Experimental Modelling and Multi-Objective Optimisation of Carbon Black, Clay-Carbon Black, and Clay-Fly Ash-Carbon Black Bricks for Sustainable Construction Applications.

Experimental Modelling and Multi-Objective Optimisation of Carbon Black, Clay-Carbon Black, and Clay-Fly Ash-Carbon Black Bricks for Sustainable Construction Applications.

Sudagani Venkata Giri Babu

Senior Lecturer in Civil Engineering, Andhra Polytechnic, Kakinada, Andhra Pradesh, India and Research Scholar, JNTUA, Anantapuramu,

ORCID iD: 0009-0009-2890-5577

Sankranthi Krishnaiah

Professor, Department of Civil Engineering, JNTUA, Anantapuramu, Andhra Pradesh, India, ORCID iD: 0000-0001-6750-501X

Abstract – The present invention proposes a systematic experimental modelling and optimisation method for developing sustainable clay- based masonry units, including Carbon Black Bricks (CBB), ClayCarbon Black Bricks (CCB), and ClayFly AshCarbon Black Bricks (CFCB). A Taguchi orthogonal array design is employed to efficiently investigate the influence of material composition on compressive strength, water absorption, and bulk density. Response Surface Methodology (RSM) is proposed to establish predictive relationships and confirm model robustness. The integrated TaguchiRSM framework reduces experimental trials while enabling reliable processproperty optimisation. The resulting composite bricks demonstrate improved mechanical performance and reduced water absorption through the utilisation of industrial by-products, providing a scalable and eco-efficient solution for sustainable brick manufacturing.

Keywords: CBB, CCB, CFCB, Taguchi, CODAS-CRITIC, ANOVA, RSM.

1. INTRODUCTION

   The construction industry is increasingly adopting sustainable material systems that reduce environmental impact while maintaining structural performance. Conventional clay bricks, though widely used, rely on high natural resource consumption and energy- intensive production. The incorporation of industrial by-products such as fly ash and carbon black offers a viable approach to enhance clay brick performance while promoting waste utilisation. However, existing modification methods remain largely empirical and lack an integrated framework combining experimental design, predictive modelling, and optimisation.

   Traditional mix design practices often involve trial-and-error experimentation, leading to increased cost and time, and they rarely address multi-objective performance requirements such as compressive strength, water absorption, and green density simultaneously. In response, the present work proposes an integrated experimental modelling strategy for Carbon Black Bricks (CBB), ClayCarbon Black Bricks (CCB), and ClayFly AshCarbon Black Bricks (CFCB). A Taguchi orthogonal array is used to efficiently investigate process parameters, and the optimised results are validated through Response Surface Methodology (RSM) to establish predictive models and confirm robustness. The combined TaguchiRSM framework provides a systematic and scalable approach for developing eco-efficient clay composite bricks.

   The novelty of the proposed invention lies in the integration of industrial waste additives with a hybrid TaguchiRSM modelling strategy, allowing simultaneous evaluation and optimisation of multiple performance responses. This integrated approach facilitates reproducible material design, reduces experimental uncertainty, and supports sustainable construction practices by promoting resource efficiency and waste valorisation.

2. LITERATURE REVIEW

   Sustainable clay-based masonry materials have received increasing attention due to the need to reduce environmental impact while maintaining mechanical performance. Recent investigations demonstrate that incorporating industrial by-products into clay bricks can significantly enhance strength, thermal efficiency, and carbon reduction potential (Singh et al., 2024; Fahmy et al., 2024). Comparative studies on clay and fly ash masonry systems indicate that optimised fly ash content improves durability and energy performance, supporting its use as a partial clay replacement (Kumar et al., 2023). Integrated frameworks combining experimental optimisation with environmental assessment further confirm the effectiveness of fly ash in improving performance while supporting sustainable construction practices (Maaze et al., 2025).

   In parallel, carbonaceous additives have emerged as promising modifiers for lightweight and thermally efficient bricks. Biochar- based studies revealed that carbon-rich materials can reduce density and improve insulation, although optimisation is required to balance porosity and strength (Xie and Wu, 2025). Research on recycled carbon materials also highlights the feasibility of recovered carbon black and carbon fibre additives for enhancing microstructural stability and crack resistance in masonry products (Irshidat et al., 2021; Crespo-López et al., 2024). Additional work on lightweight and thermally efficient clay bricks incorporating alternative additives supports the role of hybrid material systems in improving energy performance and durability (Bilgil et al., 2025; Shahat et al., 2025).

