Optimizing Durability of Concrete Made with Calcium Carbide Waste and Lateritic Soil Using Response Surface Methodology

Abstract

This study optimizes the durability performance of concrete by utilizing lateritic soil (LS) and calcium carbide waste (CCW) as partial replacements for fine aggregate and cement, respectively. A statistical method was employed to design the experiments and develop prediction models for key characteristics, including density, water absorption, and resistance to sulphuric acid attack (as measured by weight loss and compressive strength), using Response Surface Methodology (RSM). A central composite design (CCD) was employed to investigate the effects of CCW (0–20%) and lateritic soil (0–40%) on the properties of concrete. According to the results, higher CCW and laterite replacement levels reduce the durability of concrete by increasing its porosity and water absorption. Significant correlations were found in the responses that were successfully predicted by RSM-generated quadratic models. The ideal combination of 13.13% CCW and 18.7% LS was identified through multi-objective optimization, which maximized acid resistance while minimizing weight loss (8.84%) and water absorption (4.17%), resulting in an overall desirability of 75.4%. The experimental validation of this result revealed that the discrepancy between the predicted and experimental results was less than 5%. This indicates the potential of CCW-LS concrete for affordable, environmentally friendly construction in areas with limited resources.

1. Introduction

As a material used in many construction projects, concrete is undergoing various changes and modifications to meet the increasing demands associated with modern building techniques, which enhance the durability, sustainability, and performance of developed infrastructures [1]. Among these innovations is laterized concrete: a composite material that combines the unique qualities of locally accessible laterite soil with the strength of conventional concrete [2]. In addition to utilizing the natural benefits of laterite-rich areas and providing a sustainable building method, this combination offers an opportunity to address resource constraints and environmental issues while reinventing the structural uses of concrete. The core of this invention is the aggregate mix, a fundamental element that has a significant impact on the mechanical and durability properties of the concrete matrix. Concrete is a fundamental building material widely used in the construction industry due to its strength, durability, and adaptability [3]. However, large quantities of aggregates, mostly sand, gravel, and crushed stone, are required to produce concrete. These resources are insufficient, and overuse can deplete them, leading to scarcity and worsening environmental effects [4,5]. Furthermore, it may lead to local ecological disruption, water contamination, and soil erosion. The strength, workability, and general performance of concrete are influenced by aggregates, which include crushed stone, gravel, sand, and other granular elements [5,6,7].

Numerous scholars have explored the use of laterite as a partial substitute for sand, as it is widely available around the world [8,9,10]. Ettu et al. [11] investigated the feasibility of making concrete with laterite as the sole fine aggregate. It was found that a sizable range of mix compositions could produce laterized concrete that satisfied the minimum compressive strength specification for reinforced concrete. A study by Udoeyo et al. [12] examined certain properties of concrete that substitute laterite for sand aggregate, either entirely or partially. According to their findings, concrete can attain a design strength of 20 N/mm² if up to 40% of the sand is replaced with laterite. They concluded that up to 40% of the sand in concrete might be replaced with laterite. Ukpata et al. [5] examined the impact of varying aggregate sizes on the strength of concrete that used laterite as a substitute for fine aggregate. Their study revealed that using laterite instead of fine aggregate had an impact on the mechanical properties of concrete. It remained appropriate for construction even though its strength declined as the quantity of laterite increased. The necessary strength of 25 N/mm² was exceeded by 0% and 10% of laterite, although it decreased by 25%. High-strength concrete (HSC) samples of M60 grade were constructed by Raja et al. [13] by replacing manufactured sand with laterite in weight percentages of 25%, 50%, 75%, and 100%. This was done to produce suitable mixes for conducting microstructural investigations and analyzing their mechanical characteristics. The mixes also contained 10% fly ash (FA) and 10% micro silica. The study revealed that a 25% laterite substitution produced the best combination. Additionally, it was observed that the bending performance of laterite-made beams was 11.3% better than that of reference specimens.

The primary ingredient in concrete preparations is ordinary Portland cement, also known as OPC. Regrettably, there are several shortcomings associated with OPC manufacture. Essentially, a significant quantity of carbon dioxide is released into the atmosphere during the manufacturing process. This is equivalent to around 8% of all carbon dioxide released from human activity, according to quantitative calculations [14]. Second, the entire process is energy-demanding because clinker, the primary ingredient in the binder, must be made by calcining raw materials, including limestone, clay, and chalk, at a high temperature (~1500 °C). Calcium carbide waste is one of the alternative cementitious materials that has garnered considerable attention in recent years [15,16]. The waste product known as CCW is produced when calcium carbide is hydrolyzed [14]. Due to its high calcium hydroxide concentration (>80% by weight), the CCW is extremely alkaline. Due to the health risks associated with disposing of this trash in open landfills, its valorization would align with the goals of environmental sustainability. Calcium silicate hydrate (C-S-H), which resembles the hydration products of Portland cement, was recently produced by combining calcium carbide waste with rice husk ash as a novel cementitious material [17]. Hanjitsuwan et al. [18] described how sodium hydroxide and sodium silicate were used as activators to partially substitute fly ash-based geopolymer with CCW. The sulphate resistance was shown to be enhanced by the addition of CCW. Obeng et al. [15] examined the viability of incorporating calcium carbide residue (CCR) into geopolymer mortars based on metakaolin in relation to their resistance to sulphates. The incorporation of CCR enhanced compressive strength by 26.12% compared to the geopolymer without CCR, as indicated by the data. The CCR-containing geopolymer material demonstrated less resistance to sulphates than those without CCR. Even so, it was still more durable than mortar made by OPC, which lost around 3.2% of its strength after being exposed to sulphate. The addition of CCR to metakaolin-based geopolymer can lead to high compressive strength and enhanced sulphate resistance, according to the OPC findings. A combination of calcium carbide residue and bagasse ash (BA) has been evaluated by Rattanashotinunt et al. [19] as a novel cementitious material for concrete. According to the findings, using ground CCR and ground BA mixes as a binder may reduce the amount of Portland cement used by up to 70% compared to conventional concrete, which requires 300 kg/m³ of Portland cement to achieve the same compressive strength. Compressive strength, splitting tensile strength, and elastic modulus were among the mechanical characteristics of the substitute concrete that were comparable to those of ordinary cement concrete. In their alkali-activated fly ash sustainable material, Phoo-ngernkham et al. [20] also substituted CCW for fly ash at 0%, 10%, 20%, and 30% levels using sodium hydroxide and sodium silicate as activators. They found that as the CCW content increased, the mortar’s setting time decreased while its compressive and shear bond strengths increased. Additionally, CCW densified the mortar’s microstructure and increased the highest concentrations of calcium hydroxide and calcium silicate hydrates, resulting in improved strength.

