Effect of titanium dioxide as nanomaterials on mechanical and durability properties of rubberised concrete by applying RSM modelling and optimizations

The use of rubber aggregates derived from discarded rubber tyres in concrete is a pioneering approach to replacing natural aggregate (NA) and promoting sustainable building practices. Recycled aggregate in concrete serves the dual purpose of alleviating the accumulation of discarded rubber tyres on the planet and providing a more sustainable alternative to decreasing natural aggregate. Due to fact that the crumb rubber (CR) decreases the strength when used in concrete, incorporating titanium dioxide (TiO₂) as a nanomaterial to counteract the decrease in strength of crumb rubber concrete is a potential solution. Response Surface Methodology was developed to generate sixteen RUNs which contains different mix design by providing two input parameters like TiO₂ at 1%, 1.5%, and 2% by cement weight and CR at 10%, 20%, and 30% as substitutions for volume of sand. These mixtures underwent testing for 28 days to evaluate their mechanical, deformation, and durability properties. Moreover, the compressive strength, tensile strength, flexural strength and elastic modulus were recorded by 51.40 MPa, 4.47 MPa, 5.91 MPa, and 40.15 GPa when 1.5% TiO₂ and 10% CR were added in rubberised concrete after 28 days respectively. Furthermore, the incorporation of TiO₂ led to reduced drying shrinkage and sorptivity in rubberized concrete, especially with increased TiO₂ content. The study highlights that TiO₂ inclusion refines pore size and densifies the interface between cement matrix and aggregate in hardened rubberized concrete. This transformative effect results in rubberized concrete demonstrating a commendable compressive strength comparable to normal concrete.

1 Introduction

Every year, enormous amounts of scrap tires are discarded globally, with the United States, Turkey, and the European Union alone generating an average of 250 million, 10 million, and 3.4 million tons, respectively (Onuaguluchi and Panesar, 2014; Demir et al., 2015; Mohammed et al., 2016). An annual global concern has emerged regarding the improper disposal of more than 500 million waste tires after they have outlived their usefulness (Thomas et al., 2016). He immediate concern surrounding this concerning increase stems from the direct and indirect risks it poses to human wellbeing, ecological integrity, and safety (Chohan et al., 2023). In addition to promoting rodent infestation, disposing of these tires in landfills and dumpsites presents a sustained challenge due to the sluggish biodegradation process that contributes to environmental risks, especially during fire (Pelisser et al., 2011). As a viable remedy to this problem, the reprocessing of used tyres into crumb rubber (CR) for concrete has emerged. This novel methodology not only facilitates the restoration of ecological equilibrium but also possesses considerable economic merit (Guo et al., 2014).

CR extracted from the exterior surface of tire scraps, is employed as a partial substitute for sand in Portland cement (PC) concrete, resulting in what is generally defined as CR concrete, or rubberized concrete. This innovative concrete variant boasts several advantages over traditional concrete, including reduced density (Demir et al., 2015; Mohammed et al., 2016), enhanced ductileness (Shu and Huang, 2014), improved plastic capacity (Mohammed et al., 2011), heightened robustness (Mohammed, 2010), increased impact resistance (Ganjian et al., 2009), superior resistance to infiltration (Bravo and De Brito, 2012), lower thermal conductivity (Li et al., 2004) and enhanced electrical resistivity (Onuaguluchi and Panesar, 2014). Additionally, rubberized concrete is recognized for its superior durability (Youssf et al., 2014). Despite these advantages, rubberized concrete does face certain drawbacks, notably a decline in compressive, tensile, flexural, and splitting strengths, additionally Young’s modulus, with an increasing proportion of CR replacing fine aggregate. The reduced strength can be accredited to the inadequate bond between PC matrix and CR constituent part, which is a result of the hydrophobic characteristics of CR introduced during tire manufacturing with zinc stearate (Youssf et al., 2014). The ability of CR to repel water generates an airtight, non-polar layer, which increases the dimension ITZ between PC matrix and CR constituent part. The presence of a denser region undermines the integrity of the bond, concentrates strain, and ultimately results in the formation of microscopic fissures, which prematurely fail (Mohammed et al., 2012; Sadek and El-Attar, 2015; Li G. et al., 2016; Thomas et al., 2016).

To expand the practical usage and acceptance of CR concrete in construction, efforts have been focused on boosting its strength. Researchers have explored various surface treatment methods for crumb rubber (CR) particles to augment connection between CR and PC mixture. It was conducted experiments to evaluate several methods for treating surfaces, such as water, a carbon tetrachloride solution, and an adhesive admixture cleaner. The findings indicated that the compressive strength (CS) exhibited an increase of up to 57% in comparison to the reference mixture (Rostami et al., 2000). Researchers found success using aqueous NaOH to treat CR surfaces, improving the bond and subsequently elevating strengths (Segre and Joekes, 2000). However, Researchers did not witness significant mechanical strength improvements despite treating CR with NaOH and silane coupling agents (Albano et al., 2005). Authors explored the partial oxidation of CR to create hydrophilic groups, strengthening the bond with the cement matrix, albeit at an increased cost (Chou et al., 2010). It was noticed that the combined NaOH treatment with silica fume in rubberized concrete, noting a reduced strength reduction compared to untreated rubberized concrete (Pelisser et al., 2011). It was found that adding limestone powder, silica fume, and superplasticizer admixtures made the concrete stronger, but not as strong as regular concrete (Corinaldesi et al., 2011; Turki et al., 2012). Huang et al. (Huang B. et al., 2013) and Dong et al. (Dong et al., 2013) experimented with two-phase treatment for surface, finding that employing both stages was more effective in strengthening rubberized concrete. Meddah et al. (Meddah et al., 2014) attempted NaOH treatment and adding fine aggregate to roughen CR’s surface, but this method did not improve concrete strength significantly. Li et al. (Li G. et al., 2016) did a study where they used silane coupling agents and carboxylate styrene-butadiene rubber latex to treat used tire fibers. They saw improvements in the materials’ CS and FS. However, different findings from (Dong et al., 2013; Shu and Huang, 2014) suggest that CR treatment methods might not always make rubberized concrete as strong as regular concrete. This makes it less useful in construction because it is not as strong as regular concrete.

