Multi-response optimization of red mud and sand proportions in paving block production via response surface methodology (RSM)

No	Sand [%]	Red mud [%]	Compression strength [MPa]	Absorption [%]	Abrasion [mm]	Response
No	X₁	X₂	Y₁	Y₂	Y₃	Response
1	0.5	0	17.61	10.16	0.07	y₁
2	0.5	0	14.51	10.07	0.06	y₂
3	0.5	0	14.34	10.16	0.05	y₃
4	0.5	5	20.52	9.95	0.09	y₄
5	0.5	5	17.69	9.22	0.07	y₅
6	0.5	5	13.02	10.96	0.05	y₆
7	0.5	10	22.96	10.26	0.07	y₇
8	0.5	10	20.24	8.83	0.05	y₈
9	0.5	10	12.24	11.31	0.05	y₉
10	0.5	20	20.41	9.23	0.06	y₁₀
11	0.5	20	19.43	10.58	0.10	y₁₁
12	0.5	20	9.98	11.26	0.15	y₁₂

[i] Source: own work.

TABLE 2.

Analysis of variance (ANOVA) for compressive strength

Specification	Source
Specification	df	SS(adj)	MS(adj)	F-value	p-value
Model	5	108.329	21.6659	7.65	0.014
Linear	2	63.290	31.6451	11.18	0.009
Sand [%]	1	62.768	62.7680	22.17	0.003
Red mud [%]	1	0.798	0.7975	0.28	0.615
Square	2	15.221	7.6104	2.69	0.147
Sand [%] × sand [%]	1	0.079	0.0794	0.03	0.873
Red mud [%] × red mud [%]	1	15.141	15.1414	5.35	0.060
Two-way interaction	1	41.989	41.9891	14.83	0.008
Sand [%] × red mud [%]	1	41.989	41.9891	14.83	0.008
Error	6	16.989	2.8315	×	×
Total	11	125.318	×	×	×

[i] Source: own work.

TABLE 3.

Model summary

S	R²	R²(adj)	R²(pred)
1.68271	86.44%	75.15%	54.02%

[i] Source: own work.

TABLE 4.

Analysis of variance (ANOVA) for absorption

Specification	Source
Specification	df	SS(adj)	MS(adj)	F-value	p-value
Model	5	4.54310	0.90862	2.22	0.179
Linear	2	2.64710	1.32355	3.24	0.111
Sand [%]	1	2.48133	2.48133	6.07	0.049
Red mud [%]	1	0.19447	0.19447	0.48	0.516
Square	2	0.87757	0.43878	1.07	0.399
Sand [%] × sand [%]	1	0.83570	0.83570	2.05	0.203
Red mud [%] × red mud [%]	1	0.04187	0.04187	0.10	0.760
Two-way interaction	1	0.82476	0.82476	2.02	0.205
Sand [%] × red mud [%]	1	0.82476	0.82476	2.02	0.205
Error	6	2.45155	0.40859	×	×
Total	11	6.99466	×	×	×

[i] Source: own work.

TABLE 5.

Model summary

S	R²	R²(adj)	R²(pred)
0.639212	64.95%	35.74%	0.00%

[i] Source: own work.

TABLE 6.

Analysis of variance (ANOVA) for abrasion

Specification	Source
Specification	df	SS(adj)	MS(adj)	F-value	p-value
Model	5	0.007467	0.001493	4.58	0.046
Linear	2	0.003321	0.001661	5.09	0.051
Sand [%]	1	0.000188	0.000188	0.57	0.477
Red mud [%]	1	0.003166	0.003166	9.70	0.021
Square	2	0.000834	0.000417	1.28	0.345
Sand [%] × sand [%]	1	0.000029	0.000029	0.09	0.777
Red mud [%] × red mud [%]	1	0.000805	0.000805	2.47	0.167
Two-way interaction	1	0.003886	0.003886	11.91	0.014
Sand [%] × red mud [%]	1	0.003886	0.003886	11.91	0.014
Error	6	0.001958	0.000326	×	×
Total	11	0.009425	×	×	×

[i] Source: own work.

TABLE 7.

Model summary

S	R²	R²(adj)	R²(pred)
0.0180640	79.23%	61.92%	0.00%

[i] Source: own work.

Bar chart of the standardized effects for compression strength, absorption, and abrasion
Source: own work.

Bar chart and residual plot for compression strength
Source: own work.

Bar chart and residual plot for absorption
Source: own work.

Bar chart and residual plot for abrasion
Source: own work.

Contour and surface plot for compression strength
Source: own work.

Contour and surface plot for absorption
Source: own work.

Contour and surface plot for abrasion
Source: own work.

Comparison plot of actual compression strength versus response surface methodology prediction
Source: own work.

References

Authors

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DOI: https://doi.org/10.22630/srees.11102 | Journal eISSN: 2543-7496 | Journal ISSN: 1732-9353

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Language: English

Page range: 241 - 250

Submitted on: Jan 28, 2026

Accepted on: May 13, 2026

Published on: Sep 30, 2026

Published by: Warsaw University of Life Sciences - SGGW Press

In partnership with: Paradigm Publishing Services

Keywords:

response surface methodology,

red mud,

paving block,

multi-response optimization,

sustainable construction materials

Related subjects:

Architecture and design,

Architecture,

Architects, buildings,

Engineering,

Mechanical engineering,

Fundamentals of mechanical engineering,

Geosciences,

Geology and mineralogy,

Geosciences, other

© 2026 Erwin Sutandar, Tavio, Daniel Christianto, published by Warsaw University of Life Sciences - SGGW Press
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 35 (2026): Issue 3 (September 2026)

Multi-response optimization of red mud and sand proportions in paving block production via response surface methodology (RSM)

Figures & Tables

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FIGURE 11.

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