**4. Identification of the influential factors**

Based on check student for an error risk *α* = 5%, it was found that tabulated = 4.303. **Table 3** summarizes the factor effects estimation for the two responses: compressive strength (Y<sup>1</sup> ) and setting time (Y<sup>2</sup> ).


**Table 3.** Factor signification for the two responses Y<sup>1</sup> and Y<sup>2</sup> . The two models are represented by the equations given below:

Compressive strength:

$$\text{Ycal}\_1 = 47.464 - 11.51 \, 3 \text{X}\_2 + 11.49 \, 3 \text{X}\_3 - 8.808 \, \text{X}\_1 \text{X}\_2 - 13.6913 \, \text{X}\_1 \text{X}\_2 \text{X}\_3 \tag{7}$$

Setting time:

$$\text{Ycal}\_2 = 29.090 + 14.62 \,\text{5X}\_1 - 5.87 \,\text{5X}\_2 - 5.625 \,\text{X}\_3 - 3.12 \,\text{5X}\_1 \,\text{X}\_2 + 2.875 \,\text{X}\_1 \,\text{X}\_2 \,\text{X}\_3 \tag{8}$$

#### **4.1. Analysis of residue**

**Figure 4** reveals the distribution of the calculated values versus experimental values for the two responses (Y<sup>1</sup> and Y<sup>2</sup> ). The points are almost randomly distributed about the line representing exact agreement, providing good agreements between experimental values and those calculated using the model.

#### **4.2. Analysis of variance**

**Table 4** summarizes the variance analysis of the chosen responses Y<sup>1</sup> and Y<sup>2</sup> .

The main results for Y1 and Y2 are, respectively, 333.601 and 12.539, as lack of fit mean squares and 18.017 and 2.333 as the estimation of experimental variance. Thus, the values of the ratio between the lack of fit mean square and the estimation of experimental variance 18.51568 and 5.3739 for the responses Y1 and Y2 are inferior to tabled *F*4,2 0.05 and *F*3,2 0.05, respectively. Consequently, it is possible to confirm the validity of the two elaborated models. In addition, the ratios between the regression mean square and the residual mean square for the three responses Y1 and Y2 (4.638 and 5.3739) are superior to the tabled *F*4,6 0.05 and *F*5,5 0.05, respectively. Thus, the significant variables, applied to elaborate the three models, have a large significance on their responses.

*4.2.1. Optimization*

**Table 4.** Analysis of variance.

Compressive strength

Setting time

and setting time = 41 min):

.6H2

): 1125 rpm

): 5 min

Mass ratio of MgCl2

Mixing time (X<sup>2</sup>

Stirring speed (X<sup>3</sup>

**4.3. Characterization**

For selecting the optimal conditions we try to strike a compromise between the two responses

By merely regarding values and signs of these significant effects, we conclude that maximization of the two responses is reached for experience number 6 (compressive strength = 76.40 MPa

ture is illustrated in **Figure 5** with the composition point of the optimum which is located near

**Figure 6** shows the XRD pattern of MOC with an optimal condition. It can be found that phase 5 is present. This phase is the major product responsible for hardening and the strength of MOC. We measured porosity accessible to water, we found that the total porosity of MOC is


O) [5] at an ambient tempera-

Sorel Cements from Tunisian Natural Brines http://dx.doi.org/10.5772/intechopen.74315 183

to have good compressive strength and a suitable setting time.

O/MgO (X<sup>1</sup>

The phase diagram of the ternary MOC system (MgO-MgCl2

phase 5 responsible for good compressive strength of the cement.

4% which is in good accordance with other results in literature [28].

): 2.22

**Source of variation SS DF MS Ratio P**

Regression 4237.738 4 1059.4345 4.63837 0.048

Lack of fit 1334.403 4 333.601 18.51568 0.051897

Regression 2384.625 5 476.925 56.40478 0.0000

Lack of fit 37.610 3 12.539 5.3739 0.160892

Residual 1370.437 6 228.40616

Pure error 36,034 2 18.017 Total 5608.174 10 1059.4345

Residual 42.277 5 8.4554

Pure error 4.667 2 2.333 Total 2426.909 10 476.925

**Figure 4.** Calculated versus experimental values graph (a) for compressive strength (b) for setting time.


**Table 4.** Analysis of variance.

#### *4.2.1. Optimization*

The two models are represented by the equations given below:

**Table 4** summarizes the variance analysis of the chosen responses Y<sup>1</sup>

18.51568 and 5.3739 for the responses Y1 and Y2 are inferior to tabled *F*4,2

responses Y1 and Y2 (4.638 and 5.3739) are superior to the tabled *F*4,6

**Figure 4.** Calculated versus experimental values graph (a) for compressive strength (b) for setting time.

Ycal<sup>1</sup> = 47.464 − 11.51 3X<sup>2</sup> + 11.49 3X<sup>3</sup> − 8.808 X<sup>1</sup> X<sup>2</sup> − 13.6913 X<sup>1</sup> X<sup>2</sup> X<sup>3</sup> (7)