   From a methodological perspective, statistical design and modelling approaches are increasingly used to minimise experimental trials while ensuring reliable optimisation. The Taguchi method has been widely applied for parameter screening and robust experimental planning in brick manufacturing (Chaulia and Das, 2008). However, recent studies emphasise that Response Surface Methodology (RSM) provides enhanced predictive capability by modelling nonlinear interactions and validating optimal parameter settings (Benamara et al., 2025). Life-cycle carbon and thermal performance evaluations further highlight the importance of integrating modelling with sustainability assessment in modern brick research (Janpetch et al., 2026).

   Despite these advancements, limited studies simultaneously compare conventional clay bricks, claycarbon black bricks, and clay fly ashcarbon black bricks within a unified experimental modelling framework. Therefore, the present work integrates Taguchi experimental design validated by RSM to optimise multiple performance responses, including compressive strength, water absorption, and green density, for sustainable clay composite brick development.

   Despite progress in sustainable brick research, most studies examine single-additive systems and apply Taguchi or RSM independently, with limited comparative modelling of CBB, CCB, and CFCB bricks. Integrated approaches combining Taguchi- based parameter screening with RSM validation and multi-objective optimisation of compressive strength, water absorption, and density remain scarce. Therefore, this study proposes a unified experimental modelling framework to develop optimised and sustainable clay composite bricks.

3. EXPERIMENTAL MODELLING FRAMEWORK AND METHODOLOGY

   1. Experimental Design Strategy

      An integrated experimental modelling framework was adopted to develop and optimise three clay-based brick systems: conventional Carbon Black Bricks (CBB), ClayCarbon Black Bricks (CCB), and ClayFly AshCarbon Black Bricks (CFCB). The methodology combines Taguchi orthogonal array design for efficient parameter screening with Response Surface Methodology (RSM) for model validation and predictive analysis. The overall framework aims to establish robust processproperty relationships while minimising the number of experimental trials and material consumption.

      Taguchi design was first employed to investigate the influence of material composition and processing parameters on key performance responses. Based on the number of contro factors and levels, an appropriate orthogonal array (e.g., L9 or L27) was selected to ensure balanced experimental coverage. Signal-to-noise (S/N) ratio analysis was used to determine the optimal levels of parameters according to the desired response characteristics, namely larger-the-better for compressive strength and density, and smaller-the-better for water absorption.

   2. Materials and Mix Proportions

      The experimental program included three brick formulations: CBB, consisting of carbon black brick, CCB, incorporating clay and carbon black as a modifier, and CFCB, containing clay and both fly ash and carbon black as partial replacements. Clay served as the primary matrix material, while fly ash was introduced to enhance particle packing and sustainability. Carbon black was incorporated to modify microstructural characteristics and potentially improve thermal and mechanical behaviour. The percentage levels of fly ash and carbon black, along with additives, were treated as control factors in the experimental design.

   3. Taguchi-Based Experimental Modelling

      The Taguchi method was applied to identify significant parameters influencing compressive strength (CS), water absorption (WA), and green density (GD). Experimental runs defined by the orthogonal array were prepared under controlled laboratory conditions. Analysis of variance (ANOVA) was performed to evaluate the statistical significance and percentage contribution of each factor. Optimal parameter combinations were obtained by analysing S/N ratios and main effect plots.

   4. Response Surface Methodology (RSM) Validation

      To validate the optimal solutions derived from Taguchi analysis and capture nonlinear interactions among variables, Response Surface Methodology was employed as a secondary modelling layer. Regression models were developed for each response using second-order polynomial equations. Model adequacy was assessed through analysis of variance, coefficient of determination (R²), and residual analysis. RSM-based surface and contour plots were used to visualise interaction effects and confirm the robustness of the optimised parameter regions.

      Response Surface Methodology develops regression models for each response (e.g., CS, WA, Density). Since all responses are expressed as mathematical equations of the same factors, RSM can simultaneously optimise multiple objectives using a desirability function approach. This allows conflicting responses, such as maximising compressive strength and density while minimising water absorption, to be balanced within a single optimisation framework.

