Optimizing concrete strength with tapioca peel ash: a central composite design approach

ABSTRACT

Tapioca Peel Ash (TPA), a plentiful agricultural residue, demonstrates potential as a Supplementary Cementitious Material (SCM) in concrete. This research intends to maximize the efficiency of TPA integration through the Central Composite Design (CCD) approach to ascertain the optimal mix of components for enhanced performance. The physicochemical analysis assessed TPA’s pozzolanic properties. Laboratory tests analyzed the compressive and flexural strengths of concrete mixes containing various amounts of TPA, cement, and aggregates. The outcomes showed that a mixture ratio of 0.2:0.0875:0.3625:0.4625 (Cement : TPA : Fine Aggregate : Coarse Aggregate) achieved an ultimate compressive strength of 27.08 MPa. Moreover, a ratio of 0.2:0.0875:0.3625:0.525 yielded a maximum flexural strength of 9.84 MPa. Quadratic predictive models and statistical analyses were derived to determine the ideal concrete mixture that substantially improves compressive and flexural strengths. Validation via student’s t-test showed a significant correlation between experimental and simulated values, with p-values of 0.9987 and 0.9912 for compressive and flexural strengths, respectively. This research highlights the opportunity to improve concrete properties and minimize waste by effectively using TPA in construction.

Keywords:
Tapioca Peel Ash; SCM; Agro-waste; Design expert; Response Surface Methodology

1. INTRODUCTION

Concrete is a widely utilized material globally, yet it raises environmental concerns due to the significant energy consumption and carbon emissions associated with its production from cement [¹, ²]. Researchers are exploring alternative materials and mix designs to address these issues and promote sustainable construction practices. One such material is Tapioca Peel Ash (TPA), derived from tapioca processing waste [³]. Tapioca (Manihot esculenta), vital in tropical regions, generates substantial peel waste, posing environmental and health risks if improperly disposed [⁴]. Recent research indicates that Tapioca peels can be transformed into ash (TPA) and used in concrete manufacturing. TPA exhibits pozzolanic properties akin to fly ash or silica fume, enhancing concrete by reacting with calcium hydroxide to form extra-cementitious compounds [⁴, ⁵]. However, optimizing TPA integration into concrete mixes is crucial for achieving the desired performance [⁶]. The utilization of Tapioca Peel Ash (TPA) in concrete has garnered interest due to its pozzolanic properties, which enhance strength, durability, and environmental sustainability. TPA reacts with calcium hydroxide when moisture is present, forming additional cementitious compounds that reinforce concrete’s mechanical properties [⁷]. Widely accepted in civil engineering applications, TPA serves as a SCM, replacing traditional cement to improve concrete performance [⁸, ⁹]. Several studies have investigated TPA’s incorporation into concrete. OGUNBODE et al. [¹⁰] explored its use alongside kenaf bio-fibers, examining both mechanical and microstructural properties, aiming to develop sustainable concrete materials. Similarly, OSUIDE et al. [¹¹] researched TPA and wood ash as partial replacements for cement , finding that lower replacement percentages (5%, 10%, 15%) met concrete strength standards, while higher percentages (20%, 25%) were less suitable for structural use. These studies underscore the potential of TPA and related materials to mitigate environmental impact in concrete production.

The optimization of TPA concrete using the CCD technique aims to improve concrete properties through the integration of TPA as a SCM [¹², ¹³]. Statistical analysis allows researchers to create models that exemplify the correlation among variables and responses through the use of regression techniques and RSM [¹⁴]. This process identifies key factors, assesses their impacts, and determines the optimal parameters to maximize desired outcomes [¹⁵]. CCD offers benefits such as reducing both time and expenses compared to standard trial-and-error methods, facilitating efficient examination of numerous parameters and relations to enhance control over TPA concrete properties [¹⁶, ¹⁷]. By pinpointing the best variable combinations, this systematic approach enhances the concrete structures performance, environmental impact, and its economic feasibility [¹⁸]. Recent research has introduced innovative approaches to assess concrete performance by examining interactions among its constituent materials [¹⁹, ²⁰, ²¹]. These methodologies involve numerical, computational, and logical techniques. For example, HASSAN et al. [²²] investigated the utilization of micro and nano Palm Oil Fuel Ash (POFA) as SCMs in high-strength composite concrete. They employed CCD and RSM to optimize mix proportions. Experimental results validated their mathematical models, recommending an ideal blend with 10% micro-POFA and 1.50 to 2.85% nano-POFA, satisfying the requirements for both concrete fresh and hardened properties. Furthermore, ALI et al. [²³] investigated substituting Pumice Stone (PS) for the incorporation of natural coarse aggregates in concrete. Using RSM, they varied PS percentages and found that up to 30% replacement in lightweight aggregate concrete led to achieving compressive strengths exceeding 15 MPa, split tensile strengths ranging from 7% to 12% of the compressive strength, and flexural strengths ranging from 9% to 11% of the compressive strength. Their quadratic model achieved high precision, with R-squared values exceeding all responses achieved a 99% accuracy rate. Furthermore, ALI et al. [²⁴] investigated the use of Waste Foundry Sand (WFS) as a partial substitution for fine aggregate in concrete mixes, assessing its influence on both the performance of fresh and its hardened properties. Through the adjustment of WFS ratios using CCD within RSM, optimal mechanical properties were identified with 20% WFS substitution after 56 days of curing: achieving a 29.37 MPa compressive strength, 3.828 MPa splitting tensile strength, and 8.0 MPa flexural strength. They observed that substituting up to 30% of the material resulted in fresh properties comparable to those of the control mix.