Advancements in nanotechnology offer promising prospects for material development at the nanoscale, enabling precise manipulation of matter at atomic levels. Nano-engineered materials exhibit superior performance with respect to their larger-scale counterparts due to their nano-sized dimensions (Nik et al., 2010; Bahari et al., 2016; Faried et al., 2021; Mousavi et al., 2021). Within the construction sector, the emergence of titanium dioxide (TiO₂) as a nanomaterial has addressed the demand for high-performance materials at a competitive cost. TiO₂ nanoparticles, also known as Titania, have gained popularity in composites (cementitious) owing to their enhanced photochemical activity, stability, and cost-effectiveness (Nik and Bahari, 2012; Yousefi et al., 2013; Li Q. et al., 2016; Loh et al., 2018). The inclusion of nanoparticles, such as titanium, expedites the hydration process by filling microscale voids and providing sites for the early formation of hydration products (Amiri et al., 2012; Bahari et al., 2012; 2015). Studies have shown compelling results regarding the benefits of incorporating titanium nanoparticles into cementitious matrix (Abu el-Hassan et al., 2023; Ghanim et al., 2023). Consequently, Meng et al. (Meng et al., 2012) identified a 45% increase in early-age compressive strength by adding 0.05% titanium nanoparticles to cement, attributing this enhancement to accelerated C-S-H formation and pore reduction. Jayapalan et al. (Jayapalan et al., 2009) talked about how titanium nanoparticles help create nucleation sites in cement hydration products, which speeds up reactions by lowering energy barriers. Zhang et al. (Zhang R. et al., 2015) confirmed significant enhancements in CS and pore refinement in PC mortar due to the addition of titania nanoparticles, linked to accelerated cement hydration. Feng et al. (Feng et al., 2013) observed that cement paste with Titania nanoparticles had higher flexural strength. They said this was because the needle-shaped nanoparticles made the microstructure better, with fewer holes and more compact, smoother microcracks. The use of TiO₂ in rubberised concrete has several benefits, such as heightened mechanical characteristics, including augmented CS and FS, as well as enhanced toughness, resulting in more durable buildings. In addition, the use of TiO₂ improves the durability of rubberised composite by reducing water absorption and enhancing resistance to chemical degradation and freeze-thaw cycles, thus prolonging its service life. The material’s photocatalytic qualities allow for self-cleaning abilities, effectively fighting surface pollutants and preserving cleanliness. Additionally, it offers UV resistance, protecting against deterioration caused by exposure to sunshine. In addition, the use of TiO₂ in rubberised composite augments its flow of fresh mix and decreases friction during the mixing process. This, in turn, allows for simpler placement and finishing of the concrete, resulting in smoother surfaces and better-quality buildings. In summary, incorporating TiO₂ into rubber concrete not only improves its performance and durability but also promotes sustainability by using recycled rubber and minimising environmental harm.

Furthermore, utilising RSM as an optimisation technique to investigate the characteristics of rubberised concrete provides clear benefits compared to other methods. When compared to methods like the Taguchi method, RSM is more efficient because it can give useful results with fewer experimental runs. This streamlines the research process and preserves resources. In addition, RSM’s adaptability in modelling allows for the representation of detailed, non-linear connections between input variables and output responses, which is essential for comprehending the intricate nature of concrete qualities. Furthermore, RSM’s emphasis on local optimisation enables precise revisions towards optimum solutions, which is especially advantageous in concrete research where little modifications may greatly impact results. The interpretability of RSM models boosts their value by enabling investigators to differentiate the impact of individual components and their interactions on certain attributes. By combining RSM with well-crafted experimental designs, one may guarantee a methodical investigation of the design space, resulting in dependable and practical outcomes. In summary, RSM proves to be a reliable and effective technique for optimising the characteristics of rubberised concrete. It provides a well-rounded approach that combines modelling flexibility, experimental efficiency, and interpretative capability. There are many experimental investigations performed on the TiO₂ as nanomaterials (Al-Rbaihat and Al-Marafi, 2023; Bunea et al., 2023; Mostafa et al., 2023; Rawat et al., 2023) and CR as replacement for sand in concrete individually (Shahjalal et al., 2023; Youssf et al., 2023; Aghamohammadi et al., 2024) but there is very limited research were accomplished on rubberised concrete mixed with TiO₂ as nanoscale particle. Therefore, this study aims to experimentally explore the integration of titanium dioxide as a nanomaterial into rubberized concrete. The goal is to perform an optimization framework using RSM and to look at the material’s mechanical characteristics (tensile, compressive, and flexural strengths), deformation characteristics (modulus of elasticity and drying shrinkage), and durability aspects (sorptivity and porosity).

2 Experimental program

2.1 Materials

The major binding ingredient utilized in research work was Portland cement (PC), which conformed to ASTM C150/C150-16e1 (2016) requirements and had a specific gravity (SG) of 3.15. The river sand was employed as a fine aggregate, passing from a 4.75 mm mesh with a SG of around 2.65. Crushed stone, with a size of 20 mm, was employed as a coarse aggregate (CA), with an SG of about 2.60. Moreover, crumb rubber (CR), characterized by a SG of 0.92 and passed through a 1.18 mm sieve, was used as a partial substitution for sand at volumes of 10%, 20%, and 30% in this investigation. Incorporation of TiO₂ powder as a nanomaterial in rubberized concrete was a crucial aspect of the experiment. The average particle size ranged between 10 and 50 nm. To confirm uniform dispersion of nanoscale particles and prevent cohesion or agglomeration when mixed with water, a third-generation superplasticizer was employed (Zhao et al., 2017). To achieve the appropriate ability to flow, a modified polycarboxylate-based superplasticizer (SP) was utilised in the form of a water-based solution to modify the mixes. The substance is in a liquid state and has a pH of 6.2 and a SG of 1.08. Importantly, it contains no chloride ions. Water suitable for drinking and meeting standard quality criteria for concrete mixing was applied in the investigation, maintaining a water-to-cement ratio of 0.35.

2.2 Mix proportions generated by RSM

The Design Expert 10 software was used to develop RSM for optimization. Employing the Central Composite Design (CCD) method, the research focused on two key factors: CR and TiO₂ as nanomaterials. Each variable underwent testing three times, with CR at 10%, 20%, and 30% volume substitution for sand, and TiO₂ at 1%, 1.5%, and 2% addition by weight of PC. This particular approach, previously utilized by researchers (Jo et al., 2015; Al-Fakih et al., 2020; Khed et al., 2020) culminated in 16 distinct mixes. These were generated by the RSM, meticulously exploring numerous Runs of the specified variables outlined in Table 1. Evaluation in the laboratory encompassed examining each mix for its flexural strength (FS), tensile strength (TS), modulus of elasticity (ME), compressive strength (CS), drying shrinkage (DS), sorptivity, and apparent porosity (AP). Moreover, the strength of each mix after a 28-day period was scrutinized. These assessments served as the basis for the RSM study and subsequent optimization of the mixtures. RSM played a pivotal role, not only in scrutinizing the results but also in conducting an analysis of variance (ANOVA) to ensure the reliability of the conducted tests. The study harnessed RSM to discern the most optimal values for the output variables (CS, TS, FS, ME, DS, sorptivity, and AP), factoring in the substantial impact of the input variables (TiO₂ and CR) on the overall outcomes.

