Modelling and Optimizing the Durability Performance of Self Consolidating Concrete Incorporating Crumb Rubber and Calcium Carbide Residue Using Response Surface Methodology

: The world is now focusing on a sustainable environment and reducing the effects of global warming. One way to achieve such targets is to properly utilize waste and reduce greenhouse CO 2 emissions. The cement industry is responsible for almost 10% of global CO 2 emission due to the high demand for cement in the construction industry. One of the ways to minimize this effect is the partial replacement of cement by other materials in concrete. Therefore, in this study, calcium carbide residue (CCR), which is highly rich in calcium oxide, partially replaced cement for waste management. Waste tires were grinded to ﬁne sizes in crumb rubber (CR) and partially replaced the ﬁne aggregate. Therefore, this paper investigared the inﬂuence of CR and CCR on the durability properties and heat/temperature resistance of self-compacting concrete (SCC). The experiment was designed using response surface methodology to investigate the effects of CR and CCR on SCC properties, design models for properties of the SCC, and optimize the mixes to achieve the best results. The properties considered were the durability of acid attack resistance (H 2 SO 4 attack), salt attack resistance (MgSO 4 attack), and water absorption. The heat resistance considered was weight reduction and residual compressive strength after heating the samples at a 200 ◦ C and 400 ◦ C. The results ﬁndings showed that CR and CCR negatively affect the acid and salt resistance of the SCC. Furthermore, CR negatively affects the heat resistance of the SCC, while CCR slightly improved it at 200 ◦ C. The models developed using RSM were signiﬁcant with high degrees of correlation and predictability. The optimum properties achieved 2.9% CR as a ﬁne aggregate replacement and 5.5% CCR as a cement replacement. The developed models can predict the durability performance of SCC mixes in terms of acid and salt attack resistance and the effects of elevated temperatures using CR, CCR, and ﬂy ash as the variables. This will reduce the need for carrying out experimental work, thereby reducing cost and time.


Introduction
The development of environmentally friendly construction materials has become the main concern of the building and construction industry's professionals due to the global issue of ozone layer depletion caused by greenhouse gases.Cement production generates substantial by-products that intensify global warming when discharged into the atmosphere [1].In order to cut down on the consumption of cement in the building and construction sector, the partial or full substitution of cement with sustainable and eco-friendly cementitious materials has to be given serious attention.A study aimed at promoting the use of local and sustainable construction materials to reduce the impacts of the continuous use of conventional materials was conducted by Obianyo et al. [2].On the other hand, industrial wastes such as used tyres and calcium carbide dumped in the environment contribute to the significant environmental issues faced by society.Although efforts have been targeted towards industrial wastes recycling and converting these waste materials to use raw materials for utilization in diverse industries, the quantity of industrial wastes abandoned continues to increase due to industrialization [3].The need to broaden the utilization of these waste materials has led researchers to identify more applications areas.The use of calcium carbide residue and crumb rubber from waste tyres by utilizing them as replacement materials in concrete production is a good idea.Implementing it will ensure that the consumption of 100% of such industrial waste is generated.
The durability of cement-based materials such as concrete cannot be ignored due to their heterogeneous nature [4].The heterogeneity of the concrete matrix results within the concrete's microstructure, which significantly affects its durability performance [5].A review work conducted by Sofi [6] on the influence of waste rubber tyres on the durability and mechanical properties of concrete revealed a reduction in the compressive strength, flexural tensile strength, and depth of water penetration of the rubberized concrete when compared to the control mix.However, the water absorption (up to 10% replacement) and abrasion resistance were better than the control mix concrete.Hilal [7] examined the effect of CR size and content on hardened characteristics of self-compacting concrete and discovered that the addition of crumb rubber in concrete resulted in a negative effect on the selfcompacting concrete's hardened properties.However, in terms of ductility, a substantial improvement was accomplished by adding all types of waste tires.Valizadeh et al. [8] investigated the influence of specimen geometry on the tensile strengths and compressive strength of self-compacting rubberized concrete with CR granules.Their findings showed that the variations between the cubes and cylindrical specimens were higher for the selfcompacting rubberized concrete containing 20% CR in comparison to the mixes with lower CR content.In addition, a remarkable size effect on the tensile strength of selfcompacting rubberized concrete was observed as the CR aggregate was added.Another study conducted by Bušić et al. [9] on the mechanical properties of SCC containing recycled rubber and silica fume indicated that a compressive strength above 30 MPa was obtained at the optimal combinations with up to 15% of recycled rubber and 5% of silica fume for 28 days curing age According to the authors, this result suggests the possibility of applying reinforced self-compacting rubberized concrete for structural elements in the future.
Response surface methodology is a design method that generates a set of continuous statistical analysis methods that explores the links between variables and their responses [10][11][12].The major idea of RSM is to determine the relationship between the dependent and independent variables and study their interactions while obtaining their optimal responses [13].The application of RSM in modeling and optimization has been proven in various fields (e.g., food, electronic technology).Its widespread adoption is due to its practicality, economy, and relative ease of use [14].The main advantage of RSM is that the number of experimental trials required to evaluate multiple parameters and their interactions is inexpensive [15,16].RSM is used for two main purposes: modeling and optimization.The optimization work carried out using RSM covers many research areas such as waste treatment, the food industry, the welding process, and the sputtering process [17].RSM is used for modeling wire discharge machining processes [18], H 3 PO 4 activated rubber waste adsorption in water treatment applications, and wastewater treatment from plants' palm oil [19].It is also used in the field (e.g., splatter thin film coating for electronic Aapplications [20]) and as an additive in concrete for use in the construction industry [21,22].
RSM has been helpful for modelling and optimization of concrete.Mohammed et al. [23] employed RSM to develop a model that predicts paper mill concrete's compressive strength.Haruna et al. [24] also utilized RSM to predict the compressive strength of mortar by developing an optimization model.Rezaifar et al. [25] developed a model and optimized high-performance concrete using metakaolin and fly ash as variables to minimize the durability coefficient and maximize compressive strength.Mohammed et al. [26] developed a model to predict compressive strength, unit weight, and water absorption of rubber created using RSM.They also optimized the rubber to create a mix by maximizing compressive strength and minimizing water absorption.Alyamac et al. [27] developed a self-compressing engineering cement composite (SC-ECC) mixed design model using RSM.They also optimize the ECC blend by maximizing elasticity and energy absorption.Vincent [28] examined the properties of rubberized concrete containing waste tire steel reinforcement at an early age.They analyzed the compressive strength, splitting tensile strength, and flexural strength using RSM.The normal residual plots indicated that the model was very appropriate.Haruna et al. [10] used RSM to investigate the effect of NaOH on the molarity of outdoor cured geopolymer mortars containing high calcium fly ash.They further conducted optimization and discovered the best mix contains 10Molarity Sodium hydroxide concentration and 0.5 water binder ratio, which yielded maximum compressive strength and flowability within range.
Several researchers reported that CR has many advantages when used in concrete, such as improved ductility, energy absorption capacity, thermal insulation, etc. [12,29,30].However, the major drawback in using CR in concrete is its negative effect on concrete's mechanical and durability performance.Many methods of mitigating the negative effect of CR on concrete have been carried out.However, there are limited studies that utilize the hybrid of fly ash and CCR as cementitious materials to mitigate the negative effect of CR on the durability performance of SCC.Although the combination of CCR and fly ash is expected to significantly enhance the durability of SCC due to the reaction between SiO 2 from fly ash, Ca(OH) 2 can be used from CCR to generate secondary C-S-H gels.These C-S-H gels are expected to fill the pores created by the CR in the cement matrix and densify the concrete's microstructure, enhancing strength and durability.Studies in the application of RSM modelling in durability performance prediction of green SCC utilizing CR as a partial substitute to fine aggregate and CCR as cement replacement material are limited.Therefore, there is a need for more research in using RSM analysis in predicting the durability performance of various green concretes such as SCC.Therefore, in this study, RSM was used for designing the experiments developing models to predict the durability performance and elevated temperature resistance of SCC using CR and CCR as the variables.

