In this section, the fresh and hardened properties of concrete incorporating Glycerin as a PCM are discussed in detail. In the later part of this section detailed discussion on RSM is presented.
5.1 Slump
Figure 2 shows the slump values for various mix proportions listed in Table 5. Amongst the category A, B and C, the least slump is obtained for category A, i.e. M20 grade of concrete. With the increase in Glycerin content, a significant reduction in slump was observed for a given w/b ratio and grade of concrete. For example, for M20 grade concrete with a w/b ratio of 0.40, the slump value decreased from 130 mm for the control mix to 111 mm for concrete containing 10% Glycerin. Also, as the w/b ratio increased from 0.4 to 0.50, the slump value increased for all mixes. For example for A4, A9 and A14 mix the slump value was 111 mm, 117 mm and 120 mm respectively.
Understanding the effects of glycerin concentration, w/b ratio, and grade of concrete on the slump of concrete mixes is necessary to explain the observations.
Effect of Glycerin Content
The presence of glycerin has the effect of lowering the amount of water that is required for concrete mixtures. Glycerin is a classification of plasticizer. When there is a higher concentration of glycerin, there is a lower water demand, which results in a gradual decrease in slump. Because of its lubricating properties, glycerin makes it possible for cement particles to be dispersed more evenly and reduces the amount of water that is necessary for the material to be workable. Therefore, a higher glycerin concentration leads to lower slump values since it reduces the amount of water present in the mixture.
Effect of Water-to-Binder (w/b) Ratio
Workability of Concrete is Significantly Affected by the Water-to-Binder (w/b) Ratio The water-to-binder ratio has a substantial impact on the workability of concrete. Increasing the w/b ratio causes an increase in the amount of water present in the mixture, which in turn leads to greater slump values. This is because larger water content makes the mixture more fluid, which in turn makes it easier to flow throughout the mixture and causes it to slump more.
Effect of Grade of Concrete
There is a correlation between the grade of concrete and the workability of the concrete mix. Because they contain a higher percentage of cementitious material, concrete mixes of higher quality typically have a lower water requirement. Higher-grade concrete mixes, on the other hand, tend to have lower slump values when compared to lower-grade mixes, provided that the w/b ratio remains the same.
Synergic Effect:
-
When the w/b ratio and grade of the concrete remain the same, increasing the amount of glycerin in the concrete results in a reduction in slump since it reduces the amount of water that is required.
-
The slump values of all mixes are increased when the w/b ratio is increased, regardless of the amount of glycerin present or the grade of concrete present.
-
Concrete of category A (M20 grade) has the lowest slump, which can be attributed to the fact that it is of a lower grade compared to concrete of categories B and C, which results in a higher water demand.
4.2 Compressive strength
The compressive strength of mixes incorporating Glycerin for 7, 28, 56 and 90 days are shown in Fig. 3. For a given set of mixes and w/b ratio, maxima are obtained at 5% Glycerin level on all days. Also, for a given day and mix category (i.e. A B or C), the maximum values of compressive strength are obtained at a w/b ratio of 0.45, followed by 0.40 and 0.50 respectively. For example, for mix category A, A2, A7 and A12 represent the mixes with 5% Glycerin for 0.40, 0.45 and 0.50 w/b ratio respectively. For these mixes, the 28 days compressive strength is obtained as 32.2 MPa, 32.8 MPa and 31.2 MPa respectively. This can be understood by taking into account how the w/b ratio and glycerin concentration affect the compressive strength of concrete mixes:
Impact of Glycerin Content
Glycerin improves workability and lowers water requirements in concrete mixes by acting as a plasticizer. The mix enables improved cement particle dispersion at lower glycerin concentration levels, leading to an increase in compressive strength. On the other hand, high glycerin content might impair compressive strength by altering the hydration process or producing excessive air entrainment. Thus, there is a glycerin content at which compressive strength is maximized.
Impact of w/b Ratio: The concrete strength is greatly impacted by the w/b ratio. Because a lower w/b ratio encourages better hydration and denser concrete, lower w/b ratios provide stronger concrete. On the other hand, because of greater porosity and weakened cement particle bonds, higher w/b ratios result in decreased strength.
Combining these effects:
-
Compressive strength rises with increasing glycerin concentration for a particular mix and w/b ratio until it reaches an ideal level, at which point it begins to fall.