Using the CCD technique to optimize TPA concrete is a systematic approach aimed at improving concrete properties and performance [¹³, ²⁵]. This method effectively utilizes TPA, a waste material, thereby promoting sustainability and improving construction material efficiency [²⁶]. The study intentions to enhance various aspects of concrete using CCD, exploring variables and their relations to attain the desired properties of concrete. Through statistical investigation and response surface modelling, the research seeks to understand the relationship between variables and responses to identify optimal parameter values. The investigation will offer insights into TPA concrete optimization, facilitating efficient utilization of Tapioca peel ash to enhance sustainability and concrete performance. Motivated by promoting sustainable construction practices, reducing costs by substituting traditional cement with TPA, and exploring varied mixture formulations using advanced design tools like Design Expert software, the goal of the study is to promote the development of sustainable construction methods. In general, it aims to enhance sustainability, cost efficiency, and performance of concrete through TPA incorporation.

2. MATERIALS AND METHODS

2.1. Materials

2.1.1. Cement

Grade 53 Ultra Tech cement sourced from Tamil Nadu’s open market complied with IS 12269 (2013) standards for composition and adherence. Table 1 presents the physical and chemical properties of Ordinary Portland Cement (OPC) and Tapioca Peel Ash (TPA).

Table 1
Physical and chemical properties of OPC, GGBS, alccofine, and metakaolin.

COMPONENT	CEMENT	TPA
Physical Properties
Specific gravity	3.10	2.3
Specific surface area (m2/kg)	340	290
CHEMICAL COMPOSITION
CaO	66.67	7.6
SiO2	18.91	58.2
Fe2O3	4.94	5.8
Al2O3	4.51	12.5
SO3	2.5	–
MgO	0.87	4.3
K2O	0.43	3.2
Na2O	0.12	1.1

2.1.2. Water

Water is crucial in concrete, impacting its mechanical, rheological, and durability characteristics. Potable water with a pH range of 6 to 7, meeting IS 3025 (1987) standards were utilized for laboratory testing.

2.1.3. Aggregates

The study utilized river sand from Tamilnadu, India, as the fine aggregate (FA), in accordance with IS 383 (2016) standards. The sand, which passed through a 4.75 mm sieve and conformed to Zone II specifications, was characterized by a specific gravity of 2.68 and a fineness modulus of 2.88. Crushed granite, well-graded and clean, was used as the coarse aggregate (CA), conforming to IS 383 (2016) standards. It had a maximum particle size of 20 mm and a specific gravity of 2.7.

2.1.4. Tapioca peel ash (TPA)

Tapioca peels (TP) were collected from the North Western Agroclimatic Zone of Tamil Nadu, India, where this crop is extensively cultivated. The peels underwent sun-drying followed by controlled incineration in a kiln at temperatures ranges from 500 to 850° for 60 min to ensure compliance with environmental regulations. The collected ash underwent gathering and sieving to a particle size of 150 µm for use in experiments. Figure 1 depicts images of TP waste and processed ash samples during the laboratory procedures.

Figure 1
Tapioca peel ash samples.

2.2. Experimental design using CCD

RSM is a collection of mathematical and statistical techniques that are useful for modeling and analyzing problems in which a response of interest is influenced by several variables. The primary objective of RSM is to optimize this response [²⁷]. In this study, RSM was employed to explore the relationships between the proportions of ingredients (such as cement, Tapioca Peel Ash (TPA), fine aggregate, and coarse aggregate) and the resulting compressive and flexural strengths of the concrete. By developing a predictive model, RSM enables a comprehensive understanding of the effects of multiple factors and their interactions on concrete properties, ultimately guiding the optimization process. CCD in RSM integrates factorial or fractional factorial designs incorporating central and star points to accommodate curvature. In CCD, factorial points are positioned at ±1 unit per factor from the center, while star points are determined by design specifications and the quantity of variables. Face Centered Central Composite Design (FCCD), a variant of Central Composite Design (CCD), was chosen for this study because it is particularly effective in handling non-linear responses with fewer experimental runs compared to a full factorial design. FCCD is advantageous in experiments where it is essential to estimate the curvature of the response surface. The method ensures that all factor levels (including extreme values) are considered, providing a robust dataset for accurate model fitting. The decision to use FCCD was also based on its efficiency in exploring the design space thoroughly while minimizing the number of experiments needed, which is critical in resource-intensive studies like concrete testing [²⁸]. Experiment design, mathematical modeling, statistical analysis, and response optimization were facilitated by Design Expert 13.0.5.0 Software. CCD typically involves 2n factorial and axial experiments, with experimental error evaluated through replicates at the center point (n_c). The total number of experimental runs (N) needed for CCD is calculated using Equation (1) [²⁴].