   5. Brick Preparation and Testing

      1. Brick Preparation Procedure

         The carbon blackbased bricks CBB (Carbon black – Cement brick), CCB (Clay-Carbon Black-Cement brick), and CFCB (clay-fly ash-carbon black-cement brick) were prepared via semi-dry compaction using a 60-ton hydraulic press.

         • CBB: Carbon black blended with ordinary Portland cement and additives (gypsum, quarry dust, polycarboxylate ether [PCE]).

         • CCB: Clay added to carbon black, cement, and additives (gypsum, stone dust, PCE).

         • CFCB: Clay added to Fly Ash, carbon black, cement, and additives (gypsum, stone dust, PCE). Fly ash is incorporated for enhanced pozzolanic reactivity and microstructural refinement.

           All dry constituents were proportioned by weight and manually dry-mixed to ensure uniform dispersion of carbon black and to prevent particle agglomeration, as illustrated in Fig. 1.0. The polycarboxylate ether (PCE) was first dissolved in the mixing water at a dosage of 0.41.5% and then added gradually to the dry blend to obtain a semi-dry, mouldable consistency suitable for compaction.

           The prepared mixture was placed in layers into steel moulds of dimensions 9 × 4 × 3 in. (228.6 × 101.6 × 75 mm) and compacted under a pressure of approximately 2526 MPa for 1015 seconds. The demoulded green bricks were kept undisturbed under ambient laboratory conditions for 24 hours, followed by water curing for 28 days prior to testing.

           Fig. 1.0 Weighing, mixing of raw materials and curing

      2. Testing Methods:

         Compressive Strength (CS) was determined in accordance with IS 3495 (Part 1):1992 using a calibrated compression testing machine, and the maximum load at failure was recorded to evaluate the strength of the specimens. Water Absorption (WA) was assessed as per IS 3495 (Part 2):1992, where oven-dried specimens were immersed in water for 24 hours, surface-dried, and reweighed to determine the percentage absorption. Green Density (GD) was measured immediately after demoulding by recording the mass and dimensions of freshly moulded bricks prior to curing. For all parameters, the average value of three specimens was reported.

         The corresponding testing procedures are illustrated in Fig. 2.0.

         Fig 2.0 Testing of bricks

4. EXPERIMENTAL DESIGN AND RESPONSE MODELLING USING TAGUCHI AND RSM TECHNIQUES

   1. Factors and Responses; The experimental design and response modelling framework was developed to systematically analyse the performance of carbon black brick (CBB), claycarbon black (CCB), and clayfly ashcarbon black (CFCB) bricks using an integrated Taguchi and Response Surface Methodology (RSM) approach. Control factors and their respective levels were selected based on material characteristics, preliminary experimentation, and insights from relevant literature to ensure technical feasibility and sustainability considerations, as presented in the table. 1.0. The primary performance responses, compressive strength, water absorption, and green density were defined to represent structural integrity, durability, and physical stability of the developed bricks as illustrated in the table. 2.0.

      Table. 1.0 Factors and Levels:

      Brick Type	CB	Cement	Gypsum	Quary Dust	PCE	CLAY	FA
      CBB	(40,60,80)	(5,10,15)	(1,1.5,2)	(20,30,40)	(0.4,0.95,1.5)
      CCB	(25,37.5,50)	(5,10,15)	(1,1.5,2)	(20,30,40)	(0.4,0.95,1.5)	(50,57.5,65)
      CFCB	(50,60,70)	(5,10,15)	(1,1.5,2)	(20,30,40)	(0.4,0.95,1.5)	(35,40,45)	(50,60,70)

      Table. 2.0 Responses

      Response Name	Unit	Objective Type	Engineering Purpose
      Compressive Strength (CS)	MPa	Larger-the-better	Structural load capacity
      Water Absorption (WA)	%	Smaller-the-better	Durability and moisture resistance
      Green Density	g/cm³	Larger-the-better	Material stability & sustainability

   2. Taguchi Orthogonal array: A Taguchi orthogonal array of L27 was adopted to structure the experimental runs efficiently, enabling the evaluation of multiple factors with a reduced number of trials while maintaining statistical balance. Signal-to-noise

      ratio analysis was employed as an initial assessment tool to identify dominant factors influencing each response and to understand the preliminary trends in experimental outcomes. This step provided a robust screening mechanism prior to advnced modelling.