-
The mix design and curing period influence the ideal glycerin content for optimizing compressive strength.
-
Similarly, the intermediate w/b ratio of 0.45 has the maximum compressive strength for a given mix category (A, B, or C) and curing time, followed by 0.40 and 0.50, respectively. This is because a w/b ratio of 0.45 offers a balance between the two, enabling the mix to be optimally hydrated and compacted.
4.3 Thermal Conductivity, Specific Heat Capacity and Thermal Diffusivity
The impact of mix composition—including glycerin content, w/b ratio, and concrete grade—on the thermal characteristics of the concrete can help to explain variations in thermal conductivity, specific heat, and thermal diffusivity.
Effect of Glycerin Content:
Glycerin acts as a plasticizer, affecting the density and porosity of the concrete matrix. Higher glycerin content may lead to increased porosity due to air entrainment, which can reduce thermal conductivity. However, glycerin also improves workability and reduces water demand, which might enhance the uniform distribution of aggregates and cement particles, potentially increasing thermal conductivity (Fig. 4(a)).
Specific heat capacity (Fig. 4(b)) may be influenced by the presence of glycerin, as it can affect the energy required to raise the temperature of the concrete mix. The variation in thermal diffusivity (Fig. 4 (c)) can be attributed to changes in the microstructure of the concrete caused by glycerin, affecting the rate at which heat propagates through the material.
Effect of Water-to-Binder (w/b) Ratio:
The w/b ratio significantly affects the density, porosity, and hydration of the concrete. Lower w/b ratios generally result in denser concrete with lower porosity, which can enhance thermal conductivity.
Specific heat capacity may also be affected by changes in the w/b ratio, as the hydration process and formation of hydrates can influence the energy storage capacity of the concrete.
Thermal diffusivity is influenced by the porosity and density of the concrete, which are in turn affected by the w/b ratio.
Effect of Grade of Concrete:
Higher-grade concretes typically have a denser microstructure and lower porosity, which can lead to higher thermal conductivity compared to lower-grade concretes.
Specific heat capacity may vary with the grade of concrete due to differences in the composition and properties of the aggregates and cementitious materials used.
Thermal diffusivity can be influenced by factors such as aggregate size and distribution, which may vary with the grade of concrete.
Overall, the variation in thermal conductivity, specific heat, and thermal diffusivity observed in the provided data can be attributed to the complex interplay between mix composition, including glycerin content, w/b ratio, and grade of concrete, and their effects on the microstructure and thermal properties of the concrete. The interaction between Glycerin and products of hydration is presented below:
Reaction with Calcium Silicate Hydrate (C-S-H):
The primary hydration product of cement, C-S-H gel, interacts with glycerin through physical adsorption or chemical reactions. While direct chemical reactions with glycerin are less common, the porous structure of C-S-H gel allows for the physical entrapment of glycerin molecules.
C-S-H + Glycerin→ C-S-H-Glycerin Complex (1)
Reaction with Calcium Hydroxide (CH):
Another hydration product of cement is calcium hydroxide (CH). It reacts with glycerin to form calcium glycerate, although such reactions may not be significant due to the lower reactivity of glycerin compared to water.
CH + Glycerin → Calcium Glycerate + Water (2)
Heat Absorption during Phase Change:
Glycerin's PCM properties primarily manifest during its phase change from liquid to solid (during cooling) and from solid to liquid (during heating). These phase transitions absorb and release significant amounts of latent heat, thereby moderating temperature fluctuations within the concrete matrix.
Glycerin (liquid)⇌Glycerin (solid) (3)
These equations illustrate potential interactions and reactions involving glycerin and the hydration products of concrete. However, it's essential to note that the PCM properties of glycerin primarily stem from its phase change behavior rather than chemical reactions with concrete constituents. The enthalpy of fusion associated with glycerin's phase change contributes significantly to its ability to store and release thermal energy within the concrete matrix, thereby improving the thermal performance of the material.