(1) $$\text{N}={\text{2}}^{\text{n}}{\text{+ n}}_{\text{c}}{\text{+ 2n = 2}}^{\text{4}}\text{+ 1 + 2 × 4 = 25}$$

In this research involving four variables, CCD employed 12 factorial points, eight axial points, and one center replication, totalling twenty-five experimental trials.

Parameters were varied across three levels: −1, 0, and 1 (Figure 2) [²⁹].

Figure 2
Illustration of (a) FCCD model to (b) Simplified model.

2.3. Formulation of component ratios in the mixture

In CCD, blend formulation involves selecting levels for study variables to determine experimental mixture compositions [³⁰]. This includes establishing ranges of variables, establishing design points, specifying levels, computing proportions, and formulating mixtures, systematically exploring variable interactions to understand their impact on responses [³¹, ³²]. Collected data are analyzed and optimized to find the best mixture composition. For this study, the concrete mix targeted a strength of 25 N/mm², with 290 kg/m³ of cement, 1198.65 kg/m³ of coarse aggregate, and 766.35 kg/m³ of fine aggregate, following relevant literature [³³, ³⁴]. A 0.5 water-cement ratio was used. Design Expert software facilitated the CCD mixture formulation, detailed in Tables 2 and 3, showing proportions of cement, Tapioca Peel Ash (TPA), and aggregates. Factor spaces and standard error plots are presented in Figures 3 and 4, illustrating the central, factorial, and axial sections of the CCD design. Out of the total 25 design points, sixteen were situated on the factorial plane, with eight points at the mixture components’ lower and upper limits [³⁵, ³⁶]. These visuals aid in interpreting the experimental setup and ­variable ranges studied.

Table 2
Information on mixture factors.

FACTORS	LOWEST	HIGHEST	LOWER CODED LIMIT	UPPER CODED LIMIT	MEAN	STD. DEV
OPC Cement	0.15	0.25	− 1 ↔ 0.15	+ 1 ↔ 0.25	0.2000	0.0433
TPA	0.025	0.15	− 1 ↔ 0.025	+ 1 ↔ 0.15	0.0875	0.0541
Fine aggregate	0.3	0.425	− 1 ↔ 0.30	+ 1 ↔ 0.425	0.3625	0.0541
Coarse aggregate	0.4	0.525	− 1 ↔ 0.40	+ 1 ↔ 0.525	0.4625	0.0541

Table 3
Development of experimental mixtures.

RUN NO	ACTUAL UNITS				CODED UNITS
	OPC	TPA	FA	CA	OPC	TPA	FA	CA
1	0.15	0.15	0.3	0.4	−1	1	−1	−1
2	0.15	0.15	0.3	0.525	−1	1	−1	1
3	0.25	0.025	0.3	0.525	1	−1	−1	1
4	0.25	0.15	0.425	0.4	1	1	1	−1
5	0.2	0.0875	0.3	0.4625	0	0	−1	0
6	0.15	0.15	0.425	0.4	−1	1	1	−1
7	0.2	0.0875	0.425	0.4625	0	0	1	0
8	0.15	0.0875	0.3625	0.4625	−1	0	0	0
9	0.25	0.0875	0.3625	0.4625	1	0	0	0
10	0.15	0.15	0.425	0.525	−1	1	1	1
11	0.2	0.0875	0.3625	0.4	0	0	0	−1
12	0.25	0.15	0.3	0.4	1	1	−1	−1
13	0.25	0.15	0.425	0.525	1	1	1	1
14	0.15	0.025	0.3	0.4	−1	−1	–1	−1
15	0.2	0.15	0.3625	0.4625	0	1	0	0
16	0.15	0.025	0.425	0.525	−1	−1	1	1
17	0.25	0.15	0.3	0.525	1	1	−1	1
18	0.2	0.0875	0.3625	0.525	0	0	0	1
19	0.25	0.025	0.425	0.4	1	−1	1	−1
20	0.25	0.025	0.425	0.525	1	−1	1	1
21	0.25	0.025	0.3	0.4	1	−1	−1	−1
22	0.2	0.0875	0.3625	0.4625	0	0	0	0
23	0.15	0.025	0.425	0.4	−1	−1	1	−1
24	0.15	0.025	0.3	0.525	−1	−1	−1	1
25	0.2	0.025	0.3625	0.4625	0	−1	0	0

Figure 3
Experimental factor range.

Figure 4
Standard error of cube design.

2.3.1. Compressive strength characteristic

The mixture’s components were precisely measured and blended thoroughly according to the designated formulation. The resulting homogeneous concrete mixture was compacted into cubic moulds measuring 150 mm on each side. These TPA concrete samples were cured in a distilled water tank for 28 days at room temperature. Following curing, the samples were assessed, and their compressive strength (CS) was evaluated by IS 516 (2021) standards. Compression tests were performed using a Compression Testing Machine (CTM) with a capacity of 2000 kN until the cubes failed under compression [³⁷, ³⁸], as shown in Figure 5.

Figure 5
Schematic of compression, and bending load test arrangements.

