Optimizing of Self-Compacting Concrete (SCC): Synergistic Impact of Marble and Limestone Powders—A Technical and Statistical Analysis

Abstract

The disposal and recycling of industrial by-products such as marble and limestone powders pose pressing environmental challenges due to the substantial amounts of waste generated annually by marble processing plants and limestone quarries. The integration of these by-products into concrete production is justified by their widespread availability and the potential to alleviate the environmental burden. This study used a statistical mixture design approach to systematically assess the effects of limestone and marble powders, with varying fineness levels, as partial cement replacements (up to 17%) on the rheological and mechanical properties of self-compacting concrete (SCC). The experimental findings revealed that the density of the SCC mixtures ranged from 2475 to 2487 kg/m³. Mixtures incorporating limestone powder exhibited superior flowability, achieving a slump flow of up to 69 cm, an 8% improvement compared to those containing marble powder. However, marble powder with a specific surface area of 330 m²/kg demonstrated significant improvements in compressive and tensile strengths, with increases of 18%. Statistical analysis using analysis of variance (ANOVA) validated the reliability of the predictive models developed, which demonstrated coefficients of determination (R²) that exceeded 0.94 and p-values below 0.05. These models enable precise predictions of critical performance metrics, including density, slump flow, box flow, compressive strength, and tensile strength, thus reducing the need for extensive experimental procedures.

1. Introduction

To facilitate the construction of resilient infrastructure, self-compacting concrete (SCC) was developed in Japan as a high-strength and durable material [1]. Due to its advantages, including improved surface finishing without extra vibration and decreased noise pollution, higher design flexibility, shorter building duration, and decreased labor costs, it may be considered an upgraded version of normally vibrated concrete (NVC) [2,3]. SCC does not require external force to achieve compaction and may easily be consolidated under its own weight [4,5]. However, SCC requires a significant quantity of powdered material as mineral admixtures or fillers to enhance its flow capacity, which consequently leads to a concrete of higher cost and a significant carbon footprint. Researchers are now investigating novel options for building SCC using sustainable supplementary cementitious materials (SCM) to achieve environmental friendliness, increased durability, and cost effectiveness [6,7,8,9,10]. There is renewed interest in limestone and marble powders due to the inadequacy of high-quality mineral additives such as silica fume, ground granulated blast furnace slag, and fly ash to meet the growing global demand for concrete [11,12].

Concrete benefits from the widespread local availability of limestone powder, making it a viable option for materials engineers. Soroka and Setter [13] first observed that limestone filler had a nucleation impact, which increased the rate of cement hydration and structural development during the early stages. Follow-up investigations assessed the influence of limestone powder on the characteristics of concrete in its fresh and hardened states [14,15,16]. For example, it was claimed that the compressive strength was not significantly affected by the addition of limestone powder until 15% of the cement was replaced [17]. In terms of durability, the addition of limestone powder has been shown to improve the rate of carbonation in concrete [17,18]. However, it has also been seen to decrease the chloride diffusion coefficient [19], while other studies have reported that the incorporation of limestone powder leads to greater penetration of chloride ions [20,21,22,23]. Further investigation revealed that substituting Portland cement for up to 15% by weight of limestone powder does not noticeably affect the resistance to chloride penetration [24]. Studies examining the impact of limestone powder on concrete durability have also shown conflicting results [25,26,27].

Marble is a metamorphic rock formed from limestone [28] and has been a major material used in the construction of monuments from ancient times, mainly due to its aesthetic appeal [29]. The dimension stone industry discards the marble powder generated during its processing and mining [30]. Therefore, the use of marble and limestone powders in construction not only offers a sustainable waste management solution but also several technical and economic benefits. By replacing a portion of cement with marble powder, the overall cost of concrete can be reduced. The preservation of natural resources will lead to a reduction in the demand for raw materials. The inclusion of marble powder may also improve the mechanical characteristics of these materials, including flexural strength, split tensile strength, and compressive strength [31]. Several studies provide evidence for the use of waste marble powder (WMP) as a substitute for cement in concrete, demonstrating its beneficial impact on the durability and mechanical characteristics of the material, as well as its potential to contribute to sustainable building methods.