4.4 Response Surface Methodology
RSM is a powerful statistical technique that allows for the modeling and optimization of intricate relationships between input variables and thermal properties in materials. Utilizing RSM allows for streamlined experimental design, data analysis, and thermal property prediction, which in turn aids in the creation of materials that are both more efficient and cost-effective for energy-efficient building design. The current work investigates the impact of Glycerin, w/b, Grade, Slump and 28-day compressive strength (CS28) on the thermal conductivity, Specific heat capacity and thermal diffusivity of concrete containing Glycerin using central composite design (CCD). It is a powerful experimental design tool used in response surface methodology (RSM) to quickly explore and optimize system responses to numerous variables. It requires designing experimental runs to estimate linear and quadratic factor effects and discover response surface curvature. The response surface can be fitted with a second-order polynomial model to capture both linear and quadratic impacts of the components under study. CCD balances robust model coefficient estimation with minimizing experimental runs by strategically arranging design points.
4.5 Thermal Diffusivity in terms of Glycerin, w/b, Grade, Slump, CS28
Table 7
Regression coefficients for Thermal Diffusivity in terms of Glycerin, w/b, Grade, Slump, CS28
Term
|
Coef
|
SE Coef
|
T-Value
|
P-Value
|
VIF
|
Constant
|
1.98
|
5.06
|
0.39
|
0.715
|
|
Glycerin
|
0.520
|
0.487
|
1.07
|
0.346
|
289955.18
|
w/b
|
-53.8
|
29.3
|
-1.83
|
0.141
|
128120.42
|
Grade
|
-0.502
|
0.463
|
-1.08
|
0.340
|
514968.36
|
Slump
|
0.250
|
0.197
|
1.27
|
0.274
|
529385.37
|
CS28
|
0.076
|
0.157
|
0.49
|
0.651
|
79582.73
|
Glycerin*Glycerin
|
-0.0143
|
0.0132
|
-1.08
|
0.341
|
24247.12
|
w/b*w/b
|
-17.8
|
54.5
|
-0.33
|
0.761
|
363262.07
|
Slump*Slump
|
-0.00198
|
0.00188
|
-1.05
|
0.351
|
3865304.65
|
CS28*CS28
|
0.00355
|
0.00426
|
0.83
|
0.451
|
460361.01
|
Glycerin*w/b
|
1.73
|
1.70
|
1.02
|
0.367
|
766686.93
|
Glycerin*Grade
|
0.0191
|
0.0132
|
1.45
|
0.222
|
293872.65
|
Glycerin*Slump
|
-0.0112
|
0.0101
|
-1.11
|
0.329
|
2094991.82
|
Glycerin*CS28
|
-0.00647
|
0.00595
|
-1.09
|
0.338
|
88091.97
|
w/b*Grade
|
-1.374
|
0.938
|
-1.46
|
0.217
|
452916.81
|
w/b*Slump
|
0.530
|
0.628
|
0.84
|
0.446
|
3112317.64
|
w/b*CS28
|
0.705
|
0.663
|
1.06
|
0.348
|
260032.58
|
Grade*Slump
|
0.00858
|
0.00536
|
1.60
|
0.184
|
2603874.82
|
Grade*CS28
|
-0.00381
|
0.00621
|
-0.61
|
0.572
|
649477.16
|
Slump*CS28
|
-0.00393
|
0.00315
|
-1.25
|
0.281
|
1220429.72
|
The results of the RSM provide insights into how the thermal diffusivity of concrete, which contains variable dosages of glycerin, is altered by a variety of conditions. The regression coefficients for thermal diffusivity in terms of Glycerin, w/b, Grade, Slump, and CS28 are presented in Table 7. The coefficients provide a picture of the scope and direction of the influence that each factor has on the thermal diffusivity of the system. A positive coefficient implies that there is an increase in thermal diffusivity with an increase in the factor, whereas a negative coefficient suggests that the opposite effect is occurring.
The glycerin dosage exhibits a positive coefficient in this investigation, which indicates that a larger glycerin content tends to improve thermal diffusivity. However, the effect is not statistically significant (p-value > 0.05), indicating that the effect is not significant. Similar to the previous example, the interaction term between glycerin and grade exhibits a positive coefficient, which indicates that the combined influence of these components also tends to improve thermal diffusivity.
On the other hand, the water-to-binder ratio (w/b ratio) exhibits a negative coefficient, which suggests that larger w/b ratios lead to a reduction in thermal diffusivity. However, it is important to note that this effect is not statistically significant. The interaction term between w/b and grade also demonstrates a negative coefficient, which is another interesting finding. Although the coefficients for other parameters, such as slump and CS28 (which is likely a sort of concrete strength or composition), are positive, this indicates that these elements tend to increase thermal diffusivity. However, none of these impacts are statistically significant.