Materials
This research utilized type 1 ordinary Portland cement of 3.5 specific gravity in conformity with the BS EN 196-6 [27] specification as the principal binding substance.The XRF result showing the chemical composition of cement is presented in Table 1.The fly ash employed as supplementary cementitious material for this study belongs to class F under ASTM C618 [28], as shown in Table 1.The CCR samples were obtained from an industrial welding shop depot.The CCR sample was initially dried in the air for four days, and to ensure it was completely dried, and it was further dried in the oven for 24 h at 110 ± 5 • C temperature.The CCR was grinded and sieved through sieve No. 325 (45 µm) to obtain a smooth powder.The particles that passed the sieve were utilized for this experiment, and the retained ones in the sieve were trashed.The properties of CCR were also obtained using XRF and shown in Table 1.Its microstructural morphology as obtained through scanning electron microscopy is presented in Figure 1.The joint particle size distribution plot of Fine aggregate, coarse aggregate, and CR shown in Figure 2 was used for the study.In accordance with [29], CR and fine aggregate both belong to zone II class and exhibit particle size.The fine aggregate was natural river sand with a specific gravity of 2.63, water absorption of 1.96%, bulk density of 1560 kg/m 3, and mud content of 1.1%.The CR had a specific gravity of 0.95.The coarse aggregate consists of 19mm maximum-sized crushed gravel with specific gravity, bulk density, and water absorption of 2.65, 1450 kg/m 3, and 0.94%, respectively.Also, self-compaction of the concrete was achieved with the incorporation of a superplasticizer.The superplasticizer belongs to the polycarboxylate-based classification with a density of 1.11 kg/L and dosage of 2 to 15 bfl.oz/cwt of cementitious materials.to obtain a smooth powder.The particles that passed the sieve were utilized for this experiment, and the retained ones in the sieve were trashed.The properties of CCR were also obtained using XRF and shown in Table 1.Its microstructural morphology as obtained through scanning electron microscopy is presented in Figure 1.The joint particle size distribution plot of Fine aggregate, coarse aggregate, and CR shown in Figure 2 was used for the study.In accordance with [29], CR and fine aggregate both belong to zone II class and exhibit particle size.The fine aggregate was natural river sand with a specific gravity of 2.63, water absorption of 1.96%, bulk density of 1560 kg/m 3, and mud content of 1.1%.The CR had a specific gravity of 0.95.The coarse aggregate consists of 19mm maximum-sized crushed gravel with specific gravity, bulk density, and water absorption of 2.65, 1450 kg/m 3, and 0.94%, respectively.Also, self-compaction of the concrete was achieved with the incorporation of a superplasticizer.The superplasticizer belongs to the polycarboxylate-based classification with a density of 1.11 kg/L and dosage of 2 to 15bfl.oz/cwt of cementitious materials.

Experimental Design Using RSM
Response surface methodology (RSM) gathers arithmetical and analytical methods for computing the correlation among a class of independent measurable variables with one or more responses [31,32].RSM can be utilized to find functioning variables that may significantly affect the basic response or not [33].RSM could also be defined as a cornucopia of arithmetical and analytical methods for modeling and analyzing problems.The output is determinant by numerous factors (input variables) [27].RSM is also beneficial for multi-faceted models by establishing preferable goals in terms of response or variables [26].RSM analysis can be achieved with various design models, including central composite, Box-Behnken, and historical data.These can be used to generate the arithmetical correlation response and independent variables.The number of variables and each variable variation is key determinants for the design model type [34].The first-order function gives the linear model as shown in Equation (1). =  +   +   +. . . . . . . .  +  (1) where y is the modeled response, β0 is the y-intercept for which X1 = X2 = 0, β1, and β2 are the coefficients of the first and second independent variables, respectively, X1 is the first variable coefficient, X2 is the second variable coefficient, and ξ is the error.Nevertheless, the linear model doesn't match the data's response when curvature.A second-order function with a higher degree polynomial model will be utilized, as shown in Equation ( 2) [11].
The CCD has a factor planning component of 2k, where k is the number of related variables or factors operated at two levels of a low and high number [24].The variable lower and upper limits are coded with negative and positive numbers, respectively.The central point of the central composite design is the average of upper and lower limits from the factorial design [35].Hence the center point is described as the zero-point area that meets the optimal conditions.