2.3.2. Flexural strength characteristic

Flexural strength (FS) testing will adhere to IS 516 (2021) standards, utilizing 500 × 100 × 100 mm specimens as shown in Figure 5. These will be precisely measured and mixed according to specified ratios. Following demoulding, the concrete beams will be cured for 28 days before flexural testing. Each experimental batch will yield three samples, tested for flexural strength, with averages calculated from the results. This protocol ensures thorough testing with three specimens per mixture ratio to determine the average flexural strength [³⁹].

3. RESULTS DISCUSSION AND ANALYSIS

3.1. Characterization of test materials

Laboratory testing assessed construction materials for civil engineering, including aggregates and admixtures, specific gravity tests, and sieve analysis for particle size distribution and gradation. Figure 6 illustrates the findings from the sieve analysis, displaying particle size variations using a cumulative frequency distribution curve. Coarse aggregates passed sieve sizes from 69% at 10 mm to 12% at 2 mm, while fine aggregates passed sizes from 97% at 2 mm to 0.15% at 75 µm [⁴⁰]. TPA admixtures in concrete passed sizes from 99.5% at 2 mm to 78% at 75 µm, meeting IS 2720 (1985) criteria for well-distributed sand and gravel particles, which improve the durability of concrete [³⁷, ³⁸].

Figure 6
Particle size distribution of test ingredients.

3.2. Chemical analysis of test cement and TPA

Chemical analysis via X-ray fluorescence (XRF) revealed TPA contains Fe₂O₃ (5.21%), Al₂O₃ (10.67%), and SiO₂ (56.74%), totalling 72.62%. This composition exceeds 70%, indicating favorable pozzolanic properties under IS 12269 (2013). The analysis of cement revealed compositions containing 60.9% CaO, 23.6% SiO₂, and 6.1% Al₂O₃, which are essential for cement hydration [³⁹]. This process enhances eco-friendly concrete’s mechanical strength and durability. Hydration involves the integration of aluminate and silicate oxides with hydrated calcium, thereby effectively increasing concrete strength [⁴⁰].

3.3. Impact of TPA additives on laboratory mechanical responses

The ingredient quantities were calculated using the ratio conversion technique to ensure accurate measurements in each experimental batch, maintaining a water-cement ratio (w/c) of 0.5. A standard concrete density of 2400 kg/m³ guided the conversion process, ensuring consistency in relationships between volume, density, and mass [⁴¹]. The mass of each cubic mould was calculated by multiplying its volume (m³) by the concrete density. In each experimental trial, three cubes and beam samples were fabricated, and the mean compressive strength results are outlined in Table 4. Figure 7 illustrates the interactions between cement and TPA and their impact on compressive and flexural strength responses. The contour plot shows that strength properties increase as TPA replaces cement from 0.025 to 0.875. Also, the contour plot analysis shows that replacing cement with Tapioca Peel Ash (TPA) up to a ratio of 0.12 has a positive effect on the strength properties of the concrete. The increase in TPA within this range enhances the pozzolanic reaction, leading to additional calcium silicate hydrate (C-S-H) formation, which contributes to improved strength. However, when the TPA ratio exceeds 0.12, the strength properties begin to decline. This is likely due to the excessive replacement of cement, which reduces the availability of primary hydration products necessary for strength development, resulting in a decrease in the overall binding capability of the mix. The peak compressive strength achieved was 27.08 MPa using a mixture ratio of 0.2:0.0875:0.3625:0.4625 for cement, TPA, FA, and CA. In contrast, the lowest compressive strength of 16.39 MPa was associated with a mixture ratio of 0.15:0.15:0.425:0.525. Including 19% cement, 2.4% TPA, 34.6% FA, and 44% CA significantly improved the compressive strength behaviour of the green concrete. Furthermore, the peak flexural strength of 9.84 MPa was attained using a mixture ratio of 0.2:0.0875:0.3625:0.525, whereas the lowermost flexural strength of 4.01 MPa was observed with a mixture ratio of 0.15:0.15:0.425:0.525. The optimal mix, comprising 17.02% cement, 7.45% TPA, 30.85% FA, and 44.68% CA, exhibited the highest flexural strength performance for TPA-concrete [⁴², ⁴³]. The flexural strength in our study generally aligns with the expectation that it is around 10 to 20% of the compressive strength. However, variations in mixture ratios, particularly with the inclusion of Tapioca Peel Ash (TPA), can influence the distribution of stress within the concrete matrix, potentially leading to different optimal ratios for compressive and flexural strengths. The slight difference in the ratios for peak strengths observed may be due to the specific interactions between TPA and other components in the mix, which might enhance or reduce certain properties differently. The observed correlation between compressive and flexural strengths across different mix ratios, noting that while they typically align with the expected relationship (i.e., flexural strength being 10 to 20% of compressive strength), certain ratios may cause deviations due to the unique characteristics of TPA and its interaction with other components. Overall, the mechanical strength characteristics of the concrete complied with IS 456 (2000) provisions, ascribed to the pozzolanic properties of aluminosilicate oxides present in TPA when united by Portland cement. This combination promoted the creation of calcium silicate hydrate, thereby improving the durability and mechanical properties of the concrete [⁴⁴, ⁴⁵]. From these results, we understood that the compressive strength of the concrete mixes was significantly influenced by the inclusion percentages of cement, Tapioca Peel Ash (TPA), fine aggregate (FA), and coarse aggregate (CA). Higher cement content increased compressive strength due to the formation of more calcium silicate hydrates (C-S-H). TPA, with its pozzolanic properties, contributed positively up to an optimal level, beyond which excess TPA led to a decline in strength. Properly graded FA enhanced packing density, reducing voids, while the optimal CA content provided necessary internal support, both of which were essential for achieving high compressive strength.