Table 1

Table 1. Mix Proportions of CR-Concrete blended with TiO₂.

2.3 Sample preparation and testing methods

2.3.1 Mixing and casting

The process of creating the specimens involved thorough preparation of rubberized concrete blended with TiO₂ as a nanomaterial, following the guidelines specified in BS 1881: Part 125:1986. The procedure started by dry mixing the sand, CA, and CR for 50 s using a concrete mixer. Afterwards, half of the water that was being mixed was added, and the entire mixture was stirred for a duration of 1 min. Besides, PC was thereafter inserted and well blended for an extra minute. To ensure proper dispersion and prevent potential agglomeration of the nanoparticles, TiO₂ and superplasticizer were thoroughly mixed with water for 3–5 min using a high-speed stirrer (Younis and Mustafa, 2018; Orakzai, 2021). This step aimed to enhance flow of fresh mix and facilitate uniform distribution, considering the cohesive nature of nanoparticles. Once the nanoparticle mixture was ready, it was gradually incorporated into the rotary mixer containing the concrete mixture. The entire nanoparticle mixture was systematically added and blended thoroughly with the concrete mixture. Following this meticulous blending process, the samples underwent preparation and curing in controlled laboratory conditions, aligning with the standards outlined in ASTM C192/C192M-19 (2019).

2.3.2 Mechanical properties

After subjecting the rubberized concrete samples blended with varying TiO₂ concentrations to a 28-day curing process in water, a series of experimental assessments were performed. For the assessment of compressive strength, three cubical samples (100 mm × 100 mm × 100 mm) were employed per mix. Testing was performed through a 3,000 kN capacity UTM by following BS EN 12390-3 (2009) guidelines. The direct tensile test involved dog-bone-shaped samples sized at 420 mm × 120 mm × 30 mm was tested based on Japan Society of Civil Engineers (2008). This evaluation was performed at a controlled loading rate of 0.15 mm/min via a 200 kN capacity UTM equipped with built-in LVDTs. Real-time test data was collected and processed by a computer, displayed during testing. Additionally, flexural testing was carried out on beam samples measuring 500 mm × 100 mm × 100 mm through UTM apparatus at a loading rate of 0.05 kN/s by confirming BS EN 12390-5 (2009). Each mix underwent testing with three samples, and the average values of the flexural properties were presented based on these tests.

2.3.3 Deformation characteristics

The analysis of the modulus of elasticity (ME) was achieved through the static procedure specified in ASTM C469 (ASTM C469, 2002). Every mixture was evaluated utilizing four cylinders (300 mm × 150 mm). Two cylindrical samples were designated for the determination of the CS of the mixture (i.e., the stress and ultimate load), whereas the remaining two were used to ascertain the ME. Linear and lateral deformations were measured using a compressor meter in conjunction with dial gauges affixed to the sample. At the time of this measurement, 40% of the maximal load derived from the compressive experiments was applied to the sample. Eq. (1) was utilized in the computation of the ME.

$E=\raisebox{1ex}{$\left({\sigma }_2-{\sigma }_1\right)$}\!\left/ \!\raisebox{-1ex}{$\left({\epsilon }_2-0.000050\right)$}\right.(1)$

where

E is Young’s modulus of elasticity, MPa

σ₂ is the Stress corresponding to 40% of the ultimate load or ultimate Stress, MPa

σ₁ is the stress associated with a longitudinal strain of 0.000050, MPa

${\epsilon }_{{\sigma }_2}$ is the specimen’s lateral strain at mid-height at a Stress, σ₂

The evaluation of shrinkage in rubberized concrete incorporating TiO₂ mixes followed ASTM C157/C157M (2008) standard. Specimens with dimensions of 280 × 50 × 30 mm were made for this assessment. Two specimens from each mixture were made for measuring shrinkage. Over the span of 28 days, these samples were regularly measured for length changes using a length comparator. The monitoring technique included observing variations in the density of the specimens unless the difference between two successive measurements decreased to less than 0.5%. This systematic observation allowed for an accurate assessment of the shrinkage behaviour in the rubberized concrete blends containing TiO₂.

2.3.4 Durability of rubberised concrete

The evaluation of durability for rubberized concrete incorporating TiO₂ involved conducting sorptivity tests and assessing apparent porosity after 28 days. In order to perform the sorptivity test (Jalal et al., 2013), three 30 mm-thick sections were obtained from three CR concrete cubes with dimensions of 100 mm × 100 mm × 70 mm. These cubes had undergone a 28-day curing process. The specimens underwent a drying process in an oven set at 105°C for 24 h and were subsequently cooled in desiccators to ensure uniform conditions. Sidewalls were coated with epoxy resin to prevent water absorption from the sides, enabling absorption solely from the bottom. Placed in pans with tap water at a level 52 mm above the pan’s base, the specimens were allowed to absorb water. Regular mass measurements were taken after draining excess water with an absorbent cloth. A plot was generated using the cumulative absorbed volume of water per unit area against the square root of time. The slope of the fitted line to this plot provided the basis for calculating the sorptivity coefficient using Eq. 2 (Nazari and Riahi, 2011c). This coefficient served as a quantifiable measure of water absorption and permeability, contributing to the assessment of durability in the rubberized concrete incorporating TiO₂.

$f_{sc}=\frac{i}{\sqrt{t}}(2)$

Here,

fsc = coefficient of sorpitivity, mm/√min.,

i = Accumulated water volume per unit area of the surface where water enters, mm and

t = elapsed time, min. For each test, the readings up to 960 s (16 min) were ignored to find the slope of best fitted curve.