In general, the findings indicate that the dose of glycerin, the w/b ratio, and the interactions between these two elements and other factors may affect the thermal diffusivity of concrete. On the other hand, the fact that certain coefficients did not produce statistically significant results suggests that additional experiments or modifications to the model would be required to acquire a deeper understanding of the connection that exists between these elements and the thermal diffusivity of concrete that contains glycerin.
The minimum thermal diffusivity is suggested by the constant coefficient of 1.98, which comes into play when all other components are equal to zero. On the other hand, this coefficient does not meet the criteria for statistical significance (p-value = 0.715), which suggests that the model might not successfully capture the baseline diffusivity information. When compared to the other parameters that were investigated, the dosage of glycerin demonstrates a positive coefficient of 0.520 and a standard error (SE) that is comparatively low at 0.487. The coefficient suggests that an increase in the dosage of glycerin tends to improve thermal diffusivity, even though the statistical significance of this finding is not significant (p-value = 0.346).
Alternatively, the water-to-binder ratio (w/b) exhibits a negative coefficient of -53.8 and a standard error of 29.3 in its calculation. This shows that larger w/b ratios may lower thermal diffusivity, even though the p-value for this hypothesis is 0.141, which is statistically insignificant. The interaction between glycerin and the weight-to-volume ratio, on the other hand, results in a positive coefficient of 1.73, which in turn indicates that there is a potential compensating effect on diffusivity when both components are present. Several other parameters, including concrete grade, slump, and CS28, have coefficients that are not statistically significant when considered on their own. However, the interactions between these factors and glycerin or the w/b ratio may play a role in determining the thermal diffusivity of the material.
It is important to note that certain interaction components, such as glycerin grade and w/b grade, have substantially greater coefficients in comparison to other terms, which indicates that the combined impacts on diffusivity may be more significantly influenced.
The equation provided represents a predictive model for thermal diffusivity in concrete containing glycerin, derived from Response Surface Methodology (RSM). Each term in the equation corresponds to a factor or an interaction between factors, and their coefficients indicate the magnitude and direction of their influence on thermal diffusivity.
The constant term (1.98) represents the baseline thermal diffusivity when all other factors are zero. Glycerin content (0.520) has a positive coefficient, suggesting that increasing glycerin dosage tends to enhance thermal diffusivity. Conversely, the water-to-binder (w/b) ratio (-53.8) exhibits a negative coefficient, indicating that higher w/b ratios may decrease thermal diffusivity. This reflects the role of these components in altering heat transfer properties within the concrete matrix. Other individual factors such as concrete grade (-0.502), slump (0.250), and CS28 (0.076) also contribute to the model. For instance, higher concrete grades might reduce thermal diffusivity, while increased slump (a measure of concrete's consistency) and CS28 (potentially a concrete characteristic) tend to enhance it.
The equation also includes interaction terms, such as glycerin X w/b (1.73), glycerin grade (0.0191), and w/b X grade (-1.374). These interactions signify the combined effects of factors on thermal diffusivity. For example, the positive coefficient for glycerin w/b indicates that the influence of glycerin on diffusivity can be modified by the w/b ratio. Furthermore, terms like glycerin X slump (-0.0112) and slump X CS28 (-0.00393) highlight the intricate relationships between different factors. These interactions suggest that the effect of one factor on diffusivity may be influenced by the presence or level of another factor.
In summary, this equation encapsulates the complex relationships between various components and their interactions, providing a quantitative understanding of how different factors affect thermal diffusivity in concrete containing glycerin. However, it's important to note that the equation's accuracy and reliability may depend on the quality and representativeness of the data used to derive it.
4.6 Specific Heat Capacity in terms of Glycerin, w/b, Grade, Slump, CS28
Table 8 presents the regression coefficients for specific heat capacity in concrete about various factors, including Glycerin dosage, water-to-binder (w/b) ratio, concrete grade, slump, and CS28 (potentially a concrete characteristic). The baseline specific heat capacity when all other factors are zero, in this case, is -12.8, but not statistically significant (p-value = 0.541).
Individual Factors obtained in this analysis are:
Glycerin: Has a negative coefficient (-0.17), indicating a slight decrease in specific heat capacity with increasing glycerin dosage, although statistically insignificant (p-value = 0.930).
w/b ratio, Grade, Slump, and CS28: None of these factors individually show a significant impact on specific heat capacity, as indicated by their relatively high p-values.