Experimental Design Using RSM
Response surface methodology (RSM) gathers arithmetical and analytical methods for computing the correlation among a class of independent measurable variables with one or more responses [31,32].RSM can be utilized to find functioning variables that may significantly affect the basic response or not [33].RSM could also be defined as a cornucopia of arithmetical and analytical methods for modeling and analyzing problems.The output is determinant by numerous factors (input variables) [27].RSM is also beneficial for multifaceted models by establishing preferable goals in terms of response or variables [26].RSM analysis can be achieved with various design models, including central composite, Box-Behnken, and historical data.These can be used to generate the arithmetical correlation response and independent variables.The number of variables and each variable variation is key determinants for the design model type [34].The first-order function gives the linear model as shown in Equation (1).
where y is the modeled response, β 0 is the y-intercept for which X 1 = X 2 = 0, β 1, and β 2 are the coefficients of the first and second independent variables, respectively, X 1 is the first variable coefficient, X 2 is the second variable coefficient, and ξ is the error.Nevertheless, the linear model doesn't match the data's response when curvature.A second-order function with a higher degree polynomial model will be utilized, as shown in Equation (2) [11].
The CCD has a factor planning component of 2k, where k is the number of related variables or factors operated at two levels of a low and high number [24].The variable lower and upper limits are coded with negative and positive numbers, respectively.The central point of the central composite design is the average of upper and lower limits from the factorial design [35].Hence the center point is described as the zero-point area that meets the optimal conditions.The experiment was designed and statistically analyzed using RSM from design expert version 10 software in this study.The mathematic models between variables and response were developed.Modelling of a variable using response surface methodology (RSM) involves a sequence of processes to achieve the research objective, which requires recognizing the research problem based on the formulated research optimization goals.In this study, the face-centered central composite design (FCCCD) available in the RSM software having α = 1 was used to develop mathematical models to predict the relationships between the variables and responses.The independent variables considered were CR as partial replacement to fine aggregate, which varied at three levels (i.e., 0%, 10%, and 20%) by volume of sand.The second variable was CCR as partial replacement to cement and varied into three levels (i.e., 0%, 5%, and 20%) by volume of cement.The responses were weight reductions due to immersion in acidic (H 2 SO 4 ) and salt (MgSO 4 ), and water absorption.Other responses were residual compressive strength and weight reductions due to elevated temperatures (normal temperature, 200 • C, and 400 • C).The RSM software-generated thirteen (13) mixes with regards to the various combinations of the variables, as shown in Table 2. From Table 2, the water-to-binder ratio (W/B) was not constant (unified).This is due to the fact that the CCR was used as a partial replacement by volume of cement and not by weight.Due to the lower specific gravity of the CCR compared to cement, this resulted in variation in total weight of the cementitious materials, resulting in variation of the W/B ratio across the mixes.

Samples Preparation and Test Methods
BS 1881-125 [36] specifications were used for batching, sampling, and mixing the fresh concrete.The mixing of the fresh concrete was carried out with the aid of a rotating pan mixer in the Laboratory at room temperature and relative humidity.The fresh concrete was cast into the specified moulds, followed by immediately mixing and allowed to harden for one day.After that, they were demoulded and cured in water for the stated duration before the evaluation.
The durability test was conducted with resepct to acid attack, salt attack, and water absorption.Guidelines outlined in ASTM C642 [37] were used to measure the resilience of the SCC samples to acid and salt attacks.After curing in water for 28 days, the 100 mm cubes were immersed in H 2 SO 4 and MgSO 4 solutions for 28 days to measure resistance to acid and salt, respectively.Prior to immersion in the solutions, the samples were weighed.After 28 days period of immersion, the samples were reweighed and recorded.Three samples were tested for the acid and salt attacks and the average value recorded for each mixture.For the effect of elevated temperatures on the SCC mixes, 28 days of water curing was conducted on the 100 mm cube samples before testing.After curing, the samples were air-dried and weighed before subjecting to elevated temperature.The samples were then exposed to heat for 1 h at different temperatures of 200 • C and 400 • C, respectively.The specimens were air-cooled and weighed after that.The samples were then tested for compressive strength in accordance with BS EN 12390-3 [38] specification.The weight reduction was then calculated using Equation (3).Triplicate samples were tested for all of the mixtures and elevated temperature and mean value were recorded.The water absorption test was carried out using 100 mm cube samples in accordance with ASTM C642 [37] specifications.The specimens were water cured for 28 days prior to water absorption determination.Three samples were tested for water absorption and the mean value was also recorded.
where W R represents the weight reduction in %, W i and W n represent the initial and final weights respectively in kg.