The Response Surface Methodology (RSM) is a statistical technique used to develop models, assess the relationships between causes and their effects, and determine optimal experimental settings [21,22]. In RSM, tests are planned, experimental findings are gathered as responses, and numerical surface response models are generated to confirm the models’ validity and optimize the variables to provide the anticipated outcomes [23,24]. RSM offers several optimization benefits over the laborious one-element-at-a-time approach that disregards component interactions [25]. RSM was utilized for modelling and multi-objective optimization in various concrete materials [26,27,28]. To maximize the compressive strength of geopolymer mortar, Mermerdas et al. [23] conducted an optimization research using RSM to determine the ideal ratio of binder material, cooling temperature, and curing time. RSM was also utilized by Mohammed et al. [29] to provide a framework for the mix design of engineered cementitious composite mixes, after which their characteristics were numerically optimized. An RSM/CCD model was established by Haruna et al. [27] to maximize the impact resistance of fibre-reinforced concrete altered using nano-materials. In their multi-objective optimization of foamed concrete, Asadzadeh and Khoshbayan [30] used foam, cement, and water as independent variables and cost, compressive strength, and dry density as responses. The properties of concrete that incorporated glass fibre and rice husk ash were evaluated and optimized by Haque et al. [31]. RSM was also used to investigate the effects of NaOH concentration and solution-to-binder ratio on the behaviour of geopolymer mortars [32]. Each model exhibits quadratic connections at high correlation levels, as indicated by their RSM analysis, which shows a good correlation between the validated models and the relevant experimental results. Likewise, the RSM approach was used by Zahid et al. [33] to optimize the alkali-activated composite. According to their analysis, the RSM optimization technique guarantees system and product stability, enhances reliability, and reduces design time while increasing process and product efficiency.

Although the mechanical properties of laterized concrete at various replacement levels have been studied, a significant research gap remains in addressing the dual replacement of lateritic soil and calcium carbide waste in concrete. Previous research has primarily focused on each of them separately, paying little attention to how they interact to influence durability. Moreover, although the response surface methodology has been employed in other cementitious systems, it has not been widely applied in lateritic soil-based concretes, particularly when combined with CCW. To fill this gap, the current work uses RSM to optimize the durability performance of eco-friendly concrete that uses LS as a partial fine aggregate replacement and CCW as a partial cement replacement. This approach highlights the methodological contribution as well as the novelty of the material system, intending to provide affordable and sustainable solutions for areas where these materials are readily available.

2. Materials and Methods

2.1. Materials

The primary binder material was ordinary Portland cement, which met ASTM C150 [34] standard requirements and had the properties presented in

Table 1. Chemical composition of cement and CCW materials.

	Chemical Composition (%)
Oxides	SiO2	Al2O3	Fe2O3	CaO	MgO	K2O	Na2O	SrO	Nb2O5	SO2	TiO2	BaO	Sb2O3	LI
Cement	20.76	5.54	3.35	61.4	2.46	0.76	0.19	-	-	-	-	-	-	2.24
CCW	3.76	1.46	0.12	91.25	1.25	-	-	0.56	0.11	0.75	0.04	0.40	0.30	-

. Calcium carbide waste was utilized as a partial cement replacement. The source of the CCW was a professional mechanical welding facility. To achieve the required particle size retention, the CCW sample was pounded into fine particles and sieved through a 75 µm sieve after being heated to a high temperature (110 °C) to eliminate any remaining moisture. Its specific gravity is 2.34, which is lower. The chemical composition of the CCW, as revealed by the XRF study, is presented in Table 1. These results are nearly identical to those of Latifi et al. [35] and Adamu et al. [36] for CCW. This demonstrates the high concentration of CaO in the CCW, followed by SiO₂, Al₂O₃, and MgO. The laterite was collected from a borrow pit at Janguza, which is situated along Gwarzo Road in Northern Nigeria. An overview of the test results for the index properties of the lateritic soil utilized in this study is given in

Table 2. Index properties of lateritic soil.