Ycal<sup>2</sup> = 29.090 + 14.62 5X<sup>1</sup> − 5.87 5X<sup>2</sup> − 5.625 X<sup>3</sup> − 3.12 5X<sup>1</sup> X<sup>2</sup> + 2.875 X<sup>1</sup> X<sup>2</sup> X<sup>3</sup> (8)

**Figure 4** reveals the distribution of the calculated values versus experimental values for the

senting exact agreement, providing good agreements between experimental values and those

The main results for Y1 and Y2 are, respectively, 333.601 and 12.539, as lack of fit mean squares and 18.017 and 2.333 as the estimation of experimental variance. Thus, the values of the ratio between the lack of fit mean square and the estimation of experimental variance

Consequently, it is possible to confirm the validity of the two elaborated models. In addition, the ratios between the regression mean square and the residual mean square for the three

Thus, the significant variables, applied to elaborate the three models, have a large significance

). The points are almost randomly distributed about the line repre-

 and Y<sup>2</sup> .

0.05 and *F*3,2

0.05 and *F*5,5

0.05, respectively.

0.05, respectively.

Compressive strength:

**4.1. Analysis of residue**

calculated using the model.

**4.2. Analysis of variance**

and Y<sup>2</sup>

two responses (Y<sup>1</sup>

on their responses.

Setting time:

182 Cement Based Materials

For selecting the optimal conditions we try to strike a compromise between the two responses to have good compressive strength and a suitable setting time.

By merely regarding values and signs of these significant effects, we conclude that maximization of the two responses is reached for experience number 6 (compressive strength = 76.40 MPa and setting time = 41 min):

Mass ratio of MgCl2 .6H2 O/MgO (X<sup>1</sup> ): 2.22

Mixing time (X<sup>2</sup> ): 5 min

Stirring speed (X<sup>3</sup> ): 1125 rpm

The phase diagram of the ternary MOC system (MgO-MgCl2 -H2 O) [5] at an ambient temperature is illustrated in **Figure 5** with the composition point of the optimum which is located near phase 5 responsible for good compressive strength of the cement.

#### **4.3. Characterization**

**Figure 6** shows the XRD pattern of MOC with an optimal condition. It can be found that phase 5 is present. This phase is the major product responsible for hardening and the strength of MOC. We measured porosity accessible to water, we found that the total porosity of MOC is 4% which is in good accordance with other results in literature [28].

**Figure 5.** Phase diagram of the ternary MOC system [5].

The thermal conductivity of cement is 0.8 w/mK. The morphology of MOC is shown in **Figure 7**. We can see a rough surface with a dense network of needle-like crystals of 500 nm which has a high strength (phase 5). Thermal analysis of MOC is shown in **Figure 8**. Six endothermic events appear on the DTA curves of MOC during heating. Thermal decomposition requires a dehydration stage of the crystalline phase 5 Mg(OH)2 MgCl2 .8H2 O at 179°C to obtain anhydrous materials. The other deflections in this curve at 358, 414, 484, and 711°C present the decomposition stage of

. The last deflection at 1100°C represents the decomposi-

Sorel Cements from Tunisian Natural Brines http://dx.doi.org/10.5772/intechopen.74315 185

5 Mg(OH)2

MgCl2

**Figure 8.** TG and DTA curves of MOC.

**Figure 7.** SEM analysis of MOC.

tion to obtain the final solid product MgO.

and the loss of MgCl2

**Figure 6.** XRD patterns of MOC.

**Figure 7.** SEM analysis of MOC.

The thermal conductivity of cement is 0.8 w/mK. The morphology of MOC is shown in **Figure 7**. We can see a rough surface with a dense network of needle-like crystals of 500 nm which has a high strength (phase 5). Thermal analysis of MOC is shown in **Figure 8**. Six endothermic events appear on the DTA curves of MOC during heating. Thermal decomposition requires a dehydra-

MgCl2

.8H2

O at 179°C to obtain anhydrous materials.

tion stage of the crystalline phase 5 Mg(OH)2

**Figure 5.** Phase diagram of the ternary MOC system [5].

184 Cement Based Materials

**Figure 6.** XRD patterns of MOC.

The other deflections in this curve at 358, 414, 484, and 711°C present the decomposition stage of 5 Mg(OH)2 MgCl2 and the loss of MgCl2 . The last deflection at 1100°C represents the decomposition to obtain the final solid product MgO.

**Figure 8.** TG and DTA curves of MOC.
