Experimental and RSM-based optimization of sustainable concrete properties using glass powder and rubber fine aggregates as partial replacements

2.1.1 Portland cement

Ordinary Portland cement (OPC) CEM I (42.5 N) was used as the primary binder in this study. The cement was tested in accordance with the Egyptian Standard Specification ESS 4756-1/2007 [75] to ensure compliance with quality standards. The chemical analysis showed that the cement contains 63.2 % calcium oxide (CaO), 22.45 % silica (SiO₂), 4.8 % alumina (Al₂O₃), and 3.2 % iron oxide (Fe₂O₃), with a loss on ignition (LOI) of 2.25 %, confirming its suitability for concrete production (Table 1).

2.1.2 Glass powder (GP)

In this study, GP was used to partially replace OPC at 15 %, 25 %, and 35 % by weight. GP was produced from locally sourced post-consumer clear glass bottles through cleaning, drying, crushing, grinding, and sieving to achieve cement-like fineness (Figure 2). The chemical composition of GP was conducted to determine the composition of the produced GP, and the results are presented in Table 1. The analysis confirmed a high SiO₂ content (73.0 %) along with notable amounts of CaO (10.8 %) and Na₂O (11.4 %). X-ray diffraction (XRD) analysis confirmed the amorphous structure of GP, supporting its pozzolanic reactivity and suitability as a supplementary cementitious material.

Figure 2:

Production process of GP.

2.1.3 Rubber fine aggregates

Rubber fine aggregates (RF) were used as a partial replacement for natural fine aggregates (NF) at levels of 15 %, 25 %, and 35 % by weight. RF was obtained from discarded tires, which were pre-processed to remove steel wires and contaminants, shredded, ground, and sieved through a 4.76 mm mesh to achieve uniform particle size (Figure 4). The physical properties of NF and RF are summarized in Table 2. RF exhibited a significantly lower specific gravity (1.06 g/cm³) compared to NF (2.62 g/cm³). While NF showed an absorption capacity of 0.82 %, RF displayed negligible water absorption due to its non-porous surface. A sieve analysis (Figure 5) confirmed that the particle size distribution of RF was comparable to that of NF. The surface texture of the raw RF material is shown in Figures 3–5.

Figure 3:

Raw rubber material showing a smooth surface texture before processing into rubber fine aggregates.

Figure 4:

Production process of rubber fine aggregates (RF).

Figure 5:

Sieve analysis of NF and RF.

2.2.1 Analysis and optimization process

The optimization process involved evaluating the effects of [OPC-GP]% and [NF-RF]% on slump, compressive strength at 7 and 28 days, splitting tensile strength, and modulus of elasticity at 28 days using ANOVA. Statistical significance was determined through R ² values, p-values, t-tests, and diagnostic plots to ensure model adequacy. Each response was transformed into a desirability value (0–1) based on how well it met predefined performance criteria. Constraints were defined for all responses, and four optimization trials were conducted using varying goal settings to assess robustness (Table 7). A composite desirability index was used for multi-response optimization. Desirability plots (Figure 14) revealed that values near 1.0 consistently occurred when both [OPC-GP]% and [NF-RF]% exceeded 15 %. Based on this, Trial 1 was selected at 15 % GP and 15 % RF, achieving a desirability score of 1.000. Its optimality within the design space was confirmed through the ramp function graph (Figure 15). A comparison of all trials is provided in Table 9. The Trial 1 mix was then validated experimentally, with percentage errors for all responses remaining below 1.5 % (Table 10), confirming the model’s predictive accuracy. This approach ensures a balanced mix in terms of mechanical performance and workability, supporting a systematic approach for optimizing sustainable concrete mixtures.

3.2.1 Compressive strength results

The compressive strength of all mixtures was evaluated at 7 and 28 days, as shown in Table 5 and illustrated in Figures 8 and 9. The reference mixture (GP0RF0), composed of 100 % OPC and NF, achieved 32.89 MPa at 7 days and 40.37 MPa at 28 days. It also recorded the highest slump value of 95 mm (Figure 7), indicating good workability and cohesiveness.

Figure 8:

Compressive strength of concrete mixtures.

Figure 9:

Failure behavior of concrete samples under compression.