Property	Quantity
Liquid Limit (%)	40.91
Plastic Limit (%)	30.67
Plasticity Index (%)	10.23
Natural Moisture Content (%)	11.52
USCS Classification	CL
Group Name	Lean clay

. The table makes clear that the laterite soil employed in this study has a homogeneous grade with a plasticity index (PI) of 10.23%, a Cu of 9.48 (i.e., Cu < 40), and limits for liquids and plastics of 40.91% and 30.67%. The LS has a natural moisture content of 11.52% and a specific gravity of 2.54. Figure 1 shows the gradation curve for the particle size distribution of Lateritic soil, fine aggregate, and coarse aggregates, which were achieved per BS 882 [37].

2.2. Mix Proportion and Specimen Preparation

To produce the control samples of concrete, the final mix percentage of the constituent materials is shown in

Table 3. Proportion of CCW–laterite concrete mixes (in kg per cubic metre of mix).

Mix	CCW (Kg/m3)	Laterite Soil (Kg/m3)	Cement (Kg/m3)	Fine Agg. (Kg/m3)	Coarse Agg. (Kg/m3)	Water (Kg/m3)
M1(5C10L)	17.25	47	327.75	423	1495	190
M2(15C10L)	51.75	47	293.25	423	1495	190
M3(5C30L)	17.25	141	327.75	329	1495	190
M4(15C30L)	51.75	141	293.25	329	1495	190
M5(0C20L)	0	94	345.00	376	1495	190
M6(20C20L)	69	94	276.00	376	1495	190
M7(10C0L)	34.5	0	310.50	470	1495	190
M8(10C40L)	34.5	188	310.50	282	1495	190
M9(10C20L)	34.5	94	310.50	376	1495	190
M10(10C20L)	34.5	94	310.50	376	1495	190
M11(10C20L)	34.5	94	310.50	376	1495	190
M12(10C20L)	34.5	94	310.50	376	1495	190
M13(10C20L)	34.5	94	310.50	376	1495	190
M14(0C0L)	0	0	345.00	470	1495	190

. The correct proportions of constituent materials must be determined when building a concrete mix to achieve the required workability and strength. The proportioning was performed per the BS 1881, P 125 [38] design requirements, and a w/c ratio of 0.55 was used for the LS-CCW concrete mixes in the current investigation. The CCW additions were adjusted to 0%, 5%, 10%, 15%, and 20% by weight of binder material, while the replacement of fine sand content for LS is 0%, 10%, 20%, 30%, and 40%. The batches were carefully blended on a laboratory mixing tray using a hand trowel. After three minutes of thorough mixing, a dry cement and CCW mixture was combined with the fine aggregate mixture, including the laterite soil and coarse aggregate. Water was added as needed while the mixing was still in progress. Before casting the specimens, the moulds were cleaned and greased with oil. Each of the three layers of laterite concrete samples was cast and compacted by hand, with the mould gently shaken after being tamped with 25 blows from the tamping rod. The next day, the samples were removed from the moulds and allowed to be cured in water for twenty-eight (28) days in the laboratory before undergoing the water absorption test and exposure to an acidic medium. A schematic illustration of CCW-LS concrete preparation is portrayed in Figure 2.

2.3. RSM-Based Model Development

The impacts of LS and CCW on the durability performance of concrete were assessed, and the correlations between these variables and their output responses were identified using response surface methodology. The best combinations were determined by mathematical optimization, which minimized the CCW-based laterized concrete’s density, weight loss, and water absorption. The two design methodologies most often employed in civil engineering are central composite design (CCD) and Box–Behnken design (BBD) [39,40]. The RSM models can be either linear trends or higher-degree polynomials. The linear model’s first-order equation is given by Equation (1), whereas the polynomial models are shown by Equation (2).

$$y={\beta }_0+{\beta }_1{\chi }_1+{\beta }_2{\chi }_2+\dots +{\beta }_k{\chi }_k+\epsilon$$

(1)

$$y={\beta }_0+{\sum }_{j=1}^k{\beta }_j{\chi }_j+{\sum }_{j=1}^k{\beta }_{jj}{\chi }_j^2+{\sum }_{i<}{\sum }_{j=2}^k{\beta }_{ij}{\chi }_i{\chi }_j+\epsilon$$

(2)

where y represents the response models; ${\chi }_i$ and ${\chi }_j$ are the coded values of the input variables; β_i and β_j are the linear and quadratic coefficients; β_o is the y-axis intercept; and ε is the error in the developed model [41,42]. Variance analysis was used to establish the variables’ significance level, using a p-value threshold of 0.05. Significant influence on the model responses was defined as a p-value of less than 0.05, and insignificant influence was described as a p-value of higher than 0.05. These terms denote the important and interrelated variables [23,39,43]. The prediction models only contained important terms, excluding those required to preserve the order of the model. The error term (ε) in the regression model accounts for the variability in the observed responses that cannot be accounted for by the independent variables or their interactions. This covers experimental errors brought on by inconsistent materials, measuring constraints, and uncontrollable environmental influences. According to typical RSM assumptions, the error term was assumed to be independent and normally distributed, with a mean of zero and constant variance.

In this study, Design Expert version 13 was used to conduct RSM analysis. A central composite design with α varying from −1.41 to 1.41 was employed to develop a statistical model of concrete modified with LS and CCW, with CCW and LS serving as independent variables. Each variable is represented by one of five (5) levels: 0% to 20% CCW in place of cement. Similarly, laterite soils have fine aggregate material replaced at percentages of 0%, 10%, 20%, 30%, and 40%, respectively.