Durability Performance against Acid and Salt Attack
Statistical models have been generated using RSM to speculate the acid and salt attack resistance of the SCC mixes containing CR and CCR.The acid attack was measured by immersing the samples in H 2 SO 4 solution for 28 days, and then the weight reduction was calculated.Similarly, the salt attack was measured by immersing the samples in magnesium sulphate (MgSO 4 ) solution for 28 days, and then weight reduction was computed.The results are presented in Table 3.The RSM developed models to predict the weight reductions of the SCC in H 2 SO 4 and MgSO 4 solutions using CR and CCR as the variables.Furthermore, the water absorption of the SCC mixes was also modelled statistically.The developed models were explained statistically using analysis of variance (ANOVA), as presented in Table 4.The probability (P-Significance) test was used to explain the significance of the models and each model term.A model or its term has been said to be significant if its p-value is less than 0.05, implying that the null hypothesis has been proven to be statistically true.The lower the p-values, the higher the agreement of the null hypothesis with the corresponding developed models and vice versa.From Table 4, the models for predicting the weight reduction due to immersions in H 2 SO 4 and MgSO 4 and water absorption were all statistically significant with p-values far less than 0.05. the F-values of 30.16, 81.04, and 11.21 for weight reduction (H 2 SO 4 ), weight reduction (MgSO 4 ), and water absorption models, respectively, indicated that they were all significant against their corresponding null hypotheses.The significance of each of the model terms can also be explained using p < 0.05.For weight reduction due to immersion in the H 2 SO 4 model, the model terms CR, CCR, and (CR) 2 were statistically significant in the model with p values below 0.05.At the same time, interaction between CR and CCR (i.e., CR * CCR and (CCR) 2 ) were not significant as their p values are greater than 0.05.For weight reduction due to immersion in the MgSO 4 model, the terms CCR, (CR) 2, and (CCR) 2 were statistically significant, while the terms CR and CR*CCR were not significant statistically.Additionally, for the water absorption model, the terms CR, CR * CCR, and (CR) 2 were all statistically significant within the model, while the terms CCR and (CCR) 2 were not statistically significant.The statistical lack of fit, which is defined as the amount, the model predictions missed the observations, was further used to evaluate each model's significance.The F values of 5.77, 4.46, and 5.66 for weight reduction (H 2 SO 4 ), weight reduction (MgSO 4 ), and water absorption models, respectively.It implied only 6.18%, 9.15%, and 6.37% probabilities for weight reduction (H 2 SO 4 and weight reduction (MgSO 4 ).Also, the water absorption models, respectively, indicated that the lack of fit for those F-values could arise due to noise.For the model to be fit, its lack of fit should be non-significant [11,32,39].For the weight reduction (H 2 SO 4 ), weight reduction (MgSO 4 ), and water absorption model, their p-values for the lack of fits were greater than 0.05.Therefore, all of the models were said to fit well.Their lack of fit was not significantly relative to their corresponding pure errors.The developed statistical models for the weight reduction (H 2 SO 4 ), weight reduction (MgSO 4 ), and water absorption models are presented as Equations ( 4)-( 6), respectively.
where WR represents weight reduction in %, W.A represents water absorption in %, A represents crumb rubber (CR) in %, and B represents calcium carbide residue (CCR) in %.
The degree of quality, adequacy, fitness, and predictability of the durability models was further investigated and explained using the ANOVA (i.e., degree of determination (correlation)), as given in Table 5.An R 2 value of 1 (unity) implied a perfectly fitted model, while a lower R 2 value implied a poorly fitted model.All of the generated prototypes have more significant degree of correlations (R 2 ≥ 0.9), which implies that for all of the models, only less than 10% of the experimental data could not be explained by the models.The R 2 values of 0.956, 0.983, and 0.90 for the weight reduction (H 2 SO 4 ), weight reduction (MgSO 4 ), and water absorption models, respectively, implied that all of the experimental data were fitted and explained by the model except 4.4%, 1.7%, and 10% for the weight reduction (H 2 SO 4 ), weight reduction (MgSO 4 ) and water absorption models, respectively.The model's adequacy and fitness were further evaluated using the difference between the predicted and adjusted R 2 values.For a model to be fit, the speculated and adjusted R 2 values need to be reasonably in consensus to each other (i.e., their differences should be less than 0.2).For the weight reduction (MgSO 4 ) model, its predicted and adjusted R 2 agreed as their differences are less than 0.2.However, for weight reduction (H 2 SO 4 ) and water absorption models, the difference between their predicted and adjusted R 2 values was greater than 0.2.This might be due to a problem with the model or data or might indicate a large block effect.Therefore, model reduction through backward elimination was carried out to remove the non-significant model terms.The coefficient of variations (CoV) was similarly employed to determine the dispersion of test information across the predicted prototypes.From Table 5, the water absorption model had the least CoV value of 6.24%.In comparison, the weight reduction (H 2 SO 4 ) immersion had the highest CoV value of 10.89%.All of the models can be said to be a lower CoV value and can therefore be used to predict the responses with a lower residual error related to its predicted values.The signal to noise levels for each model was measured using adequate precision.Every single one of the prototypes recorded an adequate precision value greater than foru, meaning that the prototype can be applied to cruise the design domain as defined by the model type selected.
The degree of determination (correlation) for the weight reduction (H 2 SO 4 ) and water absorption models after removing the non-significant model terms through backward elimination are given in Table 5.It can be observed that after model reduction, the predicted and adjusted R 2 values for both the weight reduction (H 2 SO 4 ), and water absorption were now following one another as their differences were below 0.2.The developed mathematical models after the non-significant terms were removed for the weight reduction (H 2 SO 4 ) and water absorption models are presented as Equations ( 7) and (8), respectively.The backward elimination for the models reduction was selected algorithmically by the RSM software using, multiple model selection methods and criteria.The best one-term-smaller model (insignificant term) for the selected criteria was kept in order to improve the criterion score as in Equation (8) where the model insignificant term B representing CCR was kept.If the best one-term does not improve the cretarion score, then the whole insignifant terms were removed as in Equation ( 7) [40].
where WR represents weight reduction in %, WA represents water absorption in %, A represents crumb rubber (CR) in %, and B represents calcium carbide residue (CCR) in %.
Based on the RSM analysis, the difference between the predicted and adjusted R 2 values must be less than 0.2.If their difference is greater than 0.2, this might indicate a large block effect or possible problem with the model or data.Therefore, to fix this error, model reduction by removing the insignificant terms in the model is required [39,40].Equations ( 7) and ( 8) are the statistically modified versions of Equations ( 4) and ( 6), respectively which were obtained after model reduction through backward elimination by removing the insignificant model terms.As seen in Table 5, after the model reductions, the models' predicted, and adjusted R 2 values will be reasonably in agreement with each other.Therefore, Equations ( 7) and ( 8) are the statistically fitted models for predicting the weight reductions due to H 2 SO 4 emissions and water absorption, respectively, for the SCC mixes containing CR and CCR.
The models' adequacy and degree of correlation for predicting the durability of SCC mixes were checked and verified graphically by plotting the normal plots against internally studentized residuals.From the normal plots against internally studentized residuals as presented in Figure 3, all of the models followed the normal probability distribution.They were all set on the straight line.Hence, the normal probability distribution assumed and used for the statistical models is true.Additionally, all of the data points were reasonably aligned across the linear trend line.This further explained all of the models' high R 2 values, greater than or equal to 0.9.Consequently, the initiated models can speculate the weight reductions due to immersion in H 2 SO 4 and MgSO 4 and water absorption of the SCC mixes using CR and CCR as the variables with the opulence of accuracy and likelihood.
Figure 4 presents the 3D response surface plots for the for-weight reduction (H 2 SO 4 ), weight reduction (MgSO 4 ), and water absorption models, respectively.From Figure 4a,b, the weight reduction due to immersion in H 2 SO 4 for the SCC mixes was shown to decrease with the incorporation of 10% CR and then increase with a higher amount of CR up to 20%.From the 3D plot, the bluish portion, which indicated the lowest weight reduction due to H 2 SO 4 immersion, was obtained at the 10% CR coordinate point.The highest weight reduction was obtained at the 20% coordinate point.Therefore, the partial replacement of up to 10% fine aggregate with CR increases the acid and salt attack resistance of the SCC.This improvement in acid and salt resistance of the SCC due to the incorporation of CR can be attributed to the fact that rubber particles acted as confinement to other particles such as the cementitious matrix and protected them from separation [41].Another reason might be attributed to the bridging provided by the CR due to its higher elasticity and fiber nature.Resulting in the prevention of crack development caused by the internal pressure caused by the acid reaction within the concrete microstrip, thereby preventing spalling [42].Similar findings have been reported by Thomas et al. [41] and Bisht and Ramana [43].The increase in weight reduction due to H 2 SO 4 and MgSO 4 CR immersion can be traced to the increased voids initiated by the CR in the cement pattern due to air entrainment during mixing.These voids in the strong cement pattern expand easily in the acidic environment causing deterioration of the cement paste and higher weight reduction [44].
The models' adequacy and degree of correlation for predicting the durability of SCC mixes were checked and verified graphically by plotting the normal plots against internally studentized residuals.From the normal plots against internally studentized residuals as presented in Figure 3, all of the models followed the normal probability distribution.They were all set on the straight line.Hence, the normal probability distribution assumed and used for the statistical models is true.Additionally, all of the data points were reasonably aligned across the linear trend line.This further explained all of the models' high R 2 values, greater than or equal to 0.9.Consequently, the initiated models can speculate the weight reductions due to immersion in H2SO4 and MgSO4 and water absorption of the SCC mixes using CR and CCR as the variables with the opulence of accuracy and likelihood.

