*2.3. Test Methods*

The mortar was mechanically mixed by a mixer. Before mixing, the activator and steel slag powder was mixed uniformly. Then, metakaolin, silica fume, and cement were gradually added to obtain the cementitious materials mix, and the mixing was further continued. The mixing is done according to the following steps. First, water was added to the mixing pot followed by the addition of all the cementitious materials. The machine was started and the materials in the pot were slowly mixed at low speed for 30 s. The sand was uniformly added after 30 s, and the mixing was continued at high speed for an additional 30 s after the sand was fully added. The mixing was stopped for 90 s, and a rubber scraper was used to scrape off the paste on the blade and the wall of the mixing pot. Then, it was further mixed at high speed for 60 s. The detailed mixing procedure is shown in Figure 3. The mortar should be formed immediately after preparation. The specimens were cast in three connected test molds, each having a size of 40 mm × 40 mm × 160 mm. The mortar should be put into the test molds in two layers, and a vibrating table should be used for vibrating the layers. Each time it was vibrated 60 times. Then, the mortar molds were put into a curing box with humidity of 95% and a temperature of 20 ◦C for curing. After 24 h, the demolding was done, and the test block was cured for 180 days under standard curing conditions. Then, the mechanical properties of mortar were tested according to GB/T 17671-1999 [36]. The flexural strength testing machine is an electric flexural testing machine model DKZ-5000 with 5 kN measuring range, manufactured by Wuxi Jianyi Instrument & Machinery Co., Ltd. in Wuxi, China. Load control was selected as the test procedure of flexural strength, and the loading rate was 50 N/s. The compressive strength testing device is Hualong universal testing machine model WAW-600 with 600 kN measuring range, manufactured by Shanghai Hualong Test Instrumens Co., Ltd. in Shanghai, China. Load control was selected as the test procedure of compressive strength, and the loading rate was 2500 N/s.

**Figure 3.** Mixing progress of steel slag mortar. **Figure 3.** Mixing progress of steel slag mortar.

and the loading rate was 2500 N/s.

### *2.4. GM (0, N) Prediction Model 2.4. GM (0, N) Prediction Model*

In practice, we often encounter problems such as the lack of data, grey characteristics of the data itself, and the need to consider the correlation between predictive variables and multiple factors [37,38]. Grey system theory provides a method to solve such problems. GM (0, *N*) and GM (1, *N*) are common multi-factor grey prediction models [39,40]. GM (1, *N*) is a little complicated because it involves the first-order differentiation, whereas the GM (0, *N*) model is relatively simple to establish as it has high prediction accuracy In practice, we often encounter problems such as the lack of data, grey characteristics of the data itself, and the need to consider the correlation between predictive variables and multiple factors [37,38]. Grey system theory provides a method to solve such problems. GM (0, *N*) and GM (1, *N*) are common multi-factor grey prediction models [39,40]. GM (1, *N*) is a little complicated because it involves the first-order differentiation, whereas the GM (0, *N*) model is relatively simple to establish as it has high prediction accuracy [41,42]. The establishment of the GM (0, *N*) model is as follows [42]:

molds were put into a curing box with humidity of 95% and a temperature of 20 °C for curing. After 24 h, the demolding was done, and the test block was cured for 180 days under standard curing conditions. Then, the mechanical properties of mortar were tested according to GB/T 17671-1999 [36]. The flexural strength testing machine is an electric flexural testing machine model DKZ-5000 with 5 kN measuring range, manufactured by Wuxi Jianyi Instrument & Machinery Co., Ltd. in Wuxi, China. Load control was selected as the test procedure of flexural strength, and the loading rate was 50 N/s. The compressive strength testing device is Hualong universal testing machine model WAW-600 with 600 kN measuring range, manufactured by Shanghai Hualong Test Instrumens Co., Ltd. in Shanghai, China. Load control was selected as the test procedure of compressive strength,

[41,42]. The establishment of the GM (0, *N*) model is as follows [42]: Take ܺଵ ଵݔ) = () ଵݔ ,(1)() ଵݔ ,⋅⋅⋅,(2)() ()(݊)) as the system characteristic data sequence, Take *X* (0) <sup>1</sup> = *x* (0) 1 (1), *x* (0) 1 (2), · · · , *x* (0) 1 (*n*) as the system characteristic data sequence, and

$$\begin{array}{c} \mathcal{X}\_2^{(0)} = (\mathfrak{x}\_2^{(0)}(1), \mathfrak{x}\_2^{(0)}(2), \dots, \mathfrak{x}\_2^{(0)}(n)) \\ \mathcal{X}\_3^{(0)} = (\mathfrak{x}\_3^{(0)}(1), \mathfrak{x}\_3^{(0)}(2), \dots, \mathfrak{x}\_3^{(0)}(n)) \\ \dots \\ \mathcal{X}\_N^{(0)} = (\mathfrak{x}\_N^{(0)}(1), \mathfrak{x}\_N^{(0)}(2), \dots, \mathfrak{x}\_N^{(0)}(n)) \end{array}$$