Table 8
Regression coefficients for Specific Heat Capacity in terms of Glycerin, w/b, Grade, Slump, CS28
Term
|
Coef
|
SE Coef
|
T-Value
|
P-Value
|
VIF
|
Constant
|
-12.8
|
19.2
|
-0.67
|
0.541
|
|
Glycerin
|
-0.17
|
1.84
|
-0.09
|
0.930
|
289955.18
|
w/b
|
43
|
111
|
0.38
|
0.720
|
128120.42
|
Grade
|
0.76
|
1.75
|
0.43
|
0.686
|
514968.36
|
Slump
|
-0.124
|
0.747
|
-0.17
|
0.876
|
529385.37
|
CS28
|
-0.064
|
0.593
|
-0.11
|
0.920
|
79582.73
|
Glycerin*Glycerin
|
0.0206
|
0.0501
|
0.41
|
0.701
|
24247.12
|
w/b*w/b
|
118
|
206
|
0.57
|
0.599
|
363262.07
|
Slump*Slump
|
0.00379
|
0.00711
|
0.53
|
0.622
|
3865304.65
|
CS28*CS28
|
-0.0035
|
0.0161
|
-0.22
|
0.837
|
460361.01
|
Glycerin*w/b
|
-2.63
|
6.45
|
-0.41
|
0.704
|
766686.93
|
Glycerin*Grade
|
-0.0273
|
0.0501
|
-0.54
|
0.615
|
293872.65
|
Glycerin*Slump
|
0.0141
|
0.0381
|
0.37
|
0.730
|
2094991.82
|
Glycerin*CS28
|
0.0041
|
0.0225
|
0.18
|
0.863
|
88091.97
|
w/b*Grade
|
2.28
|
3.55
|
0.64
|
0.555
|
452916.81
|
w/b*Slump
|
-1.37
|
2.38
|
-0.58
|
0.594
|
3112317.64
|
w/b*CS28
|
-0.59
|
2.51
|
-0.23
|
0.827
|
260032.58
|
Grade*Slump
|
-0.0143
|
0.0203
|
-0.71
|
0.519
|
2603874.82
|
Grade*CS28
|
0.0061
|
0.0235
|
0.26
|
0.807
|
649477.16
|
Slump*CS28
|
0.0032
|
0.0119
|
0.27
|
0.799
|
1220429.72
|
Interaction Terms obtained in regression analysis for Specific Heat Capacity in terms of Glycerin, w/b, Grade, Slump, and CS28 are:
Interaction between Glycerin and w/b ratio, denoted as Glycerin X w/b: Has a negative coefficient (-2.63), suggesting that the combined effect of glycerin and w/b ratio decreases specific heat capacity, although statistically insignificant (p-value = 0.704).
Other interaction terms like Glycerin X Grade, Glycerin X Slump, Glycerin X CS28, and Grade X Slump have coefficients close to zero and are not statistically significant, indicating that their combined effects do not significantly influence specific heat capacity.
Overall, the regression analysis suggests that none of the individual factors or their interactions significantly affect specific heat capacity in concrete containing glycerin. The high p-values for most coefficients indicate that the observed effects could be due to random variation rather than true relationships with specific heat capacity. This implies that additional data or a different modeling approach may be necessary to accurately predict specific heat capacity in this context.
Regression analysis yielded the Eq. (2) for concrete with glycerin's specific heat capacity. Each term in the equation represents a factor or interaction of factors, with their coefficients indicating their magnitude and direction on specific heat capacity. The baseline specific heat capacity is -12.8 when all other parameters are zero. Glycerin content (-0.17) has a negative coefficient, implying a somewhat lower specific heat capacity with a higher dosage. However, the water-to-binder (w/b) ratio (43) has a positive coefficient, indicating that greater ratios enhance specific heat capacity. This shows how these components affect concrete matrix thermal characteristics.
Other elements like concrete grade (0.76), slump (-0.124), and CS28 (-0.064) also affect the model. Higher concrete grades and CS28 values enhance specific heat capacity slightly, but slump decreases it. The equation also includes interaction terms such as glycerin X w/b (-2.63) and w/b X grade (2.28), which show how variables affect specific heat capacity. The negative coefficient for glycerin*w/b shows that the w/b ratio can modify glycerin's effect on specific heat capacity.
