powder ratio test. Range analysis shows that steel slag is the most important factor affecting the standard consistency; its K value is 0.227. For silica fume, the K value is 0.202. These two values are very similar. The relationship between average standard consistency of paste and contents of slag steel power, silica fume, and fly ash is shown in Figure 11. With increasing mineral admixtures content, the two curves from fly ash and silica fume have same trend that initially decreases, reaches the minimum value, and then increases; the result is consistent with the optimum powder ratio test, but the behavior of steel slag is different from them; the lowest point does not appear, and standard consistency seems always increasing with steel slag content; the reason is steel slag is too sensitive to water, and many factors are considered in the orthogonal test. For steel slag, no matter how large the particle size is, they are irregular, so a large amount of water is necessary; therefore, it has a more notorious influence than that of silica fume. From K value, the difference between these two factors is not very significant; the mechanism by which they affect the consistence is not the same. Large specific surface area and large SiO2 content were observed for silica fume with small particle size (Figure 7). In addition, silica fume has high pozzolanic activity during the early hydration process, and it may react with the Ca(OH)2 produced due to cement hydration in a very short time to generate a low calcium C-S-H gel. Thus, the early strength of cementitious material can be increased. However, the addition of silica fume requires a larger amount of water because of the elevated heat release [19, 20]. The effect of fly ash is the smallest among the three factors, possibly because of its spherical particles. The advantages of adequate particle morphology, ball bearing, and wetting effect are significant. Therefore, the mechanical friction between particles is relatively small after particle accumulation, and the moisture required to damp the surface is reduced; less water is needed to achieve the same moisture.Figure 11
The relationship between the standard consistency average and the added mineral content.


## 3.2.2. Compressive Strength Test and the Optimum Ratio Determined

According to Table5, the effect on later strength is as follows: silica fume > fly ash > steel slag powder. The different relationship between the average 28 day compressive strength of the cement paste and the silica fume, slag steel, and fly ash content is shown in Figure 12. Range analysis shows the effect of steel slag powder and fly ash is very similar. K value of former is 35.64; the latter is 36.55. These two values are very similar. But for silica fume, K value is 41.44. Since the increase in silica fume reduces the later strength, it is necessary to consider its role for cementing materials. The influence of steel slag and fly ash on the later strength does not show remarkable differences. With the increase in curing period, the mineral phase of steel slag gradually hydrated, promoting the strength increase of the composite system, but to find whether it is steel slag, fly ash, or silica fume, there exists an optimum value; it is consistent with the result of optimum powder ratio determined by the minimum basic water requirement test. For the functional effect of fly ash, the volcano ash, filling densification, and micro aggregate effects may occur with the increase in curing period [21].Figure 12
The relationship curve between the 28-day compression average and added mineral content.According to theK value analysis results (Table 5), the best level should be 5% for the silica fume dosage because the difference between the K values at 5 and 10% dosage is not very large (238.6 MPa and 236.0 MPa). To take full advantage of the waste resources without a great sacrifice in later strength, the level of silica fume may be adjusted to 10%. The optimum levels of fly ash and steel slag are 6% and 9%. Orthogonal test results show that the strength of the ratio determined by the minimal water requirement method is the highest. In addition to the optimum ratio, ratios A2 and A4 listed in Table 4 may be selected. Moreover, as seen in Table 4, the 28 d strength determined by the ratios close to the optimum is high. The result also is consistent with Zhang’s conclusion [18].