··· as the relative factors data sequences. *X* (1) *i* is the 1-AGO sequence of *X* (0) *i* (*i* = 1, 2, ···, *N*), then call

$$\mathbf{x}\_1^{(1)}(k) = \sum\_{i=2}^{N} b\_i \mathbf{x}\_i^{(1)}(k) + a \tag{1}$$

as the GM (0, *N*) model.

and

$$B = \begin{bmatrix} \mathbf{x}\_2^{(1)}(2) & \mathbf{x}\_3^{(1)}(2) & \cdots & \mathbf{x}\_N^{(1)}(2) & 1\\ \mathbf{x}\_2^{(1)}(3) & \mathbf{x}\_3^{(1)}(3) & \cdots & \mathbf{x}\_N^{(1)}(3) & 1\\ \vdots & \vdots & & \vdots & \vdots\\ \mathbf{x}\_2^{(1)}(n) & \mathbf{x}\_3^{(1)}(n) & \cdots & \mathbf{x}\_N^{(1)}(n) & 1 \end{bmatrix}, \\ Y = \begin{bmatrix} \mathbf{x}\_1^{(1)}(2)\\ \mathbf{x}\_1^{(1)}(3)\\ \vdots\\ \mathbf{x}\_1^{(1)}(n) \end{bmatrix}$$

Then the least-squares estimate of the parameter column ∧ *b* = [*b*2, *b*3, · · ·, *bN*, *a*] *T* is

$$\stackrel{\wedge}{b} = \left(\boldsymbol{\mathcal{B}}^{\mathsf{T}}\boldsymbol{\mathcal{B}}\right)^{-1}\boldsymbol{\mathcal{B}}^{\mathsf{T}}\boldsymbol{Y} \tag{2}$$

### **3. Analysis of Results**

The 180 days compressive strength and flexural strength test results of the control group G0 (pure cement mortar specimens) are 48.0 MPa and 9.2 MPa, respectively. The orthogonal experimental results are shown in Table 5.


**Table 5.** Orthogonal experimental results of mechanical properties.

The compressive strength test results are shown in Table 5 and Figure 4a. When the steel slag powder dosage is 10%, the mix proportion G9 has the highest compressive strength (47.9 MPa). The dosages of activator, metakaolin, and silica fume are 15%, 15%, 8%, respectively. When the steel slag powder dosage is 20%, the compressive strength of the mix proportion G6 is the highest (40.6 MPa), and the corresponding dosages of activator, metakaolin, and silica fume are 10%, 5%, and 8%, respectively. When the steel slag powder dosage is 30%, the mix proportion G3 has the highest compressive strength (45.6 MPa), and the corresponding dosages of activator, metakaolin, and silica fume are 5%, 15%, and 6%, respectively. Furthermore, when the steel slag powder dosage is 40%, the mix proportion G4 has the highest compressive strength (44.6 MPa), and the corresponding dosages of activator, metakaolin, and silica fume are 5%, 20%, and 8%, respectively. As shown in Figure 4a, with the change of dosage of steel slag powder (10–40%), the highest compressive strength at each dosage level is more than 85% of the compressive strength of the control group. As shown in Figure 4a, the compressive strength of steel slag cement mortar shows an overall trend of decline from G1 to G16, while the dosage of activator (5–20%) is gradually increasing. The reason why the strength of steel slag cement mortar decreases may be that the content of stone powder increases with the increase of the activator dosage, and excessive stone powder will have negative effect on the strength of steel slag cement mortar. G9 is the mix proportion with the highest compressive strength among 16 mix proportions. The reasons may be divided into two aspects. On the one hand, the dosage of steel slag powder (10%) is relatively low, and the negative effect of low activity of steel slag powder on steel slag cement mortar is relatively small. On the other hand, it may be related to the relatively large dosage of metakaolin (15%) and silica fume (8%). SiO<sup>2</sup> in metakaolin and silica fume hydrate to form calcium silicate, which improves the compressive strength. In addition, it is difficult to identify the main cause in the condition of many factors, and further analysis is needed to determine the cause.