   3. Response Surface Methodology: To extend the analytical capability beyond Taguchi analysis, response surface models were developed to establish predictive relationships between process parameters and performance responses. The RSM framework allowed the investigation of interaction and quadratic effects, thereby enhancing the understanding of complex material behaviour. Statistical adequacy of the developed models was evaluated through analysis of variance and goodness-of-fit indicators to ensure reliability and predictive accuracy.

Finally, a multi-response optimisation strategy based on composite desirability principles was formulated to identify an optimal combination of factors that simultaneously maximises compressive strength, minimises water absorption, and maintains appropriate density characteristics. The integrated modelling and optimisation procedure provides a structured analytical foundation, enabling a smooth transition into the subsequent results and discussion section.

1. RESULTS AND DISCUSSION

   This section presents the experimental findings and analytical outcomes obtained from the integrated TaguchiRSM framework for CBB, CCB, and CFCB bricks. The influence of control factors on compressive strength, water absorption, and density is evaluated through statistical analysis and response modelling. The results are interpreted to compare brick performance, identify significant parameters, and determine optimal compositions that enhance structural efficiency and sustainability in construction applications.

   1. Taguchi Analysis: All tests were conducted using triplicate specimens to ensure experimental reliability and repeatability. The reported values of compressive strength, water absorption, and green density represent the mean of three independent measurements for each mix proportion, as presented in Table 3.0.

      Table. 3.0 CS, WA, GD of CBB, CCB and CFCB

      Run	CBB			CCB			CFCB
      	CS	WA	GD	CS	WA	GD	CS	WA	GD
      1	1.25	12.54	1.77	2.68	12.54	1.77	3.49	13.06	1.72
      2	1.21	13.00	1.78	2.70	13.00	1.78	3.55	12.40	1.76
      3	1.25	12.39	1.77	2.67	12.39	1.77	3.57	12.71	1.75
      4	2.31	13.53	1.69	3.10	13.53	1.69	3.58	13.99	1.66
      5	2.36	11.54	1.68	3.11	11.54	1.68	3.56	13.54	1.67
      6	2.39	11.41	1.70	2.97	11.41	1.70	3.52	13.30	1.67
      7	3.72	13.82	1.63	3.68	13.82	1.63	3.68	14.17	1.59
      8	3.86	12.84	1.62	3.72	12.84	1.62	3.72	13.53	1.62
      9	3.69	13.38	1.60	3.55	13.38	1.60	3.66	13.80	1.63
      10	1.92	9.23	1.81	4.59	9.23	1.81	4.84	10.11	1.81
      11	1.84	9.03	1.81	4.68	9.03	1.81	5.02	9.05	1.83
      12	1.92	8.95	1.84	4.74	8.95	1.84	4.67	12.57	1.78
      13	2.34	11.93	1.80	2.08	11.93	1.80	3.34	13.19	1.74
      14	2.34	12.17	1.78	2.03	12.17	1.78	2.82	13.18	1.72
      15	2.32	13.40	1.76	2.05	13.40	1.76	2.87	11.67	1.69
      16	2.11	12.49	1.57	2.57	12.49	1.57	3.10	13.86	1.63
      17	1.99	13.27	1.54	2.54	13.27	1.54	3.09	14.21	1.59
      18	1.89	12.29	1.57	2.62	12.29	1.57	3.08	13.91	1.60
      19	1.02	7.70	1.83	3.59	7.70	1.83	3.82	10.71	1.84
      20	1.08	7.86	1.80	3.54	7.86	1.80	3.85	9.86	1.81
      21	1.04	7.51	1.81	3.57	7.51	1.81	3.87	10.22	1.85
      22	1.76	10.95	1.69	3.89	10.95	1.69	4.08	11.31	1.70
      23	1.77	10.68	1.69	3.88	10.68	1.69	4.14	12.12	1.69
      24	1.73	10.74	1.69	3.94	10.74	1.69	4.08	11.09	1.73

      25	1.86	11.93	1.62	1.79	11.93	1.62	3.23	13.66	1.63
      26	1.85	12.96	1.59	1.77	12.96	1.59	3.13	13.57	1.64
      27	1.83	11.11	1.60	1.79	11.11	1.60	3.21	13.66	1.66

   2. Signal-to-Noise Ratios ranking of the responses: Th Signal-to-Noise (S/N) ratio ranking provides a clear understanding of how each factor influences compressive strength (CS), water absorption (WA), and green density (GD) across the three brick types (CBB, CCB, and CFCB) as presented in the table. 4.0. The variation in ranks indicates that the sensitivity of responses is strongly dependent on material composition and brick formulation.