## 3.2.3. Correlation between Minimum Basic Water Requirement and Standard Consistency

In the system determined by minimum water requirement method, we have drawn a conclusion that standard consistency evaluation can replace the minimum water requirement method to evaluate the preparation of high-density composite cement. If in the complicated system, the correlation of standard consistency and minimal water is higher; the minimum water requirement method can be really replaced by standard consistency evaluation method. To further understand the relationship between these parameters, the orthogonal test results are presented in Figure13. The plot clearly shows that the two curves have the same behavior. For a quantitative analysis, the correlation coefficient of the two curves from nine groups of ratio of the orthogonal test was determined. The correlation coefficient is 0.948, which indicates that there is a good correlation between them because they are different states of same property of composite system paste even though the quaternary system is more complicated. To determine the optimum proportion of mineral admixture for high-performance cementitious materials, the standard consistency of the mixing system could be measured to indirectly obtain information about the minimum basic water requirement. If only the optimum proportion of the cementitious material is required and not the compactness, it is only necessary to measure standard consistency. If, in addition to the optimum proportion, it is necessary to know the maximum density of the paste, the minimum basic water requirement could be measured only for the already determined optimum proportion and the density would be obtained using equation (1). In this manner, it is possible to eliminate the errors that rise from the subjective determination of the mixture state in the minimum basic water requirement tests. The proposed method not only simplifies the process but also makes the method more scientific.Figure 13
Water requirement and standard consistence as a function of the test number.


## 3.2.4. Correlation between Minimum Basic Water Requirement (Standard Consistency) and Strength

The correlations between strength (compactness) and minimum basic water requirement and strength and standard consistency are not good; they are all negative correlations as shown in Figure14. The former is −0.714 and the latter is −0.767. However, it can be seen that the paste with lower minimum basic water requirement or standard consistency has an overall higher strength, while the strength of the pastes with high water requirement is generally lower.Figure 14
Water requirement, standard consistence, and compression strength as a function of the test number.The main reason for such poor correlation is that many factors are considered in the orthogonal test. The genuine quaternary powder materials are more complicated than the binary for the minimum basic water requirement method to evaluate the compactness generally considered. Additionally, the minimum basic water requirement and compressive strength are two different properties; the influence of more factors on two properties is different though they have good consistency in binary powder because there is less influencing factors. In addition to these, the poor correlation between water requirement and strength may be due to the particle shape, which is an important factor along with size and granularity. The level of understanding for the relationship between particle shape and compactness of nonspherical particles is very limited. Some reports [20, 21] attempt to predict the compactness of nonspherical particles by considering the parameter of the sphericity, but the results show that the prediction is not accurate. In fact, minimum water requirement includes the water of particle gaps and on the surface, but the shape of the particles has a greater influence on the latter. The sphericity coefficient of steel slag particles is small and the water requirement is large, so this is also an important factor causing the poor correlation between them.The correlation between minimum basic water requirement and strength (density) and standard consistency and strength is poor in the orthogonal test, but it is higher in the binary system. The conclusion is consistent with Wang et al. [22]. Wang et al. pointed that there was a certain correlation between water absorption ratio and strength of cement-fly ash paste. The more the composition of cement paste was, the more complex the interaction between the components was and the worse the correlation between the water absorption and the strength was, but it was more effective to evaluate the correlation of the simple components of cement paste.


## 4. Conclusions

(1)
On the basis of the closest-packing theory, high-performance sulphoaluminate cement can be prepared using the minimum basic water requirement method. The optimum proportion of sulphoaluminate cement, fly ash, steel slag, and silica fume is 0.75 : 0.06 : 0.09 : 0.10. According to the results from an orthogonal test, the paste prepared from the powder with the optimal proportion has the highest strength
(2)
Steel slag and silica fume have great influence on the standard consistency and minimum basic water requirement of the paste, but the mechanism in which they act is different. Steel slag can promote the later strength of sulphoaluminate cement, and it has a good prospect as a mineral admixture. The influence of fly ash on them is less.
(3)
Whether in the system for the minimum basic water requirement method considered as binary systems or in the complicate system decided by the orthogonal test, the minimum basic water requirement has a good correlation with the standard consistency. The standard consistency determination can replace the minimum basic water requirement method to indirectly obtain this information and evaluate the compactness of the material.
(4)
The correlation between minimum basic water requirement and strength and standard consistency and strength is poor in the orthogonal test. The former is lower than the latter. This indirectly demonstrates that the standard consistency method is superior to the minimum basic water requirement method to evaluate the compactness of cementitious materials.



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*Source: 4187342-2019-01-06.xml*