Table 4
Findings regarding compressive and flexural strength.

RUN NO	COMPRESSIVE STRENGTH (MPa)					FLEXURAL STRENGTH (MPa)
	OPC (kg)	TPA (kg)	FA (kg)	CA (kg)	CS (MPa)	OPC (kg)	TPA (kg)	FA (kg)	CA (kg)	FS (MPa)
1	3.65	3.65	7.29	9.72	19.82	4.32	4.32	8.64	11.52	5.18
2	3.24	3.24	6.48	11.34	19.65	3.84	3.84	7.68	13.44	5.12
3	5.52	0.55	6.63	11.6	24.62	6.55	0.65	7.85	13.75	8.47
4	4.96	2.98	8.43	7.93	18.16	5.88	3.53	9.99	9.4	4.51
5	4.63	2.03	6.94	10.7	25.70	5.49	2.4	8.23	12.69	8.10
6	3.24	3.24	9.18	8.64	17.99	3.84	3.84	10.88	10.24	4.26
7	4.14	1.81	8.79	9.56	21.68	4.9	2.14	10.42	11.34	5.85
8	3.43	2	8.29	10.58	18.59	4.07	2.37	9.83	12.54	4.59
9	5.23	1.83	7.58	9.67	23.87	6.19	2.17	8.98	11.46	6.62
10	2.92	2.92	8.26	10.21	16.39	3.46	3.46	9.79	12.1	4.01
11	4.63	2.03	8.39	9.26	25.50	5.49	2.4	9.94	10.97	8.67
12	5.52	3.31	6.63	8.84	25.78	6.55	3.93	7.85	10.47	6.99
13	4.5	2.7	7.65	9.45	22.02	5.33	3.2	9.07	11.2	5.96
14	4.17	0.69	8.33	11.11	25.11	4.94	0.82	9.87	13.17	7.99
15	4.14	3.1	7.5	9.56	18.50	4.9	3.68	8.89	11.34	4.64
16	3.24	0.54	9.18	11.34	20.18	3.84	0.64	10.88	13.44	5.59
17	4.96	2.98	5.95	10.41	22.69	5.88	3.53	7.05	12.34	6.25
18	4.14	1.81	7.5	10.86	25.23	4.9	2.14	8.89	12.87	9.84
19	5.52	0.55	9.39	8.84	20.67	6.55	0.65	11.13	10.47	5.55
20	4.96	0.5	8.43	10.41	24.39	5.88	0.59	9.99	12.34	6.94
21	6.23	0.62	7.48	9.97	24.71	7.38	0.74	8.86	11.82	8.56
22	4.37	1.91	7.92	10.1	27.08	5.18	2.27	9.38	11.97	8.82
23	3.65	0.61	10.33	9.72	19.09	4.32	0.72	12.24	11.52	4.81
24	3.65	0.61	7.29	12.76	19.21	4.32	0.72	8.64	15.12	4.85
25	4.63	0.58	8.39	10.7	22.13	5.49	0.69	9.94	12.69	6.00

Figure 7
Influence of the TPA and cement interaction (a) Compressive strength and (b) Flexure strength.

3.4. Creation and validation of the model

Data gathered through experimental procedures, including precise ingredient proportions and mechanical performance assessments of TPA-cement blended concrete, were employed to develop a model using RSM. The approach included square root transformation and polynomial analysis to address dataset non-linearity, ensuring accurate predictions [⁴⁶]. Statistical analyses, such as fit statistics and ANOVA, assessed dataset suitability for modelling. Key metrics included R-squared, PRESS for model fitness, tests for lack of fit and cumulative sums of squares to ascertain significant polynomial orders and terms (refer to Tables 5 and 6). Quadratic models were preferred, individually achieving R-squared values of 0.8613 and 0.9069 for compressive and flexural strength. The cumulative sums of squares analysis resulted in p-values of 0.0251 for compressive strength and 0.0012 for flexural strength [³⁷, ⁴⁷].

Table 5
Overview of compressive and flexural strength statistics.

SOURCE	STD. DEV.	R2	ADJUSTED R2	PREDICTED R2	PRESS	*	STD. DEV.	R2	ADJUSTED R2	PREDICTED R2	PRESS	*
	COMPRESSIVE STRENGTH STATISTICS						FLEXURAL STRENGTH STATISTICS
Linear	2.39	0.4970	0.3964	0.2684	166.71	Su	1.40	0.4226	0.3072	0.2070	54.02
2FI	2.51	0.6137	0.3377	–0.0878	247.88		1.55	0.5079	0.1564	–0.0800	73.57
Quadratic	1.78	0.8613	0.6670	0.2314	175.14	Su	0.7963	0.9069	0.7766	0.4948	34.41	Su

• *Su – Suggested

Table 6
Accumulated sum of squares (Type I) for compressive and flexural strength model.