Technically, the inclusion of marble and limestone wastes in SCC can improve its mechanical properties. The fine particles of these waste materials fill the spaces between larger aggregates, optimizing the design of the mix and improving overall material efficiency [32,33,34] and improving compressive and tensile strength through better particle packing [35,36]. The increased density and reduced permeability afforded by these fillers enhance the resistance of SCC to chemical attack and freeze–thaw cycles, extending the useful lifetime of the structures. Furthermore, marble and limestone waste fillers improve the rheological properties of SCC by increasing the viscosity and cohesiveness of the mixture, maintain stability during transportation and placement, and reduce the risk of segregation and cement bleeding. This stability ensures uniform quality in hardened concrete, contributing to the overall reliability and performance of the structure [37,38].

Table 1. Previous studies.

References	Powder Used	Main Results
[39]	Limestone and marble powder	The use of marble or limestone fillers resulted in an increased dose of superplasticizer to maintain the target slump flow and an increase in viscosity.
[40]	Marble powder	The addition of marble powder enhanced the fresh properties of SCC. With an M/C ratio increasing to 0.43, the slump flow decreased, the T-50 increased, and the V-funnel value remained stable.
[41]	Marble powder	The inclusion of marble powder (5–30%) improved the rheological properties of both mortar and concrete. However, a decrease in compressive strength was observed with marble powder addition compared to the control mix.
[42]	Marble powder	Substituting cement with marble powder reduced both yield stress and plastic viscosity.
[43]	Marble powder	Response surface methodology can be used to model the properties of self-compacting concrete incorporating waste marble and glass powder.
[8]	Marble powder	The use of waste powders as mineral additives in SCC improved its physical, mechanical, and durability-related properties compared to the control mix.
[44]	Limestone powder	SCCs containing limestone powder showed superior hardening properties. Furthermore, the fresh and hardened properties of the SCCs improved significantly when the limestone powder was combined with the pozzolanic powder.
[45]	Limestone powder	The paste rheological thresholds showed only slight variation with an increase in the substituted content of limestone powder in the self-compacting concrete mix.
[46]	Limestone powder	The strength of SCC mixes containing limestone powder was significantly higher than that of reference concrete. Specifically, the compressive strengths of the cubes for limestone powder mixes were 60 to 80% higher at 7 days and 30 to 40% higher at 28 days.
[47]	Limestone powder	The quantity of limestone powder (LSP) is a crucial factor affecting the properties of SCC. For a higher free water content, LSP had a less significant effect on slump flow compared to lower water content. Obtaining compressive strengths of (35–50) MPa is easily possible with up to 15% cement replacement by LSP.

summarizes the findings of previous studies related to the subject of this study.

According to Table 1, which summarizes the findings of previous studies, there is an evident lack of research on the combined effect of limestone and marble powders on SCC. However, several studies have successfully used statistical methods to predict the properties of SCC with a high degree of precision, approximately 95%, compared to experimental results [48,49,50]. This underscores the validity of using statistical models for precise property predictions. A novel approach involves forecasting the combined influence of marble and limestone powders on both fresh and hardened SCC properties using a methodology like mix design, complemented by analysis of variance (ANOVA) to assess the significance of the models and parameters on response variables. The overarching objective is to establish a reliable model for estimating the properties of fresh SCC mixes that incorporate marble and limestone waste, with the aim of advancing sustainable construction practices and enhancing the efficiency and performance of concrete structures. This study contributes significantly to the advancement of sustainable construction materials by addressing both environmental concerns and performance-related challenges. The key findings can be summarized as follows.

(1) A systematic approach was developed to optimize the incorporation of limestone powder and marble powder in self-compacting concrete. Given their high calcium content, these mineral additions act as efficient fillers and can contribute to secondary hydration reactions under specific conditions. The proposed statistical mixture design methodology enables a rigorous evaluation of synergistic interactions within a ternary system of supplementary cementitious materials. This approach ensures an optimal balance between workability, mechanical strength, and durability, effectively supporting waste valorization and meeting the demand for sustainable alternatives to conventional binders.