      Table. 4.0 Signal-to-Noise Ratios ranking of the responses

      Factor	CS			WA			GD
      	RANK			RANK			RANK
      	CBB	CCB	CFCB	CBB	CCB	CFCB	CBB	CCB	CFCB
      CB	2	3	3	2	2	4	4	4	3
      Cement	4	2	4	4	1	2	2	1	2
      Gypsum	3	1	2	3	3	1	3	3	1
      Quarry Dust	1	6	1	1	6	3	1	5	6
      PCE	5	4	6	5	4	6	5	2	7
      Clay		5	5		5	5		6	4
      FA			7			7			5

      The Signal-to-Noise (S/N) ratiobased ranking clearly reveals a transition in the governing performance mechanisms across the three brick systems. In the case of CBB, the dominant influence of Quarry Dust on compressive strength, water absorption, and density indicates that the overall performance is primarily governed by packing density and particle gradation effects. The granular skeleton plays the principal structural role, and improvements in compaction and inter-particle contact directly translate into enhanced strength and reduced porosity. Thus, CBB behaves as a packing-controlled composite system where physical densification mechanisms dominate over chemical interactions.

      In contrast, the CCB system exhibits a marked shift toward binder-controlled behaviour. The dominance of Cement and Gypsum across major responses, particularly water absorption and density, along with the reduced influence of Quarry Dust, suggests that the incorporation of carbon black alters the internal pore structure and surface interaction characteristics. As a result, the binder matrix assumes a more critical role in stabilising dispersion, improving cohesion, and compensating for pore irregularities introduced by carbon black. Hence, performance in CCB is primarily dictated by binder chemistry rather than granular packing.

      For CFCB, the ranking pattern reflects a microstructure-refinement-controlled regime. While Quarry Dust continues to anchor compressive strength through structural packing, Gypsum and Cement dominate water absorption and density, indicating enhanced pore refinement and matrix densification mechanisms. The combined presence of fly ash and carbon black promotes secondary reactions and filler effects, making microstructural modification the key performance driver. Thus, CFCB represents a hybrid system where structural packing and refined binder-induced microstructure synergistically govern performance.

      ANOVA: The statistical results clearly indicate that brick composition exerts a strong and statistically significant influence on the combined responses compressive strength (CS), water absorption (WA), and green density (GD) as presented in Table 5.0.

      Table. 5.0 statistical results

      Brick	CODAS Score	Rank	Brick	CODAS Score	Rank	Brick	CODAS Score	Rank
      CBB1	0.2385	61	CCB1	0.2933	35	CFCB1	0.3134	27
      CBB2	0.2409	59	CCB2	0.2967	32	CFCB2	0.3483	25
      CBB3	0.2410	58	CCB3	0.2948	33	CFCB3	0.3403	26
      CBB4	0.2002	69	CCB4	0.2608	51	CFCB4	0.2869	42
      CBB5	0.2324	64	CCB5	0.2849	44	CFCB5	0.2912	36
      CBB6	0.2495	55	CCB6	0.2874	41	CFCB6	0.2892	38
      CBB7	0.2901	37	CCB7	0.2863	43	CFCB7	0.2754	47
      CBB8	0.3080	29	CCB8	0.2946	34	CFCB8	0.2887	39

      CBB9	0.2818	46	CCB9	0.2681	50	CFCB9	0.2844	45
      CBB10	0.3662	22	CCB10	0.5110	5	CFCB10	0.5122	4
      CBB11	0.3704	20	CCB11	0.5221	3	CFCB11	0.5571	1
      CBB12	0.3960	15	CCB12	0.5438	2	CFCB12	0.4487	10
      CBB13	0.3079	30	CCB13	0.2969	31	CFCB13	0.3118	28
      CBB14	0.2879	40	CCB14	0.2742	48	CFCB14	0.2599	52
      CBB15	0.2557	53	CCB15	0.2422	57	CFCB15	0.2692	49
      CBB16	0.1416	77	CCB16	0.1810	71	CFCB16	0.2308	65
      CBB17	0.1086	81	CCB17	0.1613	74	CFCB17	0.2166	68
      CBB18	0.1310	78	CCB18	.1899	70	CFCB18	0.2189	67
      CBB19	0.4177	13	CCB19	0.4967	6	CFCB19	0.4439	12
      CBB20	0.3928	17	CCB20	0.4728	8	CFCB20	0.4447	11
      CBB21	0.4116	14	CCB21	0.4904	7	CFCB21	0.4629	9
      CBB22	0.2266	66	CCB22	0.3642	24	CFCB22	0.3773	18
      CBB23	0.2358	62	CCB23	0.3691	21	CFCB23	0.3659	23
      CBB24	0.2324	63	CCB24	0.3727	19	CFCB24	0.3945	16
      CBB25	0.1593	75	CCB25	0.1555	76	CFCB25	0.2440	56
      CBB26	0.1150	79	CCB26	0.1091	80	CFCB26	0.2391	60
      CBB27	0.1789	72	CCB27	0.1770	73	CFCB27	0.2544	54