Additionally, terms like glycerin X slump (0.0141) and grade X slump (-0.0143) show complex interactions between components. These relationships show that one factor's effect on specific heat capacity may be affected by another. This equation reveals how components and their interactions affect glycerin-containing concrete's specific heat capacity. It's important to examine the model's limitations and the possibility of modification with further data or experimentation.
4.7 Thermal Diffusivity in terms of Glycerin, w/b, Grade, Slump, CS28
The regression coefficients for thermal diffusivity in concrete are presented in Table 9. Every coefficient is a representation of the change in thermal diffusivity that occurs when there is a unit change in the factor that corresponds to it, while all other factors remain unchanged. 1.98 is the value of the baseline thermal diffusivity when all other factors are equal to zero, and the standard error (SE) is 5.06 in this case.
Individual Factors obtained by regression analysis for thermal diffusivity in terms of Glycerin, w/b, Grade, Slump, CS28are as below:
Glycerin: The coefficient is 0.520, which indicates that the thermal diffusivity increases by 0.520 for every unit increase in the dosage of glycerin. However, this impact is not statistically significant (p-value = 0.346), hence it is not considered to be a major contribution.
There is a correlation between larger w/b ratios and a decrease in thermal diffusivity, as seen by the coefficient of -53.8, which is the value of the w/b ratio. However, the p-value for this impact is 0.141, which indicates that it is not statistically significant.
CS28, the Grade, and the Slump: At the standard significance level of 0.05, none of these components are statistically significant, although they each have coefficients that indicate the impact that they have on thermal diffusivity.
Table 9
Regression coefficients for Thermal Diffusivity in terms of Glycerin, w/b, Grade, Slump, CS28
Term
|
Coef
|
SE Coef
|
T-Value
|
P-Value
|
VIF
|
Constant
|
1.98
|
5.06
|
0.39
|
0.715
|
|
Glycerin
|
0.520
|
0.487
|
1.07
|
0.346
|
289955.18
|
w/b
|
-53.8
|
29.3
|
-1.83
|
0.141
|
128120.42
|
Grade
|
-0.502
|
0.463
|
-1.08
|
0.340
|
514968.36
|
Slump
|
0.250
|
0.197
|
1.27
|
0.274
|
529385.37
|
CS28
|
0.076
|
0.157
|
0.49
|
0.651
|
79582.73
|
Glycerin*Glycerin
|
-0.0143
|
0.0132
|
-1.08
|
0.341
|
24247.12
|
w/b*w/b
|
-17.8
|
54.5
|
-0.33
|
0.761
|
363262.07
|
Slump*Slump
|
-0.00198
|
0.00188
|
-1.05
|
0.351
|
3865304.65
|
CS28*CS28
|
0.00355
|
0.00426
|
0.83
|
0.451
|
460361.01
|
Glycerin*w/b
|
1.73
|
1.70
|
1.02
|
0.367
|
766686.93
|
Glycerin*Grade
|
0.0191
|
0.0132
|
1.45
|
0.222
|
293872.65
|
Glycerin*Slump
|
-0.0112
|
0.0101
|
-1.11
|
0.329
|
2094991.82
|
Glycerin*CS28
|
-0.00647
|
0.00595
|
-1.09
|
0.338
|
88091.97
|
w/b*Grade
|
-1.374
|
0.938
|
-1.46
|
0.217
|
452916.81
|
w/b*Slump
|
0.530
|
0.628
|
0.84
|
0.446
|
3112317.64
|
w/b*CS28
|
0.705
|
0.663
|
1.06
|
0.348
|
260032.58
|
Grade*Slump
|
0.00858
|
0.00536
|
1.60
|
0.184
|
2603874.82
|
Grade*CS28
|
-0.00381
|
0.00621
|
-0.61
|
0.572
|
649477.16
|
Slump*CS28
|
-0.00393
|
0.00315
|
-1.25
|
0.281
|
1220429.72
|
Interaction Terms obtained by regression analysis for thermal diffusivity in terms of Glycerin, w/b, Grade, Slump, CS28are as below:
The interaction between glycerin and w/b ratio: The value of the coefficient is 1.73, which indicates that the combined effect of glycerin and the w/b ratio on thermal diffusivity is positive; however, the p-value is 0.367, which indicates that the effect is not statistically significant.