(2) The results indicate that controlled incorporation of limestone and marble powders enhances both the fresh and hardened properties of self-compacting concrete. The increase in compactness, attributed to optimized particle packing and potential filler effects, leads to superior mechanical performance and reduced porosity. Experimentally validated improvements highlight the feasibility of using these materials for structural applications. Furthermore, the optimized mix proportions, established through robust statistical modeling, ensure enhanced performance compared to conventional formulations. This data-driven methodology provides a reliable framework for material selection, quality control, and large-scale implementation in sustainable construction practices.

2. Materials and Methods

The cement used in this study was Biskra CEM I 42.5 R, designed for high-performance concrete with rapid early strength. It has a surface specific area (SSA) of 326 m²/kg, and its chemical composition is detailed in

Table 2. Chemical composition of cement, limestone, and marble.

Compounds (%)	Cement	Marble	Limestone
SiO2	22.7	7.44	1
Al2O3	5.4	0.83	0.3
Fe2O3	2.7	0.75	0.3
CaO	65.7	49.73	53.3
MgO	0.7	0.66	1.1
SO3	0.6	0.01	0.07
K2O	0.4	0.02	0.04
Na2O	0.7	0.008	0.06
Loss of ignition	0.3	39.79	43.63
SSA (m2/kg)	326	330 for M* 390 for M	405
Specific gravity (g/cm3)	3.15	2.75	2.72

.

In this study, two types of fillers were used, namely limestone filler provided by the National Aggregates Company (El Khroub–Constantine) and marble powder, a by-product sourced from a marble workshop in Zidane, Sétif Province (Ain Oulmane). Marble waste was processed by crushing and grinding for 1.15 and 2.00 h to produce fine powders. The ground material was sieved to a particle size below 125 μm to meet the criteria for classification as fillers. The particle size distributions of cement, marble powder, and limestone powder (Figure 1) were analyzed using a particle size analyzer according to the NF ISO 13320-1 standard [51].

The SSA of the fillers was determined according to the EN 196-6 standard [52] to be 330 m²/kg for marble powder (M*), 390 m²/kg for marble powder finer than 80 µm (M), and 405 m²/kg for limestone filler (L). The detailed chemical composition of these materials is summarized in Table 2.

The formulation of SCC was carried out under the conditions necessary to ensure self-compacting based on the compositions proposed by the French Association of Civil Engineering (AFGC) [53]. The proportions of the constituents for 1 m³ of concrete were selected according to the following parameters and conditions.

Gravel (G) + Sand (S) + Cement (C) + Air (A) + Water (E) + super plasticizer (SP) = 1000 L

• G/S ratio ≈ 1, according to AFGC recommendations;
• Binder B dose = cement + filler = 480 kg/m³;
• SP = 1.8%.

After determining the filler content, experiments were designed to determine their impact on the properties of concrete in both fresh and hardened states. A mixture design was developed, including the three factors L, M, and M*, expressed in mass proportions, allowing for an addition of up to 20%. These factors are interdependent, and the experimental domain is constrained by the following equation:

$$\mathrm{L}+\mathrm{M}+{\mathrm{M}}^{\mathrm{*}}=1$$

(1)

where L, M, and M* represent limestone and marble powder with SSA of 405, 390, and 330 m²/kg, respectively.

The number of experiments generated by the program is calculated using the following equation:

$${\mathrm{C}}_{\mathrm{q}+\mathrm{m}-1}^{\mathrm{m}}={\displaystyle \frac{\left(\mathrm{q}+\mathrm{m}-1\right)!}{\left(\mathrm{m}!\right)\left(\mathrm{q}-1\right)!}}$$

(2)

where q is the number of factors, and m is the number of levels. With three factors and three levels, a mixture design comprising 10 mixes was developed to assess the influence of these factors on the properties of the SCC.