When OPC was partially replaced with GP (GP15RF0 to GP35RF0), compressive strength progressively declined with increasing replacement levels. At 28 days, strength decreased from 41.8 MPa (103.54 %) in GP15RF0 to 39.6 MPa (98.09 %) in GP25RF0 and 35.97 MPa (89.10 %) in GP35RF0. Slump values also declined, from 90 mm in GP15RF0 to 85 mm in GP25RF0 and 82 mm in GP35RF0 (Figure 7). These results suggest that the reduction in CaO content (10.8 % in GP vs. 63.2 % in OPC, Table 1) and the increased fineness of GP likely raised water demand and limited effective hydration at higher replacement levels. This interpretation is consistent with findings by Matos et al. [50] and Nia et al. [24], who reported that high GP dosages can reduce strength due to cement dilution and increased water demand from fine particles, despite the pozzolanic benefits at moderate levels. The higher strength in GP15RF0 may be attributed to pozzolanic activity and improved particle packing at a moderate GP content, an effect also observed by Ramdani et al. [67] and Su and Xu [27], who highlighted the positive influence of GP on strength and densification when used in limited amounts. However, reduced flowability and higher internal friction at elevated GP levels may have hindered compaction efficiency, consistent with Mehta and Monteiro [85] and further supported by El Marzak et al. [69], who demonstrated that excess fines from SCMs and rubber can impair rheology and thus affect strength. This behavior is reflected in Figure 9, where GP35RF0 exhibited more brittle and irregular failure surfaces than GP15RF0.

Replacing NF with RF (GP0RF15 to GP0RF35) also resulted in reduced compressive strength. At 28 days, strength decreased from 38.6 MPa (95.62 %) in GP0RF15 to 36.6 MPa (90.66 %) in GP0RF25 and 33.7 MPa (83.48 %) in GP0RF35. Slump values also declined from 95 mm to 91 mm and 85 mm, respectively (Figure 7). According to Table 2, RF has a lower specific gravity (1.06 g/cm³) and negligible water absorption compared to NF (2.62 g/cm³, 0.82 %), which may reduce packing density and influence the aggregate–paste interaction. The elastic and smooth surface of RF (Figure 3) may also reduce mechanical interlock. These effects are consistent with the findings of Letelier et al. [19] and Mo et al. [66], who showed that rubber particles introduce internal voids, reduce stiffness, and weaken the interfacial transition zone (ITZ), ultimately leading to strength loss. As shown in Figure 9, GP0RF35 exhibited more extensive surface cracking than GP0RF15. These outcomes also align with Dils et al. [86] and Horszczaruk et al. [87], who reported that deformable rubber aggregates impair structural integrity by reducing packing efficiency and introducing high deformability zones.

Mixtures combining GP and RF (GP15RF15 to GP15RF35) exhibited similar trends. GP15RF15 achieved a 28-day strength of 40.1 MPa (99.33 %), close to the reference. Strength declined to 37.4 MPa (92.64 %) in GP15RF25 and 34.2 MPa (84.72 %) in GP15RF35. Slump values also decreased, from 92 mm in GP15RF15 to 89 mm and 84 mm, respectively (Figure 7). The performance of GP15RF15 indicates a balanced effect, where moderate GP and RF contents maintained strength and workability. This result is in agreement with Ramdani et al. [67] and Mo et al. [66], who found that combining rubber and GP can offset strength losses caused by rubber alone due to the densifying and pozzolanic action of GP. However, increasing RF further resulted in lower strength and more fragmented fracture surfaces, as seen in Figure 9 for GP15RF35, reflecting a threshold beyond which the weakening effects of rubber dominate. This trend was also noted by El Marzak et al. [69].

In summary, compressive strength decreased with increasing GP and RF content, particularly beyond 15 %. This trend corresponded with lower slump values (Figure 7), indicating reduced flowability and compaction efficiency. The GP15RF15 mixture maintained strength comparable to the control with consistent failure behavior. These findings are in strong agreement with recent literature, including Letelier et al. [19], Mo et al. [66] and Matos et al. [50], which collectively confirm that moderate substitution levels of GP and RF can be optimized to retain structural performance, while excessive use negatively affects both workability and compressive strength due to microstructural inefficiencies.