To gauge the water absorption capacity of rubberized concrete incorporating TiO₂, three cubes from each series underwent a specific procedure. Initially, these cubes were oven-dried for 24 h at 105°C to establish their initial weight, serving as the starting weight for assessment. Subsequently, all of the samples were submerged in water for a period of 24 h to achieve saturation. Subsequently, the final mass of the specimens was measured as the saturated surface’s dry weight. The weight loss, measured as a percentage, reflected the degree to which the samples absorbed water (Nazari and Riahi, 2010). It has detected that the specimens were dried at 105°C intentionally to avoid potential microstructural alterations in the TiO₂ specimens that higher temperatures might cause, ensuring accurate water absorption measurements (Zhang and Li, 2011). Furthermore, three specimens were utilized to ascertain the apparent porosity (AP). Eq. 3 was applied to calculate AP, providing valuable insights into the material’s pore structure and its capacity for water retention.

$ApparentPorosity=\left|\frac{W_i-W_d}{W_i-W_s}\right|\times 100\%(3)$

Here,

Ww = Mass of the sample after being submerged in water for a duration of 48 h.

Wd = Mass of the specimen after the process of removing moisture by subjecting it to an oven at a temperature of 105°C for a duration of 24 h.

Ws = Mass of the sample while it is suspended in water

3 Results and discussions

3.1 Compressive strength (CS)

Figure 1 shows how the CS changed at day 28 depending on how much TiO₂ nanomaterial was added to different rubberized concrete mixtures. By progressively incorporating CR, the graph organizes mixtures containing an equivalent quantity of TiO₂ in each group. The bar graph shows the average of five mixtures that came from the CCD’s central points (1.5% TiO₂ and 20% CR). This is called MCP. The composition, consisting of a replacement volume of 10% CR for sand and a weight percentage of 1.50% TiO₂, achieved an exceptionally high CS of 51.40 MPa. With a sand replacement volume of 30% CR and a weight percentage of 2% TiO₂, the minimum CS measured after a period of 28 days was 38 MPa. It is worth mentioning that as CR concentration rises, the graph illustrates a significant drop in the CS of concrete. In line with what Najim and Hall (Nazari et al., 2010). Found, this loss of strength is due to CR not sticking well enough to the cemented cement matrix. Bashar claims that the hydrophobic nature of CR particles, which hinders their ability to combine with water and thereby creates a barrier to bonding, negatively affects the strength of composites. In line with earlier studies (Kundan and Sharma, 2020; Assaggaf et al., 2021; Fauzan et al., 2021). CR makes the composite more fragile because it is weaker and has a lower elastic modulus than microaggregate particles. Prior research (Zhang Z. et al., 2015; Alaloul et al., 2020) stated that the accumulation of CR has a detrimental impact on the CS of composites. These findings corroborate these results. Figure 1 shows that TiO₂ can be used as a nanomaterial to strengthen the rubberized concrete matrix, especially when it is mixed with up to 1.5% by weight of Portland cement (PC). The augmentation in Ca(OH)₂ absorption is attributed by researchers to the participation of TiO₂ in the pozzolanic reaction. The development of C-S-H is facilitated as a result of this hydration procedure acceleration (Wang et al., 2018). Operating as a highly efficient infill, the nanoparticles hinder the unrestricted flow of water vapor within the concrete. Evidently, the CS increased when 1.50 percent TiO₂ was incorporated instead of cement but reduced as the proportion of TiO₂ increased (Figure 5). Due to two things, the performance has gone down: the nanoparticles are not evenly distributed in the concrete matrix, and there are fewer Ca(OH)₂ crystals available, which are needed to make C-S-H gels (Najim and Hall, 2013). Higher concentrations of TiO₂ with larger surface areas were also a contributing factor in these samples’ excessive water absorption. In line with the work of Rawat et al. (Rawat et al., 2023). Sorathiya et al. (Sorathiya et al., 2018) and Orakzai (Orakzai, 2021), this study found that using 1% nano-TiO₂ instead of cement increased the CS by 22.6% after 28 days.

Figure 1

Figure 1. CS of rubberised concrete containing TiO₂.

3.2 Tensile strength (TS)

The TS is a critical measure of concrete’s tensile capacity, impacted by both TiO₂ as nanoparticle and CR content as a sand replacement by volume. Figure 2 illustrates the experimental results for rubberized concrete’s TS at 28 days, analysed via ANOVA in the RSM framework. The impact of these factors on the TS is statistically evaluated through RSM analysis. The highest recorded tensile strength, at 4.47 MPa, was achieved with 1.50% TiO2 and 10% CR, while the lowest, at 3.30 MPa, occurred with 2% TiO₂ and 30% CR replacing sand after 28 days Figure 2 highlights a reducing trend in TS with growing CR content in concrete. Partially substituting sand with CR has a detrimental effect on TS due to water’s repulsion on CR, trapping air on its surface, increasing air content in the concrete, and thickening the ITZ between aggregate and PC paste (Khed et al., 2020). This process weakens the bond between PC paste and aggregate. When a load is put on the material, the strain compatibility difference between the hardened state of PC and CR at ITZ causes stress to build up and cracks to form around the CR parts. These cracks have been recognised as weak spots by many studies (Posi et al., 2019; Shaji et al., 2019; Al-Fakih et al., 2020; Shahrul et al., 2021). However, the accumulation of TiO₂ as nanoparticle in rubberized concrete showcases a noticeable enhancement in TS. Figure 2 indicates that optimal strength is achieved when TiO₂ is up to 1.5%, after which strength begins to decline. This observed enhancement in TS might be accredited to the great surface area of TiO₂ nanoparticles, promoting pozzolanic reactions that foster C-S-H gel formation and overall strength increase (Chen et al., 2012). However, further accumulation of TiO₂ leads to decreased strength in rubberized concrete, linked to non-uniform nanoparticle dispersion, hindering Ca(OH)₂ crystal formation crucial for C-S-H gel development (Khed et al., 2020). Comparable remarks were completed by researchers (Rawat et al., 2023).

Figure 2

Figure 2. TS of Rubberised Concrete containing TiO₂.