Table 3. Fractions of fillers in the developed mixes.

Mixes	Designation	Limestone (L)	Marble 1 (M)	Marble 2 (M*)
M1	1L	1	0	0
M2	1M	0	1	0
M3	1M*	0	0	1
M4	1/2L1/2M*	0.50	0	0.50
M5	1/2L1/2M	0.50	0.50	0
M6	1/2M1/2M*	0	0.50	0.50
M7	2/3L1/6M1/6M*	0.66	0.16	0.16
M8	1/6L2/3M1/6M*	0.16	0.66	0.16
M9	1/6L1/6M2/3M*	0.16	0.16	0.66
M10	1/3L1/3M1/3M*	0.33	0.33	0.33

shows the proportions of fillers used in the developed mixes, and

Table 4. Mixture proportions for 1 m³ of self-compacting concrete [kg/m³].

	Components (kg/m3)						Additives (kg/m3)
Mix	Cement	Water	SP	Sand	Gravel		Limestone	Marble
					(3/8)	(8/16)		M	M*
M1	400	178.56	7.2	826.5	429.52	429.52	80	0	0
M2							0	80	0
M3							0	0	80
M4							40	0	40
M5							40	40	0
M6							0	40	40
M7							52.8	13.4	13.4
M8							13.4	52.8	13.4
M9							13.4	13.4	52.8
M10							26.66	26.66	26.66

summarizes the amounts of both components and additives in every mix.

The mixing process was conducted using a 30 L vertical-axis planetary mixer to ensure homogeneity. Sand was first mixed for 30 s, followed by the addition of aggregates and half of the water, with mixing for 1 min. The cement and mineral admixture were then incorporated and mixed for another 30 s. The remaining water and three-quarters of the superplasticizer were added, followed by 1 min of mixing and a resting period of 2 min. Finally, the remaining superplasticizer was introduced, and the mixing continued for 2 min, followed by an additional 5 min to ensure uniformity. Then, the SCC rheological properties were evaluated using the slump flow test (EN 12350-8) [54] and the L-box test (EN 12350-10) [55]. These standardized methods allow for a comprehensive assessment of flowability and confined filling capacity, ensuring compliance with the required performance criteria for SCC.

The samples designated for mechanical characterization were then prepared by casting in three successive layers without vibration. After 24 h, they were demolded and subsequently cured in a laboratory environment at 25 °C for 28 days, with relative humidity varying between 23% and 41%. Compressive and tensile strengths at 28 days were measured using an MCC8 hydraulic press with a capacity of 3000 kN, according to EN 12390-3 [56] and EN 12390-6 [57], respectively. The rebound hammer test, conducted in accordance with NF EN 12504-2 [58], was used to estimate the compressive strength of the concrete using a non-destructive methodology. This test is based on measuring the hardness of the concrete surface, which is empirically correlated with its compressive strength. Its use is particularly advantageous for assessing the uniformity of concrete properties between structural elements, performing comparative strength evaluations, and ensuring quality control without compromising structural integrity. Furthermore, the rebound hammer test provides a rapid and cost-effective complement to destructive testing methods, enhancing the reliability of strength characterization [58]. The experimental program is described in Figure 2.

In the evaluation of mix design models, particularly in regression analysis, various performance metrics are employed to comprehensively assess the model’s accuracy and reliability. Among these, the coefficient of determination (R²) serves as a fundamental indicator of the predictive capability of the model. This metric quantifies the proportion of variance in the dependent variable that is explained by the independent variables. A value of R² approaching 1 signifies a strong correlation between the predictions of the model and the actual observed values, indicating that the model effectively captures the majority of the variability in the dataset [59]. The root mean square error (RMSE) is a fundamental metric for evaluating regression models, particularly valued for its sensitivity to large deviations. By penalizing substantial errors more heavily than smaller ones, the RMSE provides a comprehensive measure of the discrepancy between predicted and actual values. A lower RMSE indicates higher predictive precision, making it a crucial criterion for assessing model performance and reliability [60]. Combining multiple performance metrics provides a comprehensive evaluation of model accuracy, allowing researchers to assess how well predictions align with the observed data. Each metric offers a distinct perspective on the model’s predictive performance, and together, they establish a robust assessment framework. The key equations for R² and RMSE are as follows:

$${\mathrm{R}}^2=1-{\displaystyle \frac{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{P}}_{\mathrm{y}}-\mathrm{O}\right)}{\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{P}}_{\mathrm{y}}-\mathrm{Y}\right)}}$$