SOURCE	SUM OF SQUARES	DF	MEAN SQUARE	F-VALUE	P-VALUE	*	SUM OF SQUARES	DF	MEAN SQUARE	F-VALUE	P-VALUE	*
	COMPRESSIVE STRENGTH MODEL						FLEXURAL STRENGTH MODEL
Mean vs Total	12045.50	1	12045.50				1000.71	1	1000.71
Linear vs Mean	113.26	4	28.32	4.94	0.0062	Su	28.79	4	7.20	3.66	0.0215
2FI vs Linear	26.58	6	4.43	0.7045	0.6513		5.81	6	0.9678	0.4042	0.8641
Quadratic vs 2FI	56.42	4	14.10	4.46	0.0251	Su	27.18	4	6.80	10.72	0.0012	Su
Residual	21.20	2	10.60				3.94	2	1.97
Total	12273.38	25	490.94				1068.83	25	42.75

• *Su - Suggested

3.5. Analysis of variance (ANOVA) result

After selecting an appropriate polynomial model through fit statistical analysis, ANOVA was conducted to evaluate the importance of independent variables in the combination model relative to response parameters [⁴⁸]. Table 7 presents the results for compressive strength, with a Model F-value of 4.43 indicating significance. The associated p-value of 0.0114 suggests a 1.14% likelihood that such an F-value could arise from random fluctuations. Similarly, Table 7 shows findings related to flexural strength, showing a Model F-value of 6.96, indicating significance. The corresponding p-value of 0.0020 suggests a 0.20% probability of such an F-value arising from random fluctuations [⁴⁹].

Table 7
ANOVA results for compressive and flexural strength (Quadratic Model).

SOURCE	SUM OF SQUARES	df	MEAN SQUARE	F-VALUE	P-VALUE	*	SUM OF SQUARES	df	MEAN SQUARE	F-VALUE	P-VALUE	*
COMPRESSIVE STRENGTH (QUADRATIC MODEL)							FLEXURAL STRENGTH (QUADRATIC MODEL)
Model	196.26	14	14.02	4.43	0.0114	Si	61.78	14	4.41	6.96	0.0020	Si
A-OPC	52.98	1	52.98	16.76	0.0022		10.05	1	10.05	15.85	0.0026
B-TPA	20.29	1	20.29	6.42	0.0297		7.79	1	7.79	12.28	0.0057
C-FA	39.66	1	39.66	12.55	0.0053		10.94	1	10.94	17.25	0.0020
D-CA	0.3335	1	0.3335	0.1055	0.7520		0.0145	1	0.0145	0.0228	0.8830
AB	1.0000	1	1.0000	0.3163	0.5862		0.0812	1	0.0812	0.1281	0.7279
AC	0.3660	1	0.3660	0.1158	0.7407		0.5041	1	0.5041	0.7950	0.3935
AD	7.54	1	7.54	2.38	0.1537		1.37	1	1.37	2.16	0.1725
BC	1.03	1	1.03	0.3259	0.5807		0.2970	1	0.2970	0.4684	0.5093
BD	0.0020	1	0.0020	0.0006	0.9803		0.1332	1	0.1332	0.2101	0.6565
CD	16.65	1	16.65	5.27	0.0447		3.42	1	3.42	5.40	0.0425
A2	11.00	1	11.00	3.48	0.0917		6.16	1	6.16	9.72	0.0109
B2	22.82	1	22.82	7.22	0.0228		8.63	1	8.63	13.61	0.0042
C2	0.3703	1	0.3703	0.1171	0.7393		0.0877	1	0.0877	0.1383	0.7177
D2	10.77	1	10.77	3.41	0.0947		11.17	1	11.17	17.62	0.0018
Residual	31.62	10	3.16				6.34	10	0.6341
Cor Total	227.88	24					68.12	24

• *Si - Significant

3.6. Coefficient estimates and equations obtained from the model

Regression analysis predicted each response according to the experimental plan and ANOVA in Design Expert software. Using CCD experimental data, mathematical prediction equations were formulated (Table 8), forecasting responses based on cement, TPA, FA, and CA proportions [⁵⁰].

Table 8
Equations derived from the quadratic model.

	INTERCEPT	A	B	C	D	AB	AC	AD	BC	BD	CD	A2	B2	C2	D2
Sqrt (CS)	23.85	1.72	–1.06	–1.48	–0.14	0.25	–0.15	0.686	–0.25	0.011	1.02	–2.08	–2.99	0.381	2.06
p-values		0.002	0.030	0.005	0.75	0.586	0.741	0.154	0.581	0.980	0.045	0.092	0.023	0.739	0.095
Sqrt (FS)	7.40	0.75	–0.66	–0.78	0.028	–0.07	–0.18	0.293	0.136	0.091	0.463	–1.56	–1.84	–0.19	2.09
p-values		0.003	0.006	0.002	0.883	0.728	0.394	0.173	0.509	0.656	0.043	0.011	0.004	0.718	0.002

3.7. Diagnostics plots

The graphs from diagnostic statistical analysis, shown as scatter plots depicting residuals or model prediction errors plotted against their corresponding predicted values, are crucial for improving estimation accuracy. These plots evaluate the model’s goodness-of-fit employing studentized residuals, ensuring adherence to regression assumptions and recognizing powerful remarks that could substantially influence analysis outcomes [⁵¹, ⁵²]. Unlike raw residuals, which vary due to diverse populations unless experimental runs are identical in design, studentized residuals standardize all normal distributions to a unit scale, aiding in evaluating response variables across various plots (Figures 8 to 11). These diagnostic plots establish benchmarks for choosing suitable power transformations, such as Box-Cox, to assess the impact on response variables with a λ value of 0.5. Figures 12 to 14 demonstrate how TPA interacts with concrete ingredients, influencing compressive and flexural strength responses. These findings highlight significant improvements in concrete mechanical properties, with optimal outcomes observed at 11.21% TPA as a cement replacement in the mixture [⁵³, ⁵⁴].