Elevated Temperature
The heat resistance of the SCC samples containing CR and CCR was measured in residual compressive strength and weight reduction after subjecting the concrete to different temperature exposures.The results are presented in Table 6.RSM was then used to develop models to predict the residual compressive strength and weight reduction of the SCC mixes at different temperatures.Additionally, the decrease in salt resistance due to CR was due to the high pores in the hardened cement matrix resulting from the air entrapped on the surface of the CR during mixing.This increased the internal pressure on the cement matrix by the sulfate-related growth crystals, causing internal cracks and hence deterioration of the cement paste [44,45].Furthermore, a large amount of crystals produced in the pores of the matrix by the salt solution causes large crystallization pressure causing deterioration of the cementitious matrix [46].Incorporating CCR into the SCC mixes slightly decreases its weight reduction due to immersion in H 2 SO 4 and MgSO 4 , as shown in Figure 4a,b, respectively.This implied that CCR slightly increases the resistance of the SCC mixes to acid and salt attacks.This improvement was more pronounced on the SCC mixes containing 10% CR as partial replacements to fine aggregate.The reduction in acid and salt might be attributed to the high quantity of CaO in CCR, which reacts with the cement's chemical oxides.Thus increasing pozzolanic reaction, densifying the concrete's microstructure, and reducing ingress of acids and salts [47].Regarding the water absorption, from Figure 4c, there is a significant increment in water absorption with an increase in CR content.This was attributed to the increment in the pores in the hardened cement paste caused by the hydrophobic nature of the CR.The CR captures air during mixing causing high porosity when the sample cubes have dried fully.This leads to an increment in water absorption [11,44,48].The addition of CCR slightly decreased the water absorption of the SCC mixes.This might be due to the filling effect of the CCR, which makes it fill the pores in the SCC mix and hence reduces water absorption [44,49].