3.3 Flexural strength (FS)

It is the measure used to quantify the capability of composite to withstand bending. The adhesion between aggregate and PC paste affects the FS (Khed et al., 2020). At the 28-day, the experimental outcomes for rubberized concrete comprising several contents of TiO₂ as nanoparticle are illustrated in Figure 3. The material exhibiting the greatest FS noted by 5.91 MPa when composed of 1.5% TiO₂ and 10% CR by 28 days. Conversely, the least FS was attained by 4.37 MPa at 2% TiO₂ as nanoparticle and 30% CR in place of sand together after 28 days. The trend identified suggests that as CR substitution increases, the FS of concrete declines. The decrease in toughness of CR particles relative to FA which cause of the reduction in FS. In line with this, Sharul et al. (Shahrul et al., 2021) detected that the FS of CR concrete is diminished in comparison to sand particles due to its lesser SG, strength, and load-bearing capacity. Additionally, when sand is replaced with CR, the FS is dropped as a consequence of water repulsion, air entrapment on CR surfaces, and a rise in air content in CR concrete. By increasing the thickness of ITZ that separates aggregate and cement material, their bond is weakened (Khed et al., 2020). The incorporation of TiO₂ significantly contributes to the enhancement of FS. As exposed in Figure 3, the FS of PC rises with the TiO₂ content reaching 1.5% by weight. The observed improvement can be ascribed to the filling of micropores in rubberized concrete by nanoscale particles of TiO₂, which consequently enhance its strength. Nevertheless, as TiO₂ continues to accumulate, its strength diminishes as a result of the uneven distribution of particles; this impedes the formation of Ca(OH)₂ crystals, which are vital for the development of C-S-H gels (Khed et al., 2020). Scholars have encountered comparable observations (Rawat et al., 2023).

Figure 3

Figure 3. Flexural Strength of CR Concrete containing TiO₂.

3.4 Modulus of elasticity (ME)

The ME, defining concrete’s resistance to deformation, is crucial and influenced by multiple features such as concrete’s compatibility, aggregate properties, and the ITZ (Silva et al., 2016). The ME test, following ASTM C 469 (ASTM C469, 2002), is strongly correlated with CS and often expressed by empirical equations derived from experimental studies for various concrete types (Alsalman et al., 2017). For rubberized concrete, equations estimating the modulus of elasticity based on various w/c ratios have been developed Figure 4 illustrates the modulus of elasticity results for sixteen experimental runs conducted with rubberized concrete blended with various TiO₂ concentrations at 28 days. The highest ME was observed by 40.15 GPa with addition of 1.50% TiO₂ and 10% CR, while the lowest ME was noted by 34.52 GPa at 2% TiO₂ and 30% CR replacing sand by volume after 28 days respectively. The reduction in ME with increased CR replacement is accredited to the lower stiffness of rubber elements (Khed et al., 2020). However, a noteworthy trend reversal occurred with TiO₂ addition. Across all CR replacement levels, mixes containing 1.5% TiO₂ exhibited higher ME. This improvement is associated to the nanoscale fineness of TiO₂ particles, filling micro pores within rubberized concrete and enhancing its stiffness. Yet, further TiO₂ addition led to decreased ME in rubberized concrete. This decline is associated with reduced or unavailable Ca(OH)₂ crystals necessary for C-S-H gel formation and non-uniform nanoparticle distribution in matrix (Nazari et al., 2010). These outcomes are dependable with the studies done by Rawat et al. (Rawat et al., 2023).

Figure 4

Figure 4. ME of Rubberised Concrete containing TiO₂.

3.5 Drying shrinkage (DS)

It is a significant concern in concrete in which the volume change associated to water loss within the capillary pores of matrix. Figure 5 illustrates a noteworthy decrease in rubberized concrete shrinkage with increasing TiO₂ as a nanomaterial addition. The shrinkage values for rubberized concrete blended with TiO₂ ranged between 0.05% and 0.066%, higher than the control sample’s shrinkage value of 0.04% and the typical composite shrinkage values reported (ranging from 1,200 × 10⁻⁶ to 1800 × 10⁻⁶) (Zhang et al., 2009). Observations show an increase in concrete shrinkage as the CR content in the mixture rises. This rise is accredited to the lower stiffness of CR constituent part compared to sand, causing increased deformation under drying shrinkage stress (Wang et al., 2019). Also, because CR is flexible, there is less internal restraint within the matrix compared to substituted sand particles. This makes the volume less stable and causes it to shrink more when it dries (Zhang Z. et al., 2015). Moreover, higher CR content leads to improved porosity in the composite owing to the hydrophobic character of CR. This prompts capillary water rise and subsequent volume change upon evaporation, further increasing DS (Huang X. et al., 2013). Adding TiO₂ as a nanomaterial to rubberized concrete dramatically decreased its drying shrinkage at all levels of CR replacement, which is a big surprise. This decrease is ascribed to the nanoscale fineness of TiO₂ particles, which effectively fill micropores within the mixture. During the concrete drying process, excess water evaporates from the surface, creating an air/water interface within capillary pores. The phenomenon of surface tension creates pressure on the innermost layers of such tiny pores, resulting in an inward push that causes the pore structures to contract and decreases the volume of capillaries. The higher the capillary pores, the greater the potential for concrete to shrink. Nanoparticles are very important for lowering the number of capillary voids, which in turn lowers surface tension and, as a result, lessens the shrinkage that happens when water evaporates from the concrete matrix. Joshaghani (Joshaghani, 2018) noted similar observations.

Figure 5

Figure 5. DS of Rubberised Concrete comprising TiO₂.

3.6 Sorptivity test

Following a curing period of 28 days, each specimen underwent a sorptivity test in order to evaluate capillary suction. It was possible to determine the slope of the line that links absorption with the square root of time (Nazari, 2011; Saleem et al., 2021). The absorption curve and square root of the absorption coefficient for concrete mixtures are illustrated in Figure 6 (Chen et al., 2012). The provided data illustrates the sorptive outcomes of rubberized concrete mixtures supplemented with varying quantities of TiO₂ nanomaterials. After a period of 28 days, the mixture containing 2% TiO₂ nanomaterial and 10% CR sand replacement by volume exhibited the lowest sorptivity. The water-only solution exhibited the greatest sorptivity. A higher CR content in concrete is positively correlated with increased sorptivity, according to these findings. This structure forms because rubber is hydrophobic, which raises the capillary water pressure, causes more volume change during evaporation, and then contraction. As a result, a higher CR content leads to more porosity (Huang X. et al., 2013). Notably, adding TiO₂ nanoparticles to rubberized concrete greatly decreased its ability to soak up water, no matter how much CR was replaced. The fluctuations in sorptivity levels exhibit a strong correlation with the properties of the pores. TiO₂ has a lower sorptivity because its particles are smaller and more C-S-H gel forms, which makes the pores smaller and, in turn, the sorptivity lower (Jayapalan et al., 2009; Zhang R. et al., 2015). When samples with more TiO₂ are put into the C-S-H gel, the sorptive levels go down. As a consequence, the interconnection of pores diminishes, resulting in a reduction in absorption. These observations resonate with finding from earlier research (Rawat et al., 2023).