Figure 8
Normal probability plots of residuals for target responses (a) Compressive strength and (b) Flexure strength.

Figure 9
Plots of residuals versus predicted values (a) Compressive strength and (b) Flexure strength.

Figure 10
Plots of residuals versus experimental runs (a) Compressive strength and (b) Flexure strength.

Figure 11
Box-cox transformation plots (a) Compressive strength and (b) Flexure strength.

Figure 12
Surface plots comparing OPC with TPA (a) Compressive strength and (b) Flexure strength.

Figure 13
Surface plots comparing fine aggregate with TPA (a) Compressive strength and (b) Flexure strength.

Figure 14
Surface plots comparing coarse aggregate with TPA (a) Compressive strength and (b) Flexure strength.

3.8. Optimization analysis

After conducting diagnostic statistical analysis and graphical calculations, optimization through numerical methods is employed. A desirability function maximises desired response parameters by adjusting model variables and objective function characteristics through weighted function modifications according to predefined criteria [⁵⁵]. These adjustments address multicollinearity issues to achieve a perfect desirability score of 1.0 within the constraints where 0 ≤ d(y_i) ≤ 1. Optimization seeks optimal mixture ratios within feasible factor spaces, achieving desired response parameters and level standards [⁵⁶, ⁵⁷, ⁵⁸, ⁵⁹]. Prioritizing the maximization of target responses, the proportions of the four components are adjusted within practical ranges to identify proportions yielding maximum responses, detailed in Table 9. Analytical procedures from experimental designs result in an optimized solution, illustrated in Table 10 and Figure 15, achieving a perfect desirability score of 1.0 with a ratio of 0.222:0.083:0.306:0.406. This optimization delivers a peak compressive strength of 29.832 MPa and a flexural strength of 10.948 MPa [⁶⁰].

Table 9
Criteria for optimizing model parameters.

NAME	TARGET	MINIMUM THRESHOLD	MAXIMUM THRESHOLD	LIGHTEST WEIGHT	HIGHEST WEIGHT
A: OPC	Is within the range	0.15	0.25	1	1
B: TPA	Is within the range	0.025	0.15	1	1
C: FA	Is within the range	0.30	0.425	1	1
D: CA	Is within the range	0.40	0.525	1	1
CS	Maximize	16.39	27.08	1	1
FS	Maximize	4.01	9.84	1	1

Table 10
Ideal approaches for optimization.

S.No	OPC	TPA	FA	CA	CS	FS	DESIRABILITY
1	0.223	0.088	0.300	0.404	28.732	10.224	1.000
2	0.234	0.082	0.316	0.401	27.881	9.945	1.000
3	0.208	0.067	0.318	0.406	27.630	9.957	1.000
4	0.218	0.075	0.300	0.523	27.179	9.842	1.000
5	0.221	0.075	0.309	0.524	27.102	9.882	1.000
6	0.213	0.069	0.324	0.406	27.453	9.897	1.000
7	0.212	0.075	0.301	0.524	27.080	9.883	1.000
8	0.203	0.043	0.310	0.403	27.365	9.899	1.000
9	0.213	0.085	0.300	0.524	27.131	9.843	1.000
10	0.224	0.068	0.305	0.524	27.137	9.858	1.000

Figure 15
Optimization ramps.

3.9. Contour plot for optimization

The plot depicting contours is essential for visually representing the practical experimental area during the iterative optimization of mixture designs. It utilizes 3D surfaces depicted through contour lines [⁶¹], illustrating relationships between component proportions and response parameters [⁶², ⁶³]. The 3D plots show optimal solutions based on the desirability function, with corresponding response surfaces in Figure 16. These graphs demonstrate how the preference function varies across ideal solutions tailored for multi-response optimization. Notably, the green surface indicates lower desirability, observed at TPA fractions of 0.025–0.05 and 0.15–0.125, while the red surface represents higher desirability, ranging from 0.075 to 0.12 TPA fraction [⁶⁴, ⁶⁵].

Figure 16
Three-dimensional surface plot depicting optimization solutions.