Elevated Temperature
The heat resistance of the SCC samples containing CR and CCR was measured in residual compressive strength and weight reduction after subjecting the concrete to different temperature exposures.The results are presented in Table 6.RSM was then used to develop models to predict the residual compressive strength and weight reduction of the SCC mixes at different temperatures.• C using CR and CCR as the variables.The ANOVA summary of the developed models is presented in Table 7.Using the P-Significance test, all of the models for the residual compressive strength were statistically significant, with p-values less than 0.05.Therefore, the null hypothesis for all of the models was proven to be true.The models F-values of 10.43, 4.01, and 7.85 for residual compressive strengths at 27 • C, 200 • C, and 400 • C, respectively, indicated that they were all significant against their corresponding null hypotheses.The significance of each of the model terms can also be explained using p < 0.05.For residual compressive strength at the 27 • C model, the model terms CR and (CCR) 2 were statistically significant with p values less than 0.05.All other terms were not significant as their p values were greater than 0.05.For residual compressive strengths at 200 • C and 400 • C models, only the model term CR is statistically significant.Still, all other model terms were not significant statistically.All of the model's lack fit was not significant as their p-values were greater than 0.05.The F values of 2.00, 0.011, and 0.12 for residual compressive strengths at 27 • C, 200 • C, and 400 • C models, respectively, implied that there is 25.59%, 99.82%, and 94.22%.The probabilities for residual compressive strengths at 27 • C, 200 • C, and 400 • C models, respectively.Tthat the lack of fit those F-values could arise due to noise.For the model to be fit, its Lack of fit should be non-significant [11,32,39].Therefore, all of the models were said to fit well.Their lack of fit was not significant relative to their corresponding pure errors.The developed statistical models for the residual compressive strengths at 27 • C, 200 • C, and 400 • C are presented as Equation (9a-9c), respectively.
where F C,R represents the residual compressive strength in MPa, A represents CR in %, and B represents CCR in %.The ANOVA for the residual compressive strengths models at 27 • C, 200 • C, and 400 • C was further explained in terms of the degree of determination (R 2 ) as presented in Table 8.An R 2 value of 1 (unity) implied a perfectly fitted model, while a lower R 2 value implied a model not well fitted.All of the developed models have a reasonably high degree of correlations (R 2 > 0.7), which implies that for all of the models, only less than 30% of the experimental data could not be explained by the models.The R 2 values of 0.882, 0.741, and 0.849 for residual compressive strengths models at 27 • C, 200 • C, and 400 • C, respectively, implied that all of the experimental data were fitted and explained by the model except 11.8%, 25.9%, and 15.1% for residual compressive strengths at 27 • C, 200 • C, and 400 • C models, respectively.The adjusted and predicted R 2 values were further used to check the adequacy and correlation of the models.For a good and well-fitted model, the difference between the adjusted and predicted R 2 should be less than 0.2 [39,40].For the residual compressive strength models at 200 • C and 400 • C, the difference between their predicted and adjusted R 2 values is less than 0.2.Therefore, it can be said their predicted and adjusted R 2 are reasonably in agreement with each other.However, for the residual compressive strength model at 27 • C, the difference between its predicted and adjusted R 2 value is greater than 0.2.This might be due to a problem with the model or data or might indicate a large block effect.Therefore, model reduction through backward elimination was carried out to remove the non-significant model terms.After model reduction, the differences between the predicted and adjusted R 2 values for the residual compressive strength model at 27 • C became less than 0.2, as shown in Table 8.The coefficient of variations (CoV) was also used to measure the dispersion of experimental data across the predicted models.From Table 8, the residual strength model at 200 • C had the least CoV value of 2.8%, while the residual strength model at 27 • C had the highest CoV value of 4.49% (although all of the models can be said to be lower CoV values and can therefore be used to predict responses with lower residual error related to predicted values).The signal-to-noise levels for each model were measured using adequate precision.Every one of the prototypes has a good precision value of more than four.The models can be utilized to cruise the design domain as defined by the model type selected.The developed mathematical model after the non-significant terms was removed for residual compressive strength at 27 • C is presented as Equation (10), Where the best one-term-smaller model (insignificant term), i.e., B (CCR) for the selected criteria was kept in order to improve the criterion score.
where F C,R represents the residual compressive strength in MPa, A represents CR in %, and B represents CCR in %.Equation ( 10) is the statistically fitted and modified version of Equation (9a), obtained after Equation (9a) was subjected to model reduction through backward elimination.Based on the ANOVA presented in Table 8, Equation (9a) cannot be used statistically to predict the residual compressive strength of the SCC mixes at 27 • C, as the difference between the model's predicted and adjusted R 2 values must have been greater than 0.2.Therefore, there might be a large block effect or possible problem with the model or data.Therefore, to fix this error, model reduction by removing the insignificant terms in the model is required [39,40].After model reduction, Equation (10) is the statistically fitted and acceptable model that can be used to predict the residual compressive strength at 27 • C for the SCC mixes containing CR and CCR, with agreed predicted and adjusted R 2 values as shown in Table 8.
The degree of determination and correlation of the models for predicting the residual compressive strength of the SCC mixes at temperatures of 27 • C, 200 • C, and 400 • C were validated graphically by plotting the normal plots against internally studentized residuals and the predicted versus actual plots.From the normal plots against internally studentized residuals as presented in Figure 5, all of the models followed the normal probability distribution.They were all aligned along the straight line.Therefore, the normal probability distribution assumed and used for the statistical models is true.Additionally, the data points were reasonably aligned across the linear trend line.Therefore, the experimental results agree with the predicted models.Hence, the developed model equations can predict the residual compressive strength of the SCC mixes under normal temperature (27 • C), 200 • C, and 400 • C using CR and CCR as the variables with a high degree of accuracy.The 3D plots of residual compressive strength models at 27 °C, 200 °C, and 400 °C are presented in Figure 6a-c, respectively.The residual compressive strength decreased with an increase in elevated temperature.At all of the temperatures, the residual compressive strength decreases with incrementally replacing fine aggregate with CR.At elevated temperatures, the decrease in residual compressive strength with increased substitution of The 3D plots of residual compressive strength models at 27 • C, 200 • C, and 400 • C are presented in Figure 6a-c, respectively.The residual compressive strength decreased with an increase in elevated temperature.At all of the temperatures, the residual compressive strength decreases with incrementally replacing fine aggregate with CR.At elevated temperatures, the decrease in residual compressive strength with increased substitution of sand with CR can be attributed to the continuous deterioration of the rubber particles due to intense heat resulting in poor bonding between the cement matrix and rubber particle and hence reduced strength.The addition of CCR improved the residual compressive strengths of the SCC mixes.This increment was more effective at higher temperatures of 200 • C and 400 • C.This can be as a result of the interaction of CCR with free lime to produce extra CSH and CAH, hence reducing the amount of Ca(OH) 2 and an un-moist portion of the surface fraction assisted by autoclaving, which intensify the rheology and hence improves the residual compressive strength [50].
Buildings 2022, 12, x 13 of 16 sand with CR can be attributed to the continuous deterioration of the rubber particles due to intense heat resulting in poor bonding between the cement matrix and rubber particle and hence reduced strength.The addition of CCR improved the residual compressive strengths of the SCC mixes.This increment was more effective at higher temperatures of 200 °C and 400 °C.This can be as a result of the interaction of CCR with free lime to produce extra CSH and CAH, hence reducing the amount of Ca(OH)2 and an un-moist portion of the surface fraction assisted by autoclaving, which intensify the rheology and hence improves the residual compressive strength [50].