3.2.2 Splitting tensile strength

The tensile strength results at 28 days are summarized in Table 6 and illustrated in Figure 10. The control mixture (GP0RF0) achieved the highest tensile strength of 5.5 MPa (100 %). Replacing cement with 15 % glass powder (GP15RF0) slightly improved the tensile strength to 5.8 MPa (105.45 %), which can be attributed to the filler effect of GP and its high SiO₂ content (73.0 %) (Table 1). These characteristics enhance matrix density and particle packing, thereby improving tensile behavior at lower replacement levels. This result aligns with the findings of Navaneetha et al. [10] and Matos et al. [50], who reported improved mechanical performance at moderate GP levels due to increased pozzolanic activity and refined pore structure. Similarly, Nia et al. [24] confirmed that GP enhances long-term strength through delayed pozzolanic reactions and additional C–S–H gel formation.

Figure 10:

Splitting tensile strength of concrete mixtures.

However, increasing the GP content to 25 % and 35 % led to reduced tensile strength values of 5.3 MPa (96.36 %) and 4.6 MPa (83.64 %), respectively. This decline is likely due to the higher water demand and delayed pozzolanic activity at elevated GP levels, which reduce the matrix’s early-age strength. These trends are consistent with the dilution effects and strength reductions reported by Jia et al. [23] and Tahwia et al. [26] at higher GP levels.

When replacing NFs with RFs, tensile strength decreased progressively with increasing RF content. GP0RF15 achieved a tensile strength of 5.08 MPa (92.36 %), while GP0RF25 and GP0RF35 decreased further to 4.62 MPa (84.00 %) and 4.21 MPa (76.55 %), respectively. This reduction is primarily attributed to the lower specific gravity of RF (1.06 g/cm³, Table 2), which weakens the interfacial bond between the cement paste and the aggregates, thereby reducing load transfer efficiency. Additionally, the irregular shape and elastic nature of RF particles increase void content and hinder stress distribution. These observations are consistent with findings by Letelier et al. [19], Mo et al. [66] and El Marzak et al. [69], who reported strength reductions in rubberized mixes due to poor interfacial bonding and increased porosity.

In combined replacement scenarios, the mixture GP15RF15 maintained a relatively high tensile strength of 5.35 MPa (97.27 %), suggesting a synergistic effect between moderate GP content and RF inclusion. This balance enhances matrix compactness while partially mitigating the negative impact of RF. Such synergy was also observed by Ramdani et al. [67] and Letelier et al. [19], who found that GP’s pozzolanic and filler effects can compensate for the mechanical weaknesses introduced by rubber aggregates. However, as RF content increased further in mixes GP15RF25 and GP15RF35, tensile strength declined to 4.8 MPa (87.27 %) and 4.32 MPa (78.55 %), respectively. These reductions can be attributed to the lower stiffness, hydrophobic surface, and poor interfacial bonding of rubber particles, which negatively affect stress transfer and crack resistance.

The trends presented in Figure 10 confirm that tensile strength generally decreases as the replacement levels of both GP and RF increase. The reduction is more pronounced at higher RF levels due to its low density, deformability, and bond-disrupting characteristics. These findings underscore the importance of balancing GP and RF content to achieve an optimal trade-off between mechanical performance and sustainability. A moderate replacement level, such as 15 % GP and 15 % RF, proves effective in maintaining acceptable structural performance while promoting eco-efficiency.

3.2.3 Modulus of elasticity

The modulus of elasticity results at 28 days are presented in Figure 11. The control mixture (GP0RF0) recorded the highest modulus value of 26,221.3 MPa (100 %). When 15 % of cement was replaced with glass powder (GP15RF0), the modulus slightly increased to 26,581.4 MPa (101.37 %). This improvement can be attributed to the high SiO₂ content of the glass powder (73.0 %, Table 1), which enhances particle packing and contributes to matrix densification. Similar findings were reported by Matos et al. [50] and Nia et al. [24], who observed improved microstructure and stiffness in mixtures incorporating moderate glass powder due to its pozzolanic activity and filler effect.

Figure 11:

Modulus of elasticity of concrete mixtures.

However, higher GP replacement levels (GP25RF0 and GP35RF0) resulted in reduced modulus values of 25,896.5 MPa (98.76 %) and 24,112.3 MPa (91.96 %), respectively. These reductions align with observations by Matos et al. [50] and Nia et al. [24], who reported that excessive GP content may lead to a dilution effect and delayed pozzolanic reaction, which in turn lowers stiffness and overall matrix integrity.