The flexural strength test results are given in Table 5 and Figure 4b. When the steel slag powder dosage is 10%, the mix proportion G5 has the highest flexural strength (8.8 MPa), and the corresponding dosages of activator, metakaolin, and silica fume, are 10%, 10%,

and 6%, respectively. When the steel slag powder dosage is 20%, the mix proportion G6 has the highest flexural strength (8.7 MPa), and the dosages of activator, metakaolin, and silica fume are 10%, 5%, and 8%, respectively. At 30% dosage of steel slag powder, the mix proportion G3 has the highest flexural strength (8.3 MPa), and the corresponding dosages of activator, metakaolin, and silica fume are 5%, 15%, and 6%, respectively. When the steel slag powder dosage is 40%, the mix proportion G12 has the highest flexural strength (8.4 MPa), and the corresponding dosages of activator, metakaolin, and silica fume are 15%, 10%, and 2%, respectively. As shown in Figure 4b, with the change of steel slag powder dosage (10–40%), the highest flexural strength at each level of dosage is greater than 90% of the flexural strength of the control group. As shown in Figure 4b, there is little difference in the flexural strength of steel slag cement mortar of G1–G9, and the flexural strength of G10, G11, G13, G14, G15, and G16 is relatively low, while the flexural strength of G12 is relatively high. Similar to the compressive strength, it is difficult to find out the influence law of each factor only from the test results, and further analysis is needed to determine the cause. 10%, and 6%, respectively. When the steel slag powder dosage is 20%, the mix proportion G6 has the highest flexural strength (8.7 MPa), and the dosages of activator, metakaolin, and silica fume are 10%, 5%, and 8%, respectively. At 30% dosage of steel slag powder, the mix proportion G3 has the highest flexural strength (8.3 MPa), and the corresponding dosages of activator, metakaolin, and silica fume are 5%, 15%, and 6%, respectively. When the steel slag powder dosage is 40%, the mix proportion G12 has the highest flexural strength (8.4 MPa), and the corresponding dosages of activator, metakaolin, and silica fume are 15%, 10%, and 2%, respectively. As shown in Figure 4b, with the change of steel slag powder dosage (10–40%), the highest flexural strength at each level of dosage is greater than 90% of the flexural strength of the control group. As shown in Figure 4b, there is little difference in the flexural strength of steel slag cement mortar of G1–G9, and the flexural strength of G10, G11, G13, G14, G15, and G16 is relatively low, while the flexural strength of G12 is relatively high. Similar to the compressive strength, it is difficult to find out the influence law of each factor only from the test results, and further analysis is needed to determine the cause.

The flexural strength test results are given in Table 5 and Figure 4b. When the steel slag powder dosage is 10%, the mix proportion G5 has the highest flexural strength (8.8 MPa), and the corresponding dosages of activator, metakaolin, and silica fume, are 10%,

*Crystals* **2021**, *11*, x FOR PEER REVIEW 8 of 18

15%, and 6%, respectively. Furthermore, when the steel slag powder dosage is 40%, the mix proportion G4 has the highest compressive strength (44.6 MPa), and the corresponding dosages of activator, metakaolin, and silica fume are 5%, 20%, and 8%, respectively. As shown in Figure 4a, with the change of dosage of steel slag powder (10–40%), the highest compressive strength at each dosage level is more than 85% of the compressive strength of the control group. As shown in Figure 4a, the compressive strength of steel slag cement mortar shows an overall trend of decline from G1 to G16, while the dosage of activator (5–20%) is gradually increasing. The reason why the strength of steel slag cement mortar decreases may be that the content of stone powder increases with the increase of the activator dosage, and excessive stone powder will have negative effect on the strength of steel slag cement mortar. G9 is the mix proportion with the highest compressive strength among 16 mix proportions. The reasons may be divided into two aspects. On the one hand, the dosage of steel slag powder (10%) is relatively low, and the negative effect of low activity of steel slag powder on steel slag cement mortar is relatively small. On the other hand, it may be related to the relatively large dosage of metakaolin (15%) and silica fume (8%). SiO2 in metakaolin and silica fume hydrate to form calcium silicate, which improves the compressive strength. In addition, it is difficult to identify the main cause in the condition of many factors, and further analysis is needed to determine the cause.

**Figure 4.** Strength of steel slag cement mortar with different mix proportions: (**a**) Compressive strength of experimental groups; (**b**) Flexural strength of experimental groups.