Weight Reduction due to Elevated Temperature
The weight reduction of the SCC mixes after subjecting to elevated temperatures of 200 °C and 400 °C were modelled using RSM by considering CR and CCR as the variables.The ANOVA summary for the generated prototype models is shown in Table 9.The relevance of the models was tested utilizing their P-values (i.e., p < 0.05).This is also used to

Weight Reduction Due to Elevated Temperature
The weight reduction of the SCC mixes after subjecting to elevated temperatures of 200 • C and 400 • C were modelled using RSM by considering CR and CCR as the variables.The ANOVA summary for the generated prototype models is shown in Table 9.The relevance of the models was tested utilizing their p-values (i.e., p < 0.05).This is also used to prove or disprove the null hypothesis of the models.The models for the weight reductions at 200 • C and 400 • C were significant with p-values below 0.05.The F-values of 164.73 and 12.09 for weight reduction models at 200 • C and 400 • C correspondingly show they were all relevant against their corresponding null hypotheses.The significance of each of the model terms can also be explained using p < 0.05.For weight reduction at the 200 • C model, only the terms CR and (CCR) 2 were statistically significant in the model with p values below 0.05.The remaining were not significant as their p values are above 0.05.For weight reduction at 400 • C models, only the model term CR is statistically significant.Still, all other model terms were not significant statistically.All of the model's lack fit was insignificant as their p-values were greater than 0.05.The F values of 0.04 and 0.12 for weight reductions at 200 • C and 400 • C models, respectively, implied 98.77% and 90.09% probabilities for weight reductions at 200 • C and 400 • C models.Lack of fit those F-values could arise due to noise.For the model to be fit, its lack of fit should be non-significant [11,32,39].Therefore, all of the models were said to fit well.Their lack of fit was not significant relative to their corresponding pure errors.The developed statistical models for the weight reductions at 200 • C and 400 • C are presented as Equations ( 11) and (12). WR(400 where WR represents weight reduction in %, A represents crumb rubber (CR) in %, and B represents calcium carbide residue (CCR) in %.Table 10 presents the ANOVA summary in terms of coefficient of determination for the weight reductions at 200 • C and 400 • C models.Both models have high degrees of determination (R 2 ) values.The model for weight reduction at 200 • C had an R 2 value of 0.992, which is very close to unity (perfect model).Only less than 1% of the experimental data was not well fitted into the model.Similarly, the model for weight reduction at 400 • C also has a very high R 2 value of 0.9, which implied only about 10% of the experimental data was not fully and well fitted into the model.Furthermore, for both models, their adjusted and speculated R 2 values were logically in accordance with one other as their difference is below 0.2.This implied a good and well-fitted model with a high degree of accuracy [39,40].The dispersion of experimental data across the predicted models was measured using the coefficient of variations (COV).All of the models had a low COV of less than 8.5%.All of the models can be said to be a lower COV value.They can therefore be used to predict the responses with a lower residual error related to their predicted values.The signal-to-noise levels for each model was measured using adequate precision.Each of the model has a proper precision value greater than four, meaning that the models can be utilized to cruise the design domain as defined by the model type chosen.
200 • C and 400 • C models were verified and checked graphically by plotting the normal plots against internally studentized residuals, as presented in Figure 7.Both models followed the normal probability distribution function as the data plots were aligned along the straight trend line.Therefore, the normal probability distribution assumed and used for the statistical models is true.Additionally, for all of the models, the data points were reasonably aligned across the linear trend line.Therefore, the experimental results reasonably agree with the predicted models.Hence, the developed model equations can predict the weight reductions of the SCC mixes under elevated temperatures of 200 Furthermore, for both models, their adjusted and speculated R 2 values were logically in accordance with one other as their difference is below 0.2.This implied a good and well-fitted model with a high degree of accuracy [39,40].The dispersion of experimental data across the predicted models was measured using the coefficient of variations (COV).All of the models had a low COV of less than 8.5%.All of the models can be said to be a lower COV value.They can therefore be used to predict the responses with a lower residual error related to their predicted values.The signal-to-noise levels for each model was measured using adequate precision.Each of the model has a proper precision value greater than four, meaning that the models can be utilized to cruise the design domain as defined by the model type chosen.200 °C and 400 °C models were verified and checked graphically by plotting the normal plots against internally studentized residuals, as presented in Figure 7.Both models followed the normal probability distribution function as the data plots were aligned along the straight trend line.Therefore, the normal probability distribution assumed and used for the statistical models is true.Additionally, for all of the models, the data points were reasonably aligned across the linear trend line.Therefore, the experimental results reasonably agree with the predicted models.Hence, the developed model equations can predict the weight reductions of the SCC mixes under elevated temperatures of 200 °C and 400 °C utilizing CR and CCR as the variables with greater accuracy.The 3D plots for the weight reduction at 200 °C and 400 °C are presented in Figure 8a,b, respectively.The weight reductions increase with increment in temperature due to The 3D plots for the weight reduction at 200 • C and 400 • C are presented in Figure 8a and 8b, respectively.The weight reductions increase with increment in temperature due to continuous deterioration of the cement matrix.Additionally, the weight reduction further increases with the addition in partial substitution of sand using CR at all temperatures.
The weight reduction due to CR addition was more severe at 400 • C.This might be due to the fact that the spalling due to internal pressure from heating is more severe at higher temperatures.
The weight reduction due to CR addition was more severe at 400 °C.This might be due to the fact that the spalling due to internal pressure from heating is more severe at higher temperatures.
Additionally, dehydration of C-S-H gels takes place under elevated temperature, and this causes increased internal stresses and microcracks, which consequently result in increased weight reduction [44,51,52].As shown in Figure 8a, the addition of CCR does not affect the weight reduction of the SCC when heated at 200 °C.However, at 400°C, the addition of CCR significantly increased the weight reduction of CCR.This might be due to continuous degradation of the excess C-S-H generated from the reaction of the lime from CCR and cement hydration products, causing microcracks and spalling of the cement paste, thus resulting in increased weight loss [44].

Multi-Objective Optimization Response Analysis
Multi-objective optimization has been carried out using response surface methodology (RSM) to maximize the sample's durability performance and heat resilience containing CR and CCR.The optimization used to obtain the best combinations of the variables that can be used to achieve the optimum results of performance.The CR was utilized as a partial substitution to sand.At the same time, the CCR was used as supplementary cementitious material in the SCC mix to achieve the maximum residual compressive strength and minimum weight reduction after subjecting to elevated temperature.Additionally, the optimization aimed to achieve minimum water absorption and minimum weight reductions after subjecting the concrete to H2SO4 and MgSO4 attacks.The optimization criteria are summarized in Table 11.The multi-objective optimization results obtained from the RSM software are also presented in Table 11.The best performance of the SCC mixes was achieved when 2.9% fine aggregate was partially substituted with CR and 5.5% cement with CCR.The optimal mix proportion achieved had desirability of 77%, a high value.Additionally, dehydration of C-S-H gels takes place under elevated temperature, and this causes increased internal stresses and microcracks, which consequently result in increased weight reduction [44,51,52].As shown in Figure 8a, the addition of CCR does not affect the weight reduction of the SCC when heated at 200 • C.However, at 400 • C, the addition of CCR significantly increased the weight reduction of CCR.This might be due to continuous degradation of the excess C-S-H generated from the reaction of the lime from CCR and cement hydration products, causing microcracks and spalling of the cement paste, thus resulting in increased weight loss [44].