(3)

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{\mathrm{n}}}\sum _{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{P}}_{\mathrm{y}}-\mathrm{Y}\right)}$$

(4)

where n is the number of observations, P_y is the value predicted by the model, O is the observed value, and Y is the average of the actual values,

The desirability function, originally developed by Derringer and Suich, is a widely used technique for multi-response optimization, providing a robust framework for balancing multiple objectives in experimental design [45]. This approach involves converting each measured response (Yᵢ) into a desirability value (d(Yᵢ)), which ranges from 0 to 1, with 0 indicating an undesirable outcome and 1 representing an optimal response. The global desirability index (D) is then computed as the geometric mean of individual desirability, as expressed in Equation (5) [61]:

$$\mathrm{D}=\left(\mathrm{d}\left({\mathrm{Y}}_1\right)\times \mathrm{d}\left({\mathrm{Y}}_2\right)\times \dots \times \mathrm{d}\left({\mathrm{Y}}_{\mathrm{i}}\right)\right)\left({\displaystyle \frac{1}{\mathrm{n}}}\right)=\prod _{\mathrm{i}=1}^{\mathrm{n}}{\mathrm{d}({\mathrm{Y}}_{\mathrm{i}})}^{\left({\displaystyle \frac{1}{\mathrm{n}}}\right)}$$

(5)

where n represents the total number of responses. The primary objective of the optimization process is to maximize D by adjusting key input parameters (L, M, and M*). The desirability function of each response is determined on the basis of its target value or range. For instance, responses following a “greater is better” criterion are modeled using Equation (6), while those exhibiting a “smaller is better” trend are described by Equation (7) [62]:

$$\mathrm{d}\left({\mathrm{Y}}_{\mathrm{i}}\right)\mathrm{m}\mathrm{a}\mathrm{x}=\left\{\begin{array}{c}0 {\mathrm{Y}}_{\mathrm{i}}<{\mathrm{L}}_{\mathrm{i}}\\ {\left({\displaystyle \frac{{\mathrm{Y}}_{\mathrm{i}}-{\mathrm{L}}_{\mathrm{i}}}{{\mathrm{U}}_{\mathrm{i}}-{\mathrm{L}}_{\mathrm{i}}}}\right)}^{\mathrm{r}\mathrm{i}} {\mathrm{L}}_{\mathrm{i}}\le {\mathrm{Y}}_{\mathrm{i}}\le {\mathrm{U}}_{\mathrm{i}}\\ 1 {\mathrm{Y}}_{\mathrm{i}}>{\mathrm{U}}_{\mathrm{i}}\end{array}\right.$$

(6)

$$\mathrm{d}\left({\mathrm{Y}}_{\mathrm{i}}\right)\mathrm{m}\mathrm{i}\mathrm{n}=\left\{\begin{array}{c}0 {\mathrm{Y}}_{\mathrm{i}}<{\mathrm{L}}_{\mathrm{i}}\\ {\left({\displaystyle \frac{{\mathrm{U}}_{\mathrm{i}}-{\mathrm{Y}}_{\mathrm{i}}}{{\mathrm{U}}_{\mathrm{i}}-{\mathrm{L}}_{\mathrm{i}}}}\right)}^{\mathrm{r}\mathrm{i}} {\mathrm{L}}_{\mathrm{i}}\le {\mathrm{Y}}_{\mathrm{i}}\le {\mathrm{U}}_{\mathrm{i}} \\ 1 {\mathrm{Y}}_{\mathrm{i}}>{\mathrm{U}}_{\mathrm{i}}\end{