Figure 6

Figure 6. Sorptivity of Rubberised Concrete comprising TiO₂.

3.7 Apparent porosity

Figure 7 illustrates the apparent porosity of rubberized concrete blended with various concentrations of TiO₂ as nanomaterial after a 28-day period. Interestingly, the porosity of all concrete including TiO₂ was lower than control concrete. However, the porosity of the concrete increased with rising CR content, attributed to the hydrophobic character of CR. This characteristic led to capillary water rise and increased drying shrinkage, thereby augmenting porosity with higher CR content (Huang X. et al., 2013). Conversely, across all CR replacement levels, a significant decrease in porosity was detected upon the introduction of TiO₂ as a nanomaterial in rubberized concrete. This decline in porosity can be linked to TiO₂ nanoparticles acting as effective fillers. As the nanoparticle conglomerates expanded, the surrounding void spaces were gradually filled. These “nuclei” significantly accelerated hydration rates, leading to reduced porosity as hydration accumulated rapidly within water-filled pores (Mohammadi et al., 2014). Studies by Mohammadi et al. (Mohammadi et al., 2014) showcased reduced total porosity with the substitution of titanium dioxide to calcium phosphate cement. These observations resonate with finding from earlier research by Riahi and Nazari (Nazari and Riahi, 2011b; 2011a), who observed decreased porosity when PC was partially substituted with TiO₂ at different concentrations. Their results demonstrated that the decrease in porosity was achieved with a TiO₂ content of 3%, showing reductions of 1.64%, 4.3%, 5.67%, and 5.07% in porosity with additions of 1%, 2%, 3%, and 4% TiO₂, respectively. Comparable observations were made by other researchers (Zhang and Li, 2011; Jalal et al., 2013; Sorathiya et al., 2018; Rawat et al., 2022).

Figure 7

Figure 7. Apparent Porosity of Rubberised Concrete comprising TiO₂.

4 RSM analysis

RSM stands out as a powerful statistical and mathematical approach for modelling relationships between independent variables and their corresponding responses. It is widely favoured for its ability to analyse and develop models that effectively capture these connections. Moreover, RSM extends its utility to multi-objective optimization by defining specific goals tied to either the variables or the responses (Adamu et al., 2018). In RSM analysis, several design model types are available, such as CCD models and so on. The selection amongst these options is contingent upon the quantity of factors and the extent of their individual fluctuations (Adamu et al., 2018). Given the unknown mathematical relations between replies and independent factors, the model is often formulated as a linear model represented by a first order function, as shown in Eq. 4.

$y={\beta }_0+{\beta }_1{x}_2+{\beta }_2{x}_2+{\beta }_n{x}_n+ϵ(4)$

In Equation 5, y characterizes the modelled response. Here, $\beta$ o denotes the y-intercept when both X1 and X2 are zero. The coefficients $\beta$ 1 and $\beta$ 2 correspond to the first and second independent factors, correspondingly. X1 and X2 are the coefficients of the first and second factors, correspondingly. The variable ‘e' accounts for the error in the model. However, in cases where the data exhibits curvature, a linear model might not be appropriate to capture the response accurately. In such instances, it is recommended to employ a higher degree polynomial approach, as depicted by the second order function in Eq. 5.

$y={\beta }_0+{\displaystyle \sum _{i=1}^k}{\beta }_i{x}_i+{\displaystyle \sum _{i=1}^k}{\beta }_{ii}{x}_i^2+{\displaystyle \sum _{j=2}^k}{\displaystyle \sum _{i=1}^{j=1}}{\beta }_{ij}{x}_i{x}_j+ϵ(5)$

Eq. 5 expresses the modelled response, where ‘y’ signifies the response being modelled. The variables ‘xi’ and ‘xj’ represent the coded values of the independent factors. In this context, ‘i’ denotes the linear coefficient, ‘j’ signifies the quadratic coefficient, ‘β’ is the regression constant, ‘βo’ represents the y-intercept when both Xi and Xj are zero, ‘k’ is the number of variables involved in the analysis, and ‘e’ accounts for the error (Adamu et al., 2018). The selection of the most suitable model involves considering additional terms and ensuring that the model is not aliased. The highest polynomial from the SMSS is chosen if the supplementary terms are significant. Furthermore, the model summary statistics are examined, and the model that increases the predicted and adjusted R² is selected. The predictive quadratic models for CS, TS, FS, ME, DS, sorptivity and AP were developed, as expressed in Eqs 6–12, utilizing the coded factors TiO₂ (A) and CR (B).

$CS=+47.58-1.82\times A-3.43\times B-0.79\times AB-2.80\times A^2+0.20\times B^2(6)$

$TS=+4.14-0.16\times A-0.30\times B-0.067\times AB-0.25\times A^2+0.018\times B^2(7)$

$FS=+5.47-0.21\times A-0.39\times B-0.089\times AB-0.32\times A^2+0.021\times B^2(8)$

$ME=+38.63-0.77\times A-1.43\times B-0.36\times AB-1.17\times A^2+0.057\times B^2(9)$

$\begin{array}{ll}\hfill DS& =+0.058-0.0035\times A-0.0092\times B-0.00098\times AB\hfill \\ \hfill & -0.00021\times A^2+0.0017\times B^2\hfill \end{array}(10)$

$\begin{array}{ll}\hfill Sorptivity& =+0.037-0.0023\times A+0.0025\times B+0.00051\times AB\hfill \\ \hfill & +0.00061\times A^2-0.00011\times B^2\hfill \end{array}(11)$

$AP=+18.16-1.55\times A+2.37\times B+0.44\times AB+0.14\times A^2+0.30\times B^2(12)$

4.1 Analysis of variance (ANOVA)

At a 5% significance level (Bheel et al., 2023c; 2023e; 2023f; 2023d), ANOVA was used to look at how the factors interacted with each other and how each parameter affected the responses. Subsequently, any model or term with a p-value below 0.05 is deemed significant. The ANOVA findings are shown in Table 2, indicates that all generated models are significant at a significance level of <0.01%. Looking at the specific models, certain terms stand out as significant contributors. For instance, in the CS model, terms A, B, A², and B² demonstrate significance. In the meantime, only terms A, B, and A² are important for the TS, FS, ME, and Sorptivity models. On the other hand, the DS and AP models show significance for terms A, B, and B². The significance of terms A and B across all models highlights the direct influence of both TiO₂ and CR on the responses. Additionally, the significance of A² and B² suggests that the quadratic effects of these independent factors also impact the responses. It is important to note that for the interaction between factors to affect the response, the AB term must be significant.