Multi-Objective Optimization Response Analysis
Multi-objective optimization has been carried out using response surface methodology (RSM) to maximize the sample's durability performance and heat resilience containing CR and CCR.The optimization used to obtain the best combinations of the variables that can be used to achieve the optimum results of performance.The CR was utilized as a partial substitution to sand.At the same time, the CCR was used as supplementary cementitious material in the SCC mix to achieve the maximum residual compressive strength and minimum weight reduction after subjecting to elevated temperature.Additionally, the optimization aimed to achieve minimum water absorption and minimum weight reductions after subjecting the concrete to H 2 SO 4 and MgSO 4 attacks.The optimization criteria are summarized in Table 11.The multi-objective optimization results obtained from the RSM software are also presented in Table 11.The best performance of the SCC mixes was achieved when 2.9% fine aggregate was partially substituted with CR and 5.5% cement with CCR.The optimal mix proportion achieved had desirability of 77%, a high value.

Conclusions
In this research work, response surface methodology (RSM) was utilized to design the experiment and develop models for predicting the durability performance of SCC mixes in terms of acid and salt attacks and the effects of elevated temperatures on the residual compressive strength and weight of the SCC mixes.The variables considered CR a partial sand replacement and CCR supplementary cementitious material.Hence the following conclusions were obtained from the investigation results and interpretation: 1.
The replacement of up to 10% fine aggregate with CR improved the acid resistance of SCC measured in terms of immersion in H 2 SO 4 and salt resistance measured immersion in MgSO 4 .On the contrary, higher CR content decreased the acid and salt resistance of the SCC.Similarly, partial replacement of up to 10% cement with CCR slightly improved its acid and salt attack resistance, with higher CCR contents having negative effects on the acid and salt attack resistance of the SCC mixes.

2.
The water absorption of the SCC increased with the incorporation of CR as fine aggregate replacement.It decreased with the addition of CCR as SCM.

3.
The heat resistance of the SCC measured in weight reduction and residual compressive strength of the SCC mixes after subjecting to elevated temperatures of 200 • C and 400 • C was decreased with the incorporation of CR as a fine aggregate replacement, with the reduction more pronounced on the higher temperature.4.
The addition of CCR as cement replacement slightly improved the residual compressive strength of the SCC at all temperatures.In terms of weight reduction, CCR increased the weight reduction of the SCC at temperatures above 200 • C.

5.
The models generated using RSM to predict the durability performance and heat resistance of the concrete were significant with high degrees of correlation and predictability.6.
The multi-objective optimization results showed that the best optimum or best mix combination based on minimum weight loss in terms of H 2 SO 4 and MgSO 4 attacks minimum water absorption.After being subjected to elevated temperature, the maximum residual compressive strengths and minimum weight reductions were achieved by replacing 2.9% fine aggregate with CR and 5.5% cement with CCR.

Limitations, Practical Applications, and Future Research
This study was limited to normal strength SCC mixes.The CCR was obtained from only one source.The maximum amount of CCR was limited to 10% as a partial replacement by weight of cement, and the CR was limited to 20% as a replacement by volume of fine aggregate.The research was also limited to utilizing CCR as a partial replacement to cement to mitigate the negative effects of CR on the durability performance of SCC in terms of acid attack resistance, salt attack resistance, water absorption, and effect of elevated temperature under normal and high temperatures (27 • C, 200 • C, and 400 • C).The models developed using RSM can predict the weight reductions of the SCC mixes subjected to 5% H 2 SO 4 and MgSO 4 solutions.It can also be used to predict the weight reductions and residual compressive strength of the SCC mixes after subjecting to normal and elevated temperatures of acid attack resistance, salt attack resistance, and effect of elevated temperature 27 • C, 200 • C, and 400 • C. The models developed to apply to SCC mixes containing 0% to 10% CCR as cement replacements and 0% to 20% CR as fine aggregate replacements.The developed models can predict the durability performance of SCC mixes in terms of acid and salt attack resistance and effects of elevated temperatures using CR, CCR, and fly ash as the variables.This will reduce the need for carrying out experimental work, hence reducing cost and time.The developed SCC mixes can construct structures subjected to acid attacks such as industrial storage and sewage systems structures subjected to salt attacks such as bridge piers under seas or oceans.
Future research directions include studying the effects of higher concentration and concentration times of the acid and salt solutions on the SCC mixes.Additionally, there is a need to study the effects of higher temperatures above 400 • C and higher exposure time on the performance of the SCC mixes containing higher CR and CCR contents.

Figure 7 .
Figure 7. Normal plot against internally studentized residuals for weight reduction models for (a) 200 °C model and (b) 400 °C model.

Figure 7 .
Figure 7. Normal plot against internally studentized residuals for weight reduction models for (a) 200 • C model and (b) 400 • C model.

Figure 8 .
Figure 8. 3D response surface plot for weight reduction models for (a) 200 °C model and (b) 400 °C model.

Figure 8 .
Figure 8. 3D response surface plot for weight reduction models for (a) 200 • C model and (b) 400 • C model.

Table 1 .
Properties of binder materials.

Table 1 .
Properties of binder materials.

Table 2 .
Experimental design mix and constituent materials.

Table 3 .
Results of durability test on SCC mixes.

Table 4 .
ANOVA for durability responses models.

Table 6 .
Results for elevated temperatures of SCC mixes.

Table 7 .
ANOVA for elevated temperature models for SCC mixes.

Table 8 .
Coefficient of determination for residual compressive strength models.

Table 9 .
ANOVA for weight reduction due to elevated temperature models.

Table 10 .
Coefficient of determination for weight reduction models.
• C and 400 • C utilizing CR and CCR as the variables with greater accuracy.

Table 10 .
Coefficient of determination for weight reduction models.

Table 11 .
Optimization criteria and results.