3.10. Model testing and verification

This phase serves as the final validation of the quadratic model, providing practical guidance for designers, contractors, and operators concerning its performance [⁶⁶, ⁶⁷]. The model simulation ensures that statistical analysis and inferential calculations validate its application in real-world scenarios. A Student’s t-test was used to assess the statistical significance of simulated and actual values [⁶⁶]. In this study, it was employed to compare the predicted values (from the quadratic model) with the actual experimental values of compressive and flexural strengths. Figure 17 depicts a graphical comparison of experimental and simulated responses, while Table 11 shows computed results using Microsoft Excel. The calculated p-values (T ≤ t) of 0.9986 and 0.9969 for compressive strength and flexural strength suggest that there is no notable distinction between the observed and projected outcomes, affirming the model’s validity [⁶⁸, ⁶⁹]. The high p-values confirm that the quadratic model used in this study effectively predicts the concrete’s mechanical performance. Since there is no significant difference between the predicted and observed values, the model is deemed reliable for practical applications in optimizing concrete mix designs. These p-values support the conclusion that there is no notable distinction between the observed and projected outcomes, affirming the model’s validity and its applicability in predicting the mechanical performance of the concrete mixes. This reinforces the reliability of the CCD approach in optimizing concrete mix designs and demonstrates its effectiveness in practical applications.

Figure 17
Differences between observed and predicted values.

Table 11
T-Test: comparison of paired sample mean.

	COMPRESSIVE STRENGTH		FLEXURAL STRENGTH
	ACTUAL	PREDICTED	ACTUAL	PREDICTED
Mean	21.9504	21.95	6.3268	6.3264
Variance	9.494829	8.174858333	2.838239	2.574841
Findings	25	25	25	25
Pearson correlation	0.928133196	–	0.952551	–
df	0	–	0	–
t Stat	24	–	24	–
P (T < = t) one-tail	0.001743627	–	0.0039	–
t Critical one-tail	0.4993116	–	0.49846	–
P (T < = t) two-tail	1.71088208	–	1.710882	–
t Critical two-tail	0.9986232	–	0.99692	–

4. CONCLUSION

The study intended to improve concrete mechanical properties by optimizing formulation with Tapioca Peel Ash (TPA) using a mixture design approach, adjusting cement, TPA, fine aggregate, and coarse aggregate contents.

• The study optimizes a four-component mixture to assess the mechanical strength of eco-friendly concrete, setting component ratios within established limits for optimal strength.

• Chemical analysis verified TPA as a suitable SCM, with significant amounts of Fe₂O₃ (5.21%), Al₂O₃ (10.67%), and SiO₂ (56.74%), totalling 72.62%. These findings underscore TPA’s potential as an active SCM in concrete because of its pozzolanic properties.

• The study demonstrated that the optimized concrete mix incorporating Tapioca Peel Ash (TPA) achieved an ultimate compressive strength of 27.08 MPa. The highest compressive strength was obtained with a mixture ratio of 0.223:0.088:0.300:0.404 for cement, TPA, FA, and CA, respectively. Similarly, the optimized mix produced a peak flexural strength of 10.22 MPa, highlighting the positive impact of TPA on the concrete’s flexural performance. The results indicate that as TPA replaced cement in the mix, flexural strength increased up to a certain point (0.12 TPA ratio), beyond which it started to decline. The highest flexural strength was associated with a specific mixture ratio, further validating the effectiveness of TPA in improving the mechanical properties of the concrete. The study exploited an FCCD to achieve an ultimate compressive strength of 27.08 MPa and a flexural strength of 9.84 MPa. A quadratic model was created and refined through numerical optimization, achieving a desirability rating of 1.0 with a mixture ratio of 0.223:0.088:0.300:0.404. This enhancement resulted in strengths of 28.73 MPa and 10.22 MPa, respectively.

• The study found that the compressive strength properties of the concrete were significantly influenced by the binder ratio. As TPA content increased in the mixture, compressive strength initially improved, peaking at a TPA ratio of 0.12. Beyond this point, further increases in TPA content led to a reduction in compressive strength. This suggests an optimal binder ratio range where the benefits of TPA are maximized. The flexural strength also exhibited a similar trend, with the strength increasing as TPA replaced cement up to a certain ratio. The highest flexural strength was achieved with a mix containing 17.02% cement and 7.45% TPA. The study indicates that careful adjustment of binder ratios is crucial in optimizing the flexural performance of TPA-concrete.

• Testing showed a significant connection between laboratory and pretend values using a student’s t-test, indicating CCD’s success in optimizing concrete mixes for desired properties and improving mechanical performance in sustainable concrete.

4.1. Suggestions for future research

• Forthcoming studies could investigate the influence of factors such as curing techniques, water-cement ratio, and Tapioca Peel Ash (TPA) particle size on concrete strength and durability.

• Future research should evaluate how TPA-blended concrete withstands environmental stresses using accelerated ageing and field exposure to predict long-term performance.

• Further research should analyze the eco-friendly effect of incorporating TPA in concrete through the life cycle and carbon footprint evaluations to measure its advantages over traditional concrete.

• Future research should investigate innovative statistical techniques, such as Artificial Intelligence Algorithms (AIA), to optimize TPA concrete mixes for enhanced mechanical properties, minimized material consumption, and cost-effectiveness.

• Implementing TPA concrete in construction projects and systematically monitoring its performance would offer valuable insights into its behaviour under real-world conditions. Long-term monitoring would assess structural integrity, durability, and sustainability.

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Publication Dates

• Publication in this collection
  04 Oct 2024
• Date of issue
  2024

History

• Received
  08 July 2024
• Accepted
  30 Aug 2024