Table 2

Table 2. ANOVA outcomes.

Table 3 showcases the model validation parameters, revealing remarkably high R² values across all models, fluctuating from 97% to 99.08%. These values signify the strong alignment between the models and the actual data. Additionally, the models exhibit a narrow difference (<0.2) between the adjusted R² and predicted R², meeting the criteria for a good fit. Additionally, the signal-to-noise ratio, which measures adequacy precision, exceeds the threshold of 0.4, confirming the accuracy of the models’ predictions.

Table 3

Table 3. Model verification parameters.

4.2 Response surface plots and models diagnostics

Figures 8–14 show portray the interactions between input parameters and outputs (responses) through contour plots and 3D surface plots. They specifically highlight the relationships between different input variables. For instance, Figure 8A,B demonstrate the 2D diagram and 3D plots for CS, showcasing that a significant concentration of CS was observed at a 1.5% TiO₂ level in the nanomaterial category among all TiO₂ concentrations. Additionally, it is evident that the value of strength notably enhanced when using up to 1.50% TiO₂ in the CR concrete. This enhancement can be owing to TiO₂’s ability, as a nanomaterial, to fill pores and enhance densification in the CR combination. Similar patterns are observed in the remaining response surface graphs for TS, FS, ME, DS, sorptivity, and AP, indicating the impactful relationships between input parameters and outputs.

Figure 8

Figure 8. (A) 2 D contour Diagram and (B) 3 D Surface Plots for CS.

Figure 9

Figure 9. (A) 2 D contour Diagram and (B) 3 D Surface Plots for TS.

Figure 10

Figure 10. (A) 2 D contour Diagram and (B) 3 D Surface Plots for FS.

Figure 11

Figure 11. (A) 2 D contour Diagram and (B) 3 D Surface Plots for ME.

Figure 12

Figure 12. (A) 2 D contour Diagram and (B) 3 D Surface Plots for DS.

Figure 13

Figure 13. (A) 2 D contour Diagram and (B) 3 D Surface Plots for Sorptivity.

Figure 14

Figure 14. (A) 2 D contour Diagram and (B) 3 D Surface Plots for AP.

The RSM evaluation comprises essential diagrams, including crucial model diagnostic graphs like the normal diagram of residuals (Figures 15–21). These graphs, split into (a) run versus predicted and (b) real versus predicted, serve to validate the significance of the quadratic models used for rubberized concrete with TiO₂ as nanomaterials. The plots depict residuals plotted against the run number (Figures 15–21A), showcasing a consistent distribution without any observable model drift. The data points, encapsulated within red boundary lines, maintain a sinusoidal pattern, affirming the stability of the model throughout the process (Memon et al., 2020). Additionally, the predicted versus actual plot (Figures 15–21B) demonstrates strong agreement between experimental and predicted 28-day data for CS, TS, FS, ME, DS, sorptivity, and AP models. The close alignment of distribution points and the minimal variance between experimental and predicted values confirm this agreement. Notably, the points align closely along a straight line, indicating a normal distribution pattern, further validating the model’s accuracy.

Figure 15

Figure 15. (A) Residual versus Runs plots and (B) Predicted against Actual diagrams for CS.

Figure 16

Figure 16. (A) Residual versus Runs plots and (B) Predicted against Actual diagrams for TS.

Figure 17

Figure 17. (A) Residual versus Runs plots and (B) Predicted against Actual diagrams for FS.

Figure 18

Figure 18. (A) Residual versus Runs plots and (B) Predicted against Actual diagrams for ME.

Figure 19

Figure 19. (A) Residual versus Runs plots and (B) Predicted against Actual diagrams for DS.

Figure 20

Figure 20. (A) Residual versus Runs plots and (B) Predicted against Actual diagrams for Sorptivity.

Figure 21

Figure 21. (A) Residual versus Runs plots and (B) Predicted against Actual diagrams for AP.

4.3 Multi-objective optimization

It referred to as multi-response optimization is a technique aimed at identifying the most beneficial variables to maximize various responses simultaneously. Real-world optimization problems often involve multiple conflicting objectives, necessitating the search for several optimal solutions (Bheel et al., 2023b; 2023a). Hence, this approach becomes the preferable strategy (Liu et al., 2017; Habibi et al., 2021). Optimization focuses on the model’s independent variables, enhancing their efficacy in the process. The objective function guides this optimization, setting the goals for the variables and potentially encompassing significance levels (Liu et al., 2017; MIR et al., 2017). In this process, both independent and dependent variables have objectives established using diverse criteria (Burke and Kendall, 2005; Waqar et al., 2023a). The ultimate aim is to attain objective functions without compromising any of the responses. The desired values, which are between 0 and 1, are what matter in the optimization process for each response, which ranges from 0 to 1 (Waqar et al., 2023b; 2023a; Khan et al., 2023). Elevating the DJ value enhances the favourability of the outcome, often represented as a percentage. In multi-objective optimization, the geometric mean of how desirable each response is found. This lets you find the desirability value of the composite response, which is shown in Eq. 13 (Achara et al., 2019).

$D={\left(d_1^{r1}\times d_2^{r2}\times d_3^{r3}\times \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \cdots \times d_n^{rn}\right)}^{\frac{1}{n}}(13)$

In this context, “n” represents the total number of responses considered during the optimization process, while “ri” denotes the assigned weight of significance to each function, ranging from 1 (least important) to 5 (most crucial). In this specific model, the desirability limit was set between 0% and 1%, where a value closer to 1% indicates a more favourable outcome, strengthening the optimized results impact on determining the dependent variable. These parameters outline the optimization goals of the variables. Notably, the optimization aims to maximize the responses for CS, TS, FS, and ME, whereas it aims to minimize responses for DS, sorptivity, and AP. The optimized results indicate maximum values for CS (49.47 MPa), TS (4.31 MPa), FS (5.69 MPa), ME (39.41 GPa), DS (0.051%), sorptivity (0.035 mm/s^0.5), and AP (16.48%), detailed in Table 4. The variability analysis of the model reflects a desirability of 66.10%, indicating the models ability to produce relevant and promising outcomes. These desirability results stem from the optimization method as shown in Table 4.