For rubber fine aggregate (RF) replacements, the modulus of elasticity consistently decreased with increasing RF content. The modulus values for GP0RF15, GP0RF25, and GP0RF35 were 25,724.5 MPa (98.11 %), 24,552.5 MPa (93.64 %), and 23,734.1 MPa (90.51 %), respectively. This trend is consistent with findings from Mo et al. [66] and El Marzak et al. [69], and Zhai et al. [68], who highlighted that rubber particles exhibit low stiffness, high deformability, and weak bonding at the interfacial transition zone (ITZ), all of which contribute to reduced elastic performance. The irregular surface and low specific gravity (1.06 g/cm³, Table 2) of RF also disrupt the matrix continuity and contribute to stiffness loss.

In the case of combined GP and RF replacements, the mixture GP15RF15 demonstrated a modulus of 25,914.5 MPa (98.83 %), indicating a favorable synergy between moderate GP content and limited RF replacement. Ramdani et al. [67] and Letelier et al. [19] reported similar observations, where glass powder improved the microstructure and partially compensated for the adverse effects of rubber inclusion on mechanical performance.

However, higher RF contents in the combined mixes, such as GP15RF25 and GP15RF35, led to further reductions in modulus to 24,827.7 MPa (94.69 %) and 23,831.2 MPa (90.88 %), respectively. These findings are in line with those of Mo et al. [66] and El Marzak et al. [69], who confirmed that beyond certain thresholds, rubber content dominates the mechanical response, resulting in reduced stiffness and weaker structural behavior.

Overall, the trend in modulus of elasticity is consistent with the patterns observed in compressive and tensile strength, supporting the correlation between elastic stiffness and load-bearing capacity. The GP15RF15 mixture exhibited the most balanced performance, combining improved matrix densification from GP with an acceptable level of rigidity despite RF inclusion. These results emphasize the need to optimize the proportions of GP and RF to maintain mechanical performance while promoting sustainability in concrete production (as concluded in Section 3.2).

3.2.4 Heatmap correlation analysis and results

A heatmap correlation analysis was conducted to examine the relationships between [OPC-GP]%, [NF-RF]%, and key performance indicators: slump, compressive strength, splitting tensile strength, and modulus of elasticity. The correlation matrix, generated using Python and visualized with Seaborn (Figure 12), provided insights into how changes in material composition influence both fresh and hardened concrete properties.

Figure 12:

Correlation heatmap; factors and response metrics.

The analysis showed a strong negative correlation between [OPC-GP]% and slump (r = −0.67), which aligns with the reduced workability observed in Section 3.1 as glass powder content increased. For instance, slump values decreased from 95 mm in GP0RF0 to 82 mm in GP35RF0. This reduction is attributed to the high surface area and fineness of the glass powder, which elevates water demand and internal friction. These findings are consistent with the conclusions of Sun et al. [82], who reported that high-surface-area materials lower workability due to increased internal resistance.

[OPC-GP]% exhibited minimal correlation with compressive strength at 7 days (r = 0.01), compressive strength at 28 days (r = 0.04), Splitting tensile strength at 28 days (r = 0.04), and modulus of elasticity at 28 days (r = −0.07). These weak associations suggest that the impact of glass powder on mechanical properties is nuanced, depending on the balance between pozzolanic reactivity and cement dilution. Conversely, [NF-RF]% displayed strong negative correlations with all mechanical properties: compressive strength at 7 days (r = −0.74), compressive strength at 28 days (r = −0.75), splitting tensile strength at 28 days (r = −0.77), and modulus of elasticity at 28 days (r = −0.71). These results are aligned with experimental outcomes discussed in Sections 3.2.1–3.2.3, where increasing rubber aggregate content reduced performance due to its low specific gravity, elastic nature, and limited bonding ability (see Table 2 and Figure 3).

Slump correlated positively with compressive strength at 7 days (r = 0.60), compressive strength at 28 days (r = 0.61), tensile strength at 28 days (r = 0.57), and modulus of elasticity at 28 days (r = 0.66). These moderate to strong correlations underscore the role of adequate workability in enhancing mechanical performance through improved compaction and reduced voids. For example, GP15RF0 and GP15RF15, with slump values of 90 mm and 92 mm, recorded high compressive strength values of 41.8 MPa and 40.1 MPa at 28 days, respectively.