Table 4. Mix proportions of independent variables determined by the RSM.

Variables	Coded	Unit	Coded Variable Levels
			−1.41421	−1	0	1	1.41421
CCW	A	%	0	5	10	15	20
LS	B	%	0	10	20	30	40

provides a summary of the mixed proportions of independent variables determined by the RSM program using different combinations of parameters. The thirteen (13) mixtures contain five (5) centre points and eight (8) axial points. Repeated mix combinations serve as the focal points. The repeated mixes, often referred to as duplicated design points, are used to assess how well the model fits the data. The residual error is compared to the “Pure Error” resulting from duplicate design points in the “Lack of Fit Tests” chart. A low probability value (“Prob > F”) indicates a significant lack of fitness, meaning the model shouldn’t be used as a response predictor.

2.4. Tests on Hardened CCW-LS Concrete

The standard parameters listed in the BS EN 12390-3 [44]. The guidelines were applied to determine the compressive strength of the concrete specimens. To assess the compressive strength of CCW-LS concrete, concrete cubes measuring 100 mm × 100 mm × 100 mm in size were used. Nine (9) specimens were made for each combination, three (3) for each testing day, and tested following immersion in a solution of 5% sulphuric acid. After being submerged for seven to twenty-eight days, three (3) laterized concrete cubes were taken out of the acid medium concentrations, carefully cleaned with tap water, and allowed to air-dry in the lab for a few hours before their compressive strengths were measured.

The water absorption test was conducted using concrete cube samples measuring 100 × 100 × 100 mm in size, in accordance with ASTM C642 [45]. The tests were conducted following seven (7) and twenty-eight (28) days of curing. The testing involved drying the laterized concrete samples for at least 24 h at 110 °C in an oven. Following their removal from the oven, the samples were allowed to cool gradually for a few hours, reaching an ambient temperature of around 20 to 25 °C, before being weighed. After that, the samples were submerged in water for a minimum of 48 h. The samples were then surface dried using paper towels to eliminate any remaining surface moisture before being weighed again. The water absorption capacity of the samples was determined using Equation (3):

$$Water absorption \left(\mathrm{\%}\right)={\displaystyle \frac{M_B-M_A}{M_A}}$$

(3)

where M_A is the mass of the sample that was oven-dried, and M_B is the mass of the sample that was surface-dried following immersion. Each sample’s water absorption was computed, and the average was then determined for every mixture.

3. Experimental Results and Discussions

3.1. Density

Figure 3 portrays the density results of concrete mixes incorporating varying proportions of CCW and LS before and after exposure to an acidic environment for 7 and 28 days. A general decrease in density was noted for all combinations following exposure in the acidic solution, with greater losses noted at 28 days as opposed to 7 days. All of the mixes had densities between around 2400 and 2650 kg/m³ before immersion, which is within the usual range for normal-weight concrete [46]. The LS and CCW content both had an impact on the initial density. Because CCW has a lower specific gravity than Portland cement and may introduce more air voids after mixing, mixes with increased CCW concentrations seemed to have somewhat lower starting densities [47]. The initial density was also somewhat decreased by increasing the LS content, most likely because of the lateritic soil’s increased porosity and lower particle density in comparison to conventional river sand. All combinations showed a discernible decrease in density following seven days of immersion in acid. This is triggered mainly by the gradual breakdown of calcium silicate hydrates (C–S–H) under acid assault and the leaching of calcium hydroxide (Ca(OH)₂), which leads to the loss of solid mass and the formation of microvoids [48]. Higher CCW replacement mixes (15–20%) exhibited somewhat higher density losses, indicating a decreased acid resistance. This might be because a less dense C–S–H gel formed and more unreacted Ca(OH)₂ was present, which is extremely vulnerable to acid dissolution [49]. The deterioration tendency is further shown by the 28-day immersion findings, which show increasing density losses. The cementitious matrix can dissolve, and hydration products can also dissolve, allowing for deeper acid penetration due to the prolonged exposure time. However, other blends showed somewhat smaller density losses, suggesting a potential synergistic impact, with modest degrees of CCW and LS replacement (e.g., Mix 6 with 20% LS and 10% CCW). As also noted in mixed cement systems with pozzolanic materials, the finer LS particles may have partially filled gaps, boosting packing density and providing some resistance to acid intrusion [50]. Ultimately, the findings demonstrate that concrete’s physical integrity is greatly impacted by acid exposure, with gradual density losses occurring with extended immersion. High replacement levels often result in lower acid resistance because of increased matrix porosity and worse-quality hydration products. The amount of CCW and LS also affects the degree of decrease.

3.2. Durability Performance

In this investigation, sulphuric acid was selected as the primary aggressive medium, as acid attack is one of the most severe and common types of chemical degradation in concrete, particularly in acidic soils, industrial effluent zones, and sewer infrastructure. A reliable accelerated test for chemical resistance is produced when sulphuric acid aggressively interacts with calcium hydroxide, decalcifying calcium silicate hydrate (C–S–H) and forming gypsum and ettringite. The selection of water absorption as an indirect durability measure was based on its significant correlation with permeability, which regulates the ingress of harmful substances. Nonetheless, it is well understood that actual service environments frequently incorporate a variety of degradation processes, including carbonation, freeze–thaw cycles, and chloride infiltration. These were outside the current scope of our study; however, to offer a more thorough performance evaluation, it is recommended that future research examine CCW–LS concretes under combined durability exposures.