Table 4

Table 4. Optimization of outcomes.

4.4 Model validation

Experimental validation aimed to understand the disparities between the predicted response values derived from the optimization process and the actual experimental values. The optimal parameters, concrete samples were created, incorporating various proportions of CR as a sand substitute alongside TiO₂ nanomaterials as cementitious components. The comparison between predicted and experimental values of CS, TS, FS, ME, DS, Sorptivity and AP is expressed as a percentage error, i.e 2.45%, 2.80%, 1.93%, 1.50%, 5.88%, 5.71%, and 4.92% respectively and all responses exhibit an error percentage of less than 6%. This low error percentage across all responses signifies a high level of precision in approach. The discrepancy ($\delta$) between empirical and anticipated readings for individual responses was calculated using Eq. 14, demonstrating the model’s precision in predicting outcomes accurately. In essence, this signifies a high degree of consistency between the anticipated and observed values, affirming the model’s accuracy.

$\delta =\left|\frac{{\vartheta }_E-{\vartheta }_P}{{\vartheta }_P}\right|\times 100\%(14)$

5 Conclusion

This research endeavour focuses on exploring the impact of titanium dioxide as nanomaterials on rubberized concrete, specifically delving into its influence on mechanical, deformation, and durability aspects. Drawing insights from the obtained results, the following key conclusions emerge:

• The introduction of titanium dioxide nanoparticles notably enhanced the mechanical attributes of rubberized concrete. The optimum CS, TS, FS, and ME were recorded by 51.40 MPa, 4.47 MPa, 5.91 MPa, and 40.15 GPa when 1.5% TiO₂ and 10% CR were added in rubberised concrete after 28 days respectively. After addition of 1.5% of TiO₂ along with 10% of CR, these all properties were getting reduced after 28 days respectively.

• The enhancements in the mechanical characteristics of the rubberized concrete stemmed from the uniform distribution of TiO₂ nanoparticles. Acting as nucleation sites for cement hydrates, these nanoparticles facilitated improved performance. Their sizable surface area accelerated the hydration rate, effectively contributing to the observed improvements.

• As the content of TiO₂ in the mixture increases, both the drying shrinkage and sorptivity of rubberized concrete decrease. These findings validate that water absorption percentage and capillary absorption height diminish with the application of TiO₂ nanoparticles. Notably, the ITZ in concrete experiences improvement attributed to the heightened reactivity and the filler effect induced by TiO₂ nanomaterial.

• The integration of TiO₂ nanoparticles led to a notable reduction in the apparent porosity of rubberized concrete. Acting as nanofillers, these nanoparticles enhanced the concrete’s resistance to water permeability, contributing to this reduction in porosity.

• Augmenting the fraction of nanoparticles frequently bolsters the durability of the resultant rubberized concrete. This improvement can be linked to the finer particles integrated into the cement mix and the reinforcing filler effect imparted by the nanoparticles.

• Predictive models for responses were formulated and validated through both ANOVA and experimental validation. These models exhibit robustness, boasting high coefficient of determination (R²) values within the range of 97%–99%. Employing multi-objective optimization, we pinpointed the optimal input variable values at 1.50% for TiO₂ nanoparticles and 10% for CR. These values were attained with a desirability value of 66.10%, signifying a favourable outcome according to the optimization process.

• Based on the experimental findings, employing 1.5% titanium dioxide as a nanoparticle in rubberized concrete yields optimal results, suggesting its favourable application within the construction industry. This recommendation stems from observed outcomes that highlight its effectiveness in practical construction scenarios.

6 Future recommendations

• Extend testing periods beyond 28 days to assess long-term performance and durability of CR concrete blended with TiO₂.

• Optimize the proportion of CR and TiO₂ used in high strength concrete in order to achieve the optimal balance between improving characteristics and maintaining structural soundness.

• Expand the scope of assessment to include additional characteristics such as abrasion resistance, chloride ion penetration resistance, and resistance to chemical attack of rubberized concrete inclusion of TiO₂ as nanoscale particle.

• Conduct a life cycle assessment to examine the ecological consequences of producing rubberized concrete addition with TiO₂ in comparison to conventional concrete.

• Validate laboratory results by conducting field tests on rubberized concrete accumulation with TiO₂ as nanoparticle and applying them to real-world building situations to ensure practicality and applicability.

Data availability statement

The raw data supporting the conclusion of this article will be made available by the authors, without undue reservation.

Author contributions

GA: Conceptualization, Formal Analysis, Methodology, Resources, Writing–review and editing, Funding Acquisitions. IC: Data curation, Formal Analysis, Software, Writing–review and editing. MA: Methodology, Validation, Visualization, Writing–review and editing. NB: Conceptualization, Data curation, Investigation, Methodology, Writing–original draft, Writing–review and editing. MA: Data curation, Methodology, Software, Writing–review and editing. TN: Formal Analysis, Validation, Visualization, Writing–review and editing. YG: Formal Analysis, Methodology, Validation, Visualization, Writing–review and editing. HA: Conceptualization, Formal Analysis, Methodology, Visualization, Writing–review and editing.

Funding

The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This work is funded and supported by the Deanship of Scientific Research at Najran University under the Research Priorities and Najran Research funding program grant code (NU/NRP/SERC/12/12).

Acknowledgments

The authors are thankful to the Deanship of Scientific Research at Najran University for funding this work under the Research Priorities and Najran Research funding program grant code (NU/NRP/SERC/12/12).

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Abbreviations

CR, Crumb Rubber; UV, Ultraviolet; TiO₂, Titanium Dioxide; SG, Specific Gravity; RSM, Response Surface Methodology; CA, Coarse Aggregate; RA, Rubber Aggregates; SP, Superplasticizer; NA, Natural Aggregate; CCD, Central Composite Design; MPa, Mega Pascal; DS, Drying Shrinkage; GPa, Giga Pascal; AP, Apparent Porosity; PC, Portland Cement; ANOVA, Analysis Of Variance; CS, Compressive Strength; UTM, Universal Testing Machine; TS, Tensile Strength; JSCE, Japan Society of Civil Engineers; FS, Flexural Strength; LVTD, Longitudinal Variable Displacement Transducer; ME, Modulus of Elasticity; Ca(OH)₂, Calcium Hydroxide; NaOH, Sodium Hydroxide; ITZ, Interficial Transition Zone; -S-H, Calcium Silicate Hydrates; SMSS, Sequential Model Sum of Squares.

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