Compressive strength at 7 days strongly correlated with compressive strength at 28 days (r = 0.94), tensile strength at 28 days (r = 0.96), and modulus of elasticity at 28 days (r = 0.95), indicating consistent strength progression. Similarly, compressive strength at 28 days correlated almost perfectly with splitting tensile strength (r = 0.99) and modulus of elasticity (r = 0.99), reinforcing its reliability as a predictor of other mechanical outcomes. Moreover, tensile strength and modulus of elasticity at 28 days showed a near-perfect correlation (r = 0.98), highlighting the intrinsic link between tensile behavior and material stiffness. This further supports the observations in Section 3.2.3 and emphasizes the importance of integrated mix design.

In summary, the correlation analysis confirms that moderate GP levels improve compressive strength and modulus of elasticity, likely due to enhanced pozzolanic action and particle packing. This is supported by Mhaya et al. [73], who showed that GP refines pore structure and densifies the matrix, reducing chloride penetration, enhancing corrosion resistance, and lowering capillary permeability in GP–rubber concretes. GP also promotes cohesive ITZ formation and C–S–H development, contributing to long-term durability. Conversely, higher RF content correlates with reduced mechanical performance due to its deformability, low specific gravity, and weak matrix bonding. However, RF’s hydrophobic and elastic nature can mitigate crack propagation and water absorption, as evidenced by reduced surface erosion in GP–RF blends. These findings underscore the importance of optimizing GP and RF ratios to achieve both mechanical strength and durability, supporting sustainable concrete design.

3.3.1 ANOVA results and model significance

The statistical significance of the developed models was assessed using Analysis of Variance (ANOVA), as summarized in Table 6. All models were highly significant, with p-values less than 0.0001, confirming strong correlations between the process factors ([OPC-GP]% and [NF-RF]%) and the responses. For slump, the model showed an F-value of 187.61, with significant contributions from both linear and quadratic terms, especially [NF-RF]% (F = 130.95). The compressive strength at 7 days model achieved an F-value of 209.49, where the quadratic term of [OPC-GP]% had a dominant influence (F = 164.35). For compressive strength at 28 days, the model demonstrated an F-value of 209.86, with the linear term of [NF-RF]% exerting the most substantial effect (F = 751.75). Similarly, the splitting tensile strength at 28 days model recorded an F-value of 168.84, dominated by the linear and quadratic terms of [NF-RF]% (F = 614.23 and F = 177.03, respectively). The modulus of elasticity at 28 days achieved an F-value of 93.39, with significant contributions from the linear term of [NF-RF]% (F = 333.82) and the quadratic terms. The low residual mean square values across all models further confirm their precision and reliability in predicting the behavior of concrete mixtures with varying levels of glass powder and rubber fine aggregates.

3.3.2 Model validation

The accuracy and reliability of the models were validated using statistical metrics, including R ², adjusted R ², predicted R ², and adequate precision, as summarized in Table 7. All responses exhibited R ² values greater than 0.99, indicating that the models explain more than 99 % of the variability in the responses. The adjusted R ² values were closely aligned with the R ² values, confirming the models’ robustness even after accounting for the number of predictors. The predicted R ² values ranged between 0.93 and 0.98, demonstrating strong predictive accuracy for unseen data. Additionally, the adequate precision values for all responses exceeded 26, signifying an adequate signal-to-noise ratio, which ensures the models can effectively navigate the design space. The low coefficients of variation (C.V.%), ranging from 0.78 % to 2.5 %, further highlight the consistency and precision of the models. These results validate the models’ reliability for predicting the slump, compressive strength, splitting tensile strength, and modulus of elasticity of concrete mixtures with varying levels of glass powder and rubber fine aggregates. It is important to note that while the developed RSM models show excellent predictive accuracy within the tested range (0–35 % replacement levels) for both factors, their application beyond this domain may be limited. RSM is inherently sensitive to the experimental range, and extrapolation should be approached with caution to avoid unreliable predictions.