3.2.1. Resistance to Sulphuric Acid (H₂SO₄) Media

The findings of measuring the impact of acid attack on laterized concrete mixtures, as shown in Figure 4 below, are presented. The laterized concrete samples exhibited weight loss ranging from 5.05% to 16.2% at both 7 and 28 days following immersion in an acidic environment, while the control sample had a maximum weight decrease of 11.92%. It is clear from the results that the cementitious material-containing concrete samples were less resistant to acid attack than the control concrete samples. All samples lost between 7.13% and 16.2% of their weight after 28 days in acid, relative to the control sample. Since CCW particles are smaller, they fill up all the holes in laterized concrete, lessening the impact of acid attack. The cement component of concrete reacts with sulfuric acid to transform calcium hydroxide into calcium sulphate (gypsum), which can be converted into calcium sulfoaluminate (ettringite). Weight is dependent on both volume and density; hence, the development of calcium sulphate causes the concrete to soften (a reduction in density).

Figure 5 shows the compressive strength of concrete mixes with different ratios of CCW and LS, both before and after they are submerged in an acidic medium. Exposure to the acidic environment gradually decreased the compressive strength of all combinations, with the largest losses occurring after 28 days. This deterioration is consistent with the known mechanisms of acid attack in cementitious materials, in which acids decalcify calcium silicate hydrates (C–S–H) and react with calcium hydroxide (Ca(OH)₂), resulting in leaching, gypsum formation, and ultimately microstructural disintegration [46,51]. The control mix (Mix 14: 0CC0L) had a high compressive strength (~20 N/mm²) before acid immersion, whereas Mix 6 (20C20L) had the highest value (~23 N/mm²). Strength was often increased by moderate CCW inclusion (5–20%) and low LS content (≤20%) because of the filler effect and pozzolanic reaction of CCW, which refines the pore structure and aids in the production of secondary C–S–H [52,53]. On the other hand, mixes with a high LS replacement (≥30%) showed lower initial strengths, perhaps because they included clayey fines that hindered hydration and had less cement [54]. Many mixtures saw strength losses ranging from 5 to 10% after 7 days of immersion. At this point, the damage is mostly superficial, and the microstructural density of the concrete limits the amount of acid penetration. Comparing CCW-containing mixes to high-LS mixtures, the former, especially those with 5–10% CCW, maintained a larger percentage of their initial strength. This confirms research by Bawab et al. [55], which shows that lowering the quantity of free lime available for acid reactions can increase the acid resistance of pozzolanic materials. Strength loss increased with prolonged acid exposure, surpassing 20% in most mixes and reaching around 33% for mixes with a high LS concentration (e.g., Mix 5: 0C20L, Mix 4: 15C30L). The most substantial acid resistance was exhibited by Mix 7 (10CC0L), which, after 28 days, retained nearly 80% of its initial strength. In contrast, the low CCW, high-LS mixes performed the worst, keeping less than 65%. According to these results, CCW can improve durability in acidic settings if the LS content is maintained within ideal bounds.

3.2.2. Water Absorption

An essential durability metric is water absorption, which shows how easily water and other hostile substances may permeate the concrete matrix. The general permeability, interaction, and pore structure of hardened concrete are closely interrelated. The concrete mixes made with various quantities of CCW and LS had water absorption values shown in Figure 6. According to ASTM C642 [45], the measured water absorption values were between roughly 4.0% and 5.0%, which are within permissible bounds for structural concrete. It is generally accepted that increased water absorption results from a higher lateritic soil composition. Mixes 6 (20C20L) and 7 (10C40L), for instance, had the highest absorption rates. This is because lateritic soil has a larger porosity and is more water-retentive than conventional fine aggregate. The clay minerals and iron oxides present in the tiny particles of lateritic soil may enhance capillary suction and microvoid volume, which would encourage water infiltration [54]. On the other hand, mixtures with a low lateritic soil content and a moderate CCW concentration (10–15% cement replacement) tend to absorb water less. Some of the lowest absorption values (~4.0%) were found in Mix 2 (15C0L) and Mix 12 (10C20L). According to Elinwa and Abdulkadir [56], the filler effect and pozzolanic reactivity of CCW, which refines the pore structure and generates more calcium silicate hydrate (C-S-H) gel, are probably the cause of the decrease in absorption in these scenarios. Nevertheless, the pore refinement impact of CCW is less successful in reducing the rise in water absorption at greater lateritic soil replacement levels (>20%). This implies that whereas CCW can increase microstructural density, excessive lateritic soil adds sufficient porosity to negate any benefits. These results suggest that the best balance is offered by mixes with ≤20% lateritic soil and 10–15% CCW, which provide relatively low water absorption while preserving the sustainability advantages of employing alternative materials.

4. Statistical Modelling and Optimization

4.1. Analysis of Variance

A summary of the variance analysis for every response is shown in

Table 5. Analysis of variance results for the response models.