      The analysis of variance clearly indicates that the factor has a statistically significant influence on the response, as illustrated in the table. 6.0. The very high F-value (1694.58) combined with a P-value of 0.000 confirms that the variation among factor levels is not due to random experimental noise but is a real and dominant effect. The factor sum of squares (4917.2) constitutes the major portion of the total variation (5265.4), while the error contribution (348.2) is comparatively small, demonstrating strong experimental control and minimal unexplained variability.

      Table. 6.0 Analysis of Variance

      Source	DF	Adj SS	Adj MS	F-Value	P-Value
      Factor	2	4917.2	2458.6	1694.58	0.000
      Error	240	348.2	1.45
      Total	242	5265.4
      S=1.2045;R=93.39%;R-sq(adj)=93.33%;R-sq(pred)=93.22%

      The coefficient of determination (R² = 93.39%) shows that more than 93% of the total variability in the response is explained by the factor. The close agreement between R² (93.39%), adjusted R² (93.33%), and predicted R² (93.22%) indicates excellent model adequacy without overfitting. The negligible difference among these values confirms that the model possesses strong predictive capability and can reliably estimate new observations within the studied range.

      The standard error of regression (S = 1.2045) is relatively low, suggesting good precision of estimation and limited dispersion around the fitted model. Overall, the statistical indicators collectively demonstrate that the factor exerts a dominant and consistent influence on the response, the experimental design is robust, and the developed model is statistically sound and suitable for optimisation and further predictive analysis.

   3. Single Optimum from Taguchi results: In the present study, the CODAS (Combinative Distance-based Assessment) method was employed to identify the optimal experimental run. Within the CODAS framework, the relative weights of the response parameters were determined using the CRITIC (Criteria Importance Through Intercriteria Correlation) method to ensure objective weight allocation. The same author (Giri Babu S V et al , 2025) implemented the hybrid approach for sustainability evaluation. The hybrid approach is implemented to determine relative weights of the responses and is presented in Table 7.0.

      From the results, it is observed that CFCB 11 ranked as the best, followed by CCB12 and CCB 11

      Table. 7.0 Optimum Mixes

      Brick type	Rank	Single optimum factor levels	CS	WA	GD
      CFCB 11	1	Clay40, FA60, CB50, Cement15, Gypsum1.5, Quarry Dust40, PCE0.4	5.02	9.05	1.83
      CCB 12	2	Clay57.5, CB25, Cement15, Gypsum 2, Quarry Dust30, PCE1.5	4.74	8.95	1.84
      CCB 11	3	Clay57.5, CB25, Cement15, Gypsum 1.5, Quarry Dust30, PCE0.4	4.68	9.03	1.81

   4. Response Surface Methodology (RSM): Response Surface Methodology (RSM) was employed to validate and refine the Taguchi-based optimum conditions for each brick system, as illustrated in Figures 3.0 to 5.0. A desirability function approach was applied to determine the multi-response optimum, and the predicted response values were subsequently compared with experimental results to evaluate model adequacy and predictive accuracy.

      Based on the composite desirability approach, the CFCB formulation emerged as the preferred single optimum solution, achieving the highest overall desirability value (D = 0.9976). This indicates the most balanced simultaneous optimisation of compressive strength (5.0041 MPa), water absorption (9.0467%), and green density (1.8693 g/cm³) among the three brick systems, as presented in Table 8.0.

      The optimal composition derived from the three brick formulations, as illustrated in Figures 3.0 to 5.0, is summarised in Table 9.0.

      Table. 8.0 Optimum Responses and Desirability values.