Other interaction factors, such as Glycerin X Grade, Glycerin X Slump, and Slump X CS28, also exhibit coefficients and corresponding p-values, which indicates that they may have an impact on thermal diffusivity when taken into consideration jointly.
It is important to note the following numbers:
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The w/b ratio has the highest coefficient magnitude, which is 53.8, indicating that it may have a significant role in determining thermal diffusivity.
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The coefficient magnitude for Slump X CS28 was the smallest, coming up at 0.00393, which indicates that the interaction between Slump and CS28 has a relatively minimal impact on thermal diffusivity.
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The coefficient for the quadratic term of the w/b ratio is not statistically significant, which suggests that the quadratic effect of the w/b ratio may not be present in the model. The maximum p-value for the w/b X w/b ratio is 0.761, which indicates that the coefficient is not statistically significant.
Equation (3) predicts concrete thermal diffusivity based on Glycerin dose, water-to-binder (w/b) ratio, concrete grade, slump, and CS28.
Analysis of Pareto Chart
Figure 5(a) shows the Pareto Chart for Thermal Diffusivity and Specific Heat Capacity. The Pareto Chart of Standardized Effects for Thermal Diffusivity ranks factors based on their standardized effects on thermal diffusivity. As evident from the Fig. 5(a) Factor B (w/b ratio) has the highest standardized effect, followed by factor A (Glycerin). This indicates that the w/b ratio has the most significant influence on thermal diffusivity, followed by Glycerin dosage. This observation aligns with the regression equation for thermal diffusivity, where the w/b ratio (factor B) has a large coefficient magnitude (-53.8), indicating its substantial impact. Glycerin (factor A) also has a positive coefficient (0.520), albeit smaller than the w/b ratio.
Figure 5(b) shows the Pareto Chart for Specific Heat Capacity. Similar to the chart for thermal diffusivity, factor B (w/b ratio) has the highest standardized effect on specific heat capacity, followed by factor A (Glycerin). This finding corresponds with the regression equation for specific heat capacity, where the w/b ratio (factor B) has a coefficient of 43, indicating its significant influence. Glycerin (factor A) also has a negative coefficient (-0.17), though smaller in magnitude compared to the w/b ratio. Overall, the Pareto charts reinforce the importance of w/b ratio and Glycerin dosage in influencing thermal diffusivity, as observed in both the standardized effects and regression analysis.
Contour Plots and Surface Plots:
The contour plots depict the relationships between various factors and the responses of thermal diffusivity, specific heat capacity, and thermal conductivity in the concrete containing Glycerin. For example, Fig. 6(a) shows the contour plots of Thermal Diffusivity. Each subplot shows the contours representing different levels of thermal diffusivity. The x and y axes represent different combinations of factors, while the colors represent different levels of thermal diffusivity. For example, in the subplot "w/b X Glycerin," the x-axis represents the w/b ratio, the y-axis represents Glycerin dosage, and the colors represent different values of thermal diffusivity. These plots help visualize how changes in factor combinations affect thermal diffusivity. Figure 6(b) presents the contour plots of Specific Heat Capacity. Similar to the plots for thermal diffusivity, each subplot shows contours representing different levels of specific heat capacity. For instance, in the subplot "Grade X Glycerin," the x-axis represents concrete Grade, the y-axis represents Glycerin dosage, and the colors represent different values of specific heat capacity. The contour plots of Thermal Conductivity are shown in Fig. 6(c). These plots provide insights into how factor combinations influence thermal conductivity in the system. Overall, these contour plots offer a visual representation of the relationships between various factors and the responses of thermal diffusivity, specific heat capacity, and thermal conductivity. They help researchers understand how different factors interact to influence these thermal properties in the system under study.
The surface plots are shown in Fig. 7 (a). describe how factors affect thermal diffusivity, specific heat capacity, and thermal conductivity in the concrete containing Glycerin on a 3D surface providing a more detailed visualization. The Thermal diffusivity surface plots are shown in Fig….while Specific heat capacity surface plots and thermal conductivity plots are shown in Fig…(b) and …(c) respectively. These charts show how factor combinations affect system thermal conductivity. These surface plots show how factors affect thermal diffusivity, specific heat capacity, and thermal conductivity and are similar to the contour plots.