Responses	Factors	Sum of Squares	Dof	Mean Squared	F-Value	p-Value	Remark
Density Kg/m3	Model	7581.51	5	1516.30	29.84	0.0001	significant
	A-CCW	3739.11	1	3739.11	73.58	<0.00301
	B-Lateritic soil	23.80	1	23.80	0.468	0.5157
	AB	1156.00	1	1156.00	22.75	0.0020
	A2	37.20	1	37.20	0.732	0.4205
	B2	2662.20	1	2662.20	52.39	0.0002
	Residual	355.72	7	50.82
	Lack of Fit	149.72	3	49.91	0.9690	0.4898	not significant
Weight Loss (%)	Model	17.81	5	3.56	62.57	<0.0001	significant
	A-CCW	0.5816	1	0.5816	10.21	0.0151
	B-Lateritic soil	5.87	1	5.87	103.16	<0.0001
	AB	0.4624	1	0.4624	8.12	0.0247
	A2	2.58	1	2.58	45.24	0.0003
	B2	9.42	1	9.42	165.41	<0.0001
	Residual	0.3985	7	0.0569
	Lack of Fit	0.3301	3	0.1100	6.43	0.0521	not significant
Compressive strength (MPa)	Model	24.35	5	4.87	24.05	0.0003	significant
	A-CCW	10.19	1	10.19	50.34	0.0002
	B-Lateritic soil	1.91	1	1.91	9.41	0.0181
	AB	3.80	1	3.80	18.78	0.0034
	A2	3.39	1	3.39	16.75	0.0046
	B2	3.96	1	3.96	19.56	0.0031
	Residual	1.42	7	0.2024
	Lack of Fit	0.6291	3	0.2097	1.06	0.4575	not significant
Water absorption (%)	Model	0.8087	5	0.1617	41.82	<0.0001	significant
	A-CCW	0.0045	1	0.0045	1.17	0.3159
	B-Lateritic soil	0.0394	1	0.0394	10.18	0.0153
	AB	0.0930	1	0.0930	24.05	0.0017
	A2	0.6701	1	0.6701	173.28	<0.0001
	B2	0.0045	1	0.0045	1.16	0.3175
	Residual	0.0271	7	0.0039
	Lack of Fit	0.0128	3	0.0043	1.19	0.4182	not significant

. The hardened density, weight loss, compressive strength, and water absorption of CCW-LS concrete were all predicted using a fitted quadratic model generated through regression analysis. The model was chosen from the highest-order polynomial where the additional terms were essential and the program did not alias. Table 5 shows that the models for water absorption, weight loss, compressive strength, and density have low p-values of less than 0.01% and very high F-values of 29.84, 62.57, 24.05, and 21.27, respectively. This suggests that the chosen models are significant, as there is a mere 0.01% probability that noise could have caused these F-values.

The CCW and lateritic soil contents are shown in Table 5 as A and B, respectively. At the 5% significance level, a t-test was used to assess the significance of the model terms. Since their respective p-values were less than 0.05, A, AB, and B² were the significant model variables for hardened density. However, for both weight loss and compressive strength, the corresponding model terms were significant. All terms were significant for water absorption, except for the insignificant terms A and B². It is essential to note that the insignificant model variables have little to no effect on the responses.

The empirical models established for the CCW-LS concrete mixes at 28 days of curing are portrayed in Equations (4), (5), (6), and (7), respectively, for density (D), weight loss (WL), compressive strength (F_C), and water absorption (WA). These models use both positive and negative symbols to indicate the synergistic effects of the factors on the responses, and they contain all variables. It is essential to highlight that the generated model for each response is quadratic.

$$D=2267.00-21.62A-1.72B-17.00AB+2.31A^2+19.56B^2$$

(4)

$$WL=8.33+0.2696A-0.8568B+0.3400AB+0.6085A^2+{1.16B}^2$$

(5)

$$F_C=13.42+1.23A+0.4880B-0.9750AB+0.8087A^2-0.7912B^2$$

(6)

$$WA=4.09-0.0238+0.0701B+0.1525AB+0.3104A^2+0.0254B^2$$

(7)

where D stands for density (kg/m³) at 28 days, WL for weight loss (%), F_C for compressive strength (MPa), WA for water absorption (%), A for CCW content (%), and B for lateritic soil (LS) content (%).

4.2. Three-Dimensional and Contour Plots for the Various Responses

The study utilized contours and three-dimensional (3D) plots of RSM to show the correlation between the two independent variables and their resulting responses. The 3D response surface plot and two-dimensional (2D) contour plot representing the interaction effects of Lateritic Soil and Calcium Carbide Waste on the density of concrete exposed to an acidic environment are shown in Figure 7. A nonlinear relationship between the two variables and the concrete density can be seen in the 3D plot. The figure makes it clear that a decrease in density is typically the result of rising CCW content. Comparing CCW to OPC, it is found that CCW has a lower specific gravity and less cementitious properties.

On the other hand, especially at low CCW levels, increasing the LS content first encourages a rise in density. This behaviour can be the result of the tiny lateritic particles’ filler effect, which can improve particle packing and lessen matrix porosity. When applied in moderate amounts, lateritic soils, which are often rich in iron and aluminum oxides, may help to densify the composite matrix [57]. Excessive LS integration, however, may dilute the fine aggregate skeleton, raise the total water consumption, and perhaps decrease mix cohesion, which might eventually result in a lower density. According to the 3D figure, the lowest density occurs when both CCW and LS are at their optimal replacement levels, while the highest density is attained at low CCW and high LS. This illustrates that although each constituent may be beneficial in moderation, excessive replacement of them all disrupts the concrete’s compactness. One important measure of concrete durability, especially under harsh conditions, is its density. Increased porosity is frequently associated with lower density, which makes it easier for potentially hazardous substances like acids to gain access. As a result, the trends shown in Figure 8 suggest that mixtures with high CCW and LS concentration are more vulnerable to acid attack because of their increased permeability and decreased density. However, denser blends offer a more compact matrix that may withstand degradation and acid infiltration effectively [46].

Figure 8 shows how resistant the concrete samples were to acidic environments based on weight loss (%) after exposure to an aggressive acidic environment. LS and CCW together have an impact on how long concrete lasts under these circumstances, as shown by the 3D and contour response surface plots. Better resistance to acid-induced degradation is demonstrated by lower weight loss values, as the 3D plot in Figure 9a makes clear. Weight loss often increases as the amount of CCW and LS is increased above specific levels, as illustrated in the plot. This trend reveals that although both materials have a beneficial impact on sustainability and cost-cutting, their overuse might weaken the concrete’s capacity to withstand acidic media. A clear nonlinear interaction between CCW and LS is visible in the plot’s surface morphology. Near the centre coded levels (i.e., moderate replacement levels), the least amount of weight loss is seen, suggesting an ideal mix in which the matrix reaches its maximal densification and chemical stability. Combinations that have high amounts of both CCW and LS, on the other hand, typically show more weight loss; this might be because of increased porosity and compromised matrix consistency.

The 3D and contour response surface plots representing the interaction effects of Lateritic Soil and CCW on the compressive strength of concrete exposed to an acidic environment are shown in Figure 9. The 3D plot reveals a nonlinear interaction between the two variables, indicating that both materials have a significant impact on compressive strength under acidic conditions. Generally, a higher CCW content enhances compressive strength, particularly when combined with higher percentages of lateritic soil. This improvement is attributed to CCW’s pozzolanic activity, which enhances strength and acid resistance by reacting with calcium hydroxide to form a more calcium–silicate–hydrate (C-S-H) gel. Bawab et al. [55] have demonstrated that low early-age strength or increased porosity may result in a slight decrease at very high CCW doses. Likewise, compressive strength was positively impacted by the partial replacement of fine aggregate with lateritic soil. Because it contains a lot of tiny particles and aluminosilicates, lateritic soil fills in matrix gaps and increases microstructural density in line with research by Raja et al. [58]. This results in decreased permeability and enhanced resistance to acidic degradation. Additionally, when both CCW and LS are at lower replacement levels, the compressive strength is most sensitive to changes in both CCW and LS. These findings imply that using CCW and LS together not only increases strength but also strengthens the concrete’s resistance to acidic attack.

Figure 10 presents the 3D and 2D contour response surface plots used to evaluate the effect of CCW and LS on the water absorption of concrete. The 3D plot displays a saddle-shaped, nonlinear surface, suggesting intricate interactions between the two factors in determining the behaviour of water absorption. After rising from low to moderate proportions, both CCW and LS levels showed a declining pattern in water absorption values, which peaked at intermediate levels (coded values close to zero). This behaviour indicates a synergistic relationship in which the optimal proportions of CCW and LS work together to reduce water absorption and enhance the impermeability of concrete. An ideal balance in the mixture composition is implied by the lowest water absorption, which is seen in the central area of the design space. Water absorption is relatively high at lower quantities of CCW, most likely because of inadequate filler action and insufficient pozzolanic activity. When the content reaches moderate levels, CCW functions effectively as a micro-filler and pozzolan, resulting in matrix densification and reduced pore connectivity. At higher replacement levels, however, there is a noticeable increase in water absorption, which may be attributed to excessive fines creating weak spots and poor particle packing in the matrix [59]. For LS, a comparable trend is apparent. Excessive quantities introduce a larger volume of non-reactive particles, which may increase porosity and capillary absorption. In contrast, moderate inclusion increases packing density and decreases water ingress through physical packing and a probable pozzolanic reaction [60]. The contour plot in Figure 10b further illustrates the interaction effects, with the lowest water absorption occurring within a specific circular area. This area represents the optimal combination of CCW and LS for minimizing water intake. To improve durability-related features, the response indicates that the optimal ratio of both materials is essential.

4.3. Validation of the Developed Models for the Responses

Table 6. Validation of the response models.

Response	Density Kg/m3	Weight Loss (%)	Compressive Strength (MPa)	Water Absorption (%)
Standard deviations	7.13	0.2386	0.4499	0.0622
Mean	2280.46	9.42	13.39	4.29
CoV. (%)	0.326	2.53	3.36	1.45
R2	0.9552	0.9781	0.9450	0.9676
Predicted R2	0.8253	0.9625	0.7786	0.9445
Adjusted R2	0.9232	0.8652	0.9057	0.8645
Adequate precision	18.21	21.83	18.45	16.63

displays the distinct features of each response model that was developed. The R² values of the models were used to evaluate their quality and reliability. All models exhibit high R² values, nearly equal to unity (i.e., R² > 0.9), as shown in Table 6. Similarly, the adjusted R² values of 0.9232, 0.8652, 0.9057, and 0.8645 are quite consistent with the predicted R² values of 0.8253, 0.9625, 0.7786, and 0.9445. The models are sufficient for all response models, as the adjusted and predicted R² difference is less than 0.2.

Standard deviations (SD) were used to assess the variations in the experimental data of each model. The measured data are in good agreement with the high R² values of the developed models, as evidenced by the minimal SD values of each model compared to their mean values. The signal-to-noise ratio is measured by adequate precision (AP), and a model is considered to have adequate precision if the ratio exceeds four. According to the models’ adequate precision values of 18.21, 21.83, 18.45, and 16.63, they are both suitable and desired. To summarize, the established models are suitable for estimating the hardened density, weight loss, compressive strength, and water absorption of CCW–lateritic soil concrete.

As shown in Figure 11, the predicted findings are displayed on the y-axis. In contrast, the actual findings are plotted on the x-axis, allowing for a clear evaluation of the degree of precision and fitness of the generated models. The model’s acceptable precision of fit is demonstrated by the distribution of points along the straight line, as shown in Figure 11, where the anticipated and actual results coincide. The highly anticipated R² values show that the developed models for hardened density, weight loss, compressive strength, and water absorption are highly predictable.

4.4. Multi-Objective Optimization and Validation

A numerical optimization was conducted using the desirability function approach, a method frequently employed in multi-objective optimization scenarios, to determine the ideal mix proportions of CCW and LS for enhanced concrete durability [41]. Each response is converted into a dimensionless desirability scale, ranging from 0 (totally undesirable) to 1 (most desired), using the technique. This technique then aggregates the responses into a single overall desirability score. The goal of this study’s optimization was to determine the best mix of independent factors to produce a CCW-LS concrete mixture that minimizes density, weight loss, and water absorption while maximizing compressive strength. To optimize the responses and capture all possible solutions, all parameters were established within a certain range.

Table 7. Multi-objective optimization criteria and results.

Variables and Responses		Criteria for Optimization			Results and Verification
		Desired Goal	Lower Limit	Upper Limit	Predicted Result (Y)	Experimental Result (X)	Error (∈) (%)
Variables	A-CCW (%)	In range	0	20	13.12	13.12	-
	B-Lateritic soil (%)	In range	0	40	18.70	18.70	-
Responses	Dry density (Kg/m3)	Minimize	2245	2329	2253.616	2586.25	2.16
	Weight loss (%)	Minimize	8.13	11.92	8.835	9.25	4.49
	Compressive strength (MPa)	Maximize	11.10	16.81	14.396	14.50	3.73
	Water absorption (%)	Minimize	4.00	4.74	4.173	4.25	1.81
Desirability (%)					75.4

defines the multi-objective optimization constraints for the variables and responses.

The 3D desirability surface plot, which combines several optimization models into a single desirability score, is displayed in Figure 12. The plot displayed a dome-shaped surface, with the mid-levels of both CCW and LS having the highest desirability of 75.4%. This means that the most effective way to achieve multiple performance goals is to employ a balanced replacement approach. The desirability drastically decreases to almost nothing at lower levels of both CCW and LS. This implies a decrease in durability and strength parameters. The desirability falls to moderate levels at extremely high levels, most likely because of adverse consequences such as poor workability, increased porosity, and residue from unreacted material. According to the optimization findings, if the ratios are maintained within the statistically established ideal range, a partial substitution of cement with 13.12% CCW and fine aggregate with 18.7% LS can produce significant increases in the durability of concrete. In addition to helping to conserve resources and reduce waste, this approach supports the development of sustainable building materials.

Using the optimized mixture ratios shown in Table 7, a second series of laboratory tests was carried out to confirm the sufficiency of the optimization data retrieved from the Design-Expert program and all the response models. The latter step was done to ensure that the proportions of the optimized mixture were accurate. Three specimens were produced for each test parameter, and the mean values of each were reported. After 28 days, results were evaluated and contrasted with the predicted results. Using Equation (8) [21], the discrepancy (absolute relative error) between the experimental and predicted results was computed

$$\in =1-{\displaystyle \frac{Predicted value \left(Y\right)}{Experimental value \left(X\right)}}\times 100$$

(8)

For each of the responses that were taken into consideration, Table 7 displays the RSM predicted findings together with the corresponding experimental data. The calculated percentage errors demonstrated a high degree of agreement between the actual and predicted outcomes, with an average percentage error of less than 5%.

5. Conclusions

This study has effectively demonstrated that employing calcium carbide waste (CCW) and lateritic soil as partial substitutes for cement and fine aggregate in concrete production is both feasible and efficient. Response Surface Methodology (RSM) was employed to gain valuable insights into the interactions between these materials and their impact on durability-related properties, including water absorption, compressive strength, and acid resistance. The following are the main conclusions from this research study:

• Concrete samples with higher CCW and LS replacement levels absorb more water and are less resistant to acid, due to the increased pore volume and permeability. A higher LS replacement level and longer exposure to an acidic medium resulted in a general decrease in compressive strength.
• The proposed RSM quadratic models for water absorption, density, weight loss, and compressive strength demonstrated good predictability, indicating their potential for predicting the durability behaviour of the produced concrete.
• The RSM-based optimization produced the optimal mix of 13.12% CCW (replacement of cement) and 18.70% LS (replacement of fine aggregate), minimizing water absorption (4.17%) and weight loss (8.84%) while maximizing compressive strength (14.4 MPa) with 75.4% desirability.
• With percentage errors of less than 5%, validation testing revealed a high degree of agreement between the experimental and predicted values.