      Brick	CS		WA		GD		Overall
      	Response	Desirability	Response	Desirability	Response	Desirability
      CBB	2.5153	0.5265	9.7172	0.6502	1.8416	1.000	0.6966
      CCB	4.6261	0.9616	7.5081	1.0000	1.8401	1.0000	0.9870
      CFCB	5.0041	0.9928	9.0467	1.0000	1.8693	1.0000	0.9976

      Table. 9.0 Optimum composition obtained through RSM is:

      Optimum factor levels	CS	WA	GD
      Clay41.46, FA70, CB50, Cement15, Gypsum2, Quarry Dust 40, PCE1.5 (CFBC brick)	5.00	9.05	1.86

      Fig. 3.0 Response Surface Method -CFCB

      Fig. 4.0 Response Surface Method -CCB

      Fig. 5.0 Response Surface Method -CBB

   5. Validation of Taguchi with RSM: Treating the Taguchi results as actual experimental values and the RSM outputs as predicted responsesconstitutes a valid validation approach, since the Taguchi method provides directly observed performance data, whereas Response Surface Methodology (RSM) develops a statistical regression model for prediction. The comparison of these results through percentage error analysis (presented in Table 10.0) enables quantification of the agreement between the experimental observations and model predictions. When the prediction error remains within an acceptable range, it confirms the adequacy, reliability, and practical applicability of the developed RSM model for multi-response optimisation.

      Table. 10.0 Absolute %Error

      Method	Predicted (RSM)	Actual (Taguchi)	% Abs error
      CS	5.00	5.02	0.3984
      WA	9.05	9.05	0.0000
      GD	1.86	1.83	1.6393

      The RSM predictions show excellent agreement with Taguchi experimental values, with very low percentage errors for CS, WA, and GD. The negligible deviation confirms that the developed response surface models accurately represent the experimental behaviour. This validates the reliability and robustness of the optimised conditions obtained through the integrated TaguchiRSM approach. However, validation needs to be carried out for the optimum composition of the brick obtained by RSM

      1. DISCUSSION OF RESULTS:

         The integrated TaguchiRSM analysis demonstrates that brick performance is governed by distinct composition-driven mechanisms. The S/N ratio results indicate that compressive strength and green density are primarily influenced by densification and binder interactions, whereas water absorption is more sensitive to pore connectivity and process variability. This confirms that optimisation must consider multiple responses simultaneously rather than focusing on a single performance indicator.

         To obtain a single balanced solution, a CRITICCODAS approach was adopted. The CRITIC method objectively determined the relative importance of CS, WA, and GD based on data variability and inter-criteria conflict, while CODAS ranked the brick alternatives considering their distance from the negative ideal solution. This hybrid framework ensured that the final selection was not based on simple majority agreement but on statistically derived criterion weights and compromise ranking logic. In RSM, the composite desirability optimisation demonstrated that CFCB achieved the highest overall desirability, reflecting superior simultaneous optimisation of compressive strength, water absorption, and green density. Overall, the results indicate that sustainable brick performance is governed by composition-specific mechanisms, particle packing in CBB, hydration-driven bonding in CCB, and pozzolanic densification in CFCB. The close agreement between RSM predictions and experimental results further validates the robustness and reliability of the optimised solutions.

         1. CONCLUDING REMARKS:

            The present study establishes a systematic multi-response optimisation framework for sustainable brick systems by integrating Taguchi design, RSM validation, and CRITICCODAS decision modelling. The results confirm that brick performance is composition-dependent, with different systems exhibiting dominance in strength, durability, or densification behaviour. The CRITICCODAS approach enabled an objective and balanced selection of the most suitable brick alternative by considering the relative importance and compromise ranking of CS, WA, and GD simultaneously. Validation through RSM demonstrated strong agreement between predicted and experimental outcomes, confirming the robustness of the developed models. Overall, the integrated methodology provides a reliable and application-oriented decision-support tool for designing optimised and performance- balanced sustainable brick materials.

         2. Limitations and Future Scope

The study was conducted within controlled laboratory conditions and limited material ranges, which may not fully represent field- scale variability. Although RSM predictions closely matched experimental results, further validation experiments under real manufacturing conditions are necessary to confirm industrial applicability. Future research should incorporate long-term durability testing and large-scale production trials to enhance the practical implementation of the optimised brick systems.

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