3.3.3 Diagnostics and surface plots

The reliability of the RSM models was validated using diagnostic and response surface plots, as shown in Figure 13. The normal probability plots of studentized residuals (Figure 13-I) confirm normally distributed residuals, ensuring unbiased predictions. The predicted versus actual plots (Figure 13-II) demonstrate strong linear correlations, validating the models’ accuracy. The perturbation plots (Figure 13-III) highlight the sensitivity of responses to changes in individual factors ([OPC-GP]% and [NF-RF]%), emphasizing the dominant influence of quadratic terms, particularly on compressive strength and modulus of elasticity.

Figure 13:

Diagnostics plots: (I) normal plot of the studentized residual, (II) predicted versus actual values plot, (III) perturbation plot, and (IV) 3D surface plot, for: (a) slump, (b) compressive strength at 7 days (c) compressive strength at 28 days, (d) splitting tensile strength at 28 days, (e) modulus of elasticity at 28 days.

The 3D surface plots (Figure 13-IV) illustrate the interaction effects of [OPC-GP]% and [NF-RF]% on key responses. For Slump, workability decreases with increasing [OPC-GP]% and [NF-RF]%, consistent with Section 3.2.1, where higher glass powder content increased water demand and rubber aggregates disrupted matrix continuity. For compressive strength, surface plots at 7 and 28 days show a parabolic trend: moderate [OPC-GP]% (15 %) enhances strength due to the pozzolanic activity of glass powder, while excessive [NF-RF]% reduces strength due to poor bonding and elastic deformability, aligning with Sections 3.2.1 and 3.2.3. Similarly, splitting tensile strength peaks at balanced levels of 15 % GP and 15 % RF (GP15RF15), achieving 5.35 MPa, as discussed in Section 3.2.2. For modulus of elasticity, surface plots mirror compressive strength trends, with peak values at 15 % GP and low RF content. Higher RF levels reduce stiffness due to their lower specific gravity and elastic nature, as highlighted in Section 3.2.3 and the correlation heatmap.

In summary, the 3D surface plots visualize the nonlinear interactions between [OPC-GP]% and [NF-RF]%, confirming earlier trends. Balanced replacement levels of 15 % GP and 15 % RF provide the best compromise between mechanical performance and workability, as supported by statistical models, experimental data, and correlation analysis.

3.3.4 Multiple response optimization

Multiple response optimization was performed using the desirability function to determine the optimal replacement levels of GP and RF for balanced concrete performance. The responses evaluated included slump, compressive strength at 7 and 28 days, splitting tensile strength, and modulus of elasticity at 28 days. Table 8 summarizes the constraints applied across four optimization trials, with goals set to either maintain values within specified ranges or maximize performance. All input factors and responses were assigned equal weights and high importance.

The desirability plots (Figure 14) show that values near 1.0 consistently occur when both [OPC-GP]% and [NF-RF]% exceed 15 %, establishing this threshold as a minimum for satisfying all performance criteria. Below this level, desirability declines sharply due to unmet targets. Based on this, Trial 1 was designed using 15 % GP and 15 % RF, marking the beginning of a stable optimal region. Trial 1 achieved a desirability score of 1.000, with strong performance across all responses: slump (91.49 mm), compressive strength at 28 days (39.82 MPa), splitting tensile strength (5.26 MPa), and modulus of elasticity (25,822.91 MPa). Trial 3 yielded a comparable mix (14.70 % GP and 15.61 % RF) with similar results. Trial 2 showed the highest strength and stiffness but excluded RF, reducing its sustainability contribution, with a desirability score of 0.987. Trial 4, which used the highest GP and RF content (25.19 % and 28.80 %), prioritized material substitution but resulted in lower mechanical performance and a desirability score of 0.770. A full comparison is provided in Table 9.

Figure 14:

Desirability function plots showing optimal design region: (a) 2D contour and (b) 3D surface.

Considering both performance and sustainability, Trial 1 is recommended as the most balanced mix. The ramp function graph (Figure 15) illustrates its optimal position within the design space. For validation, the Trial 1 mix was experimentally tested and compared with model predictions (Table 10). Percentage errors for slump, compressive strength (7 and 28 days), splitting tensile strength, and modulus of elasticity were 0.55 %, 1.34 %, 0.70 %, 0.94 %, and 0.35 %, respectively. These low errors confirm the model’s accuracy in predicting the performance of the optimized sustainable concrete mixture.

Figure 15:

Ramp function graph for optimum responses (Trial 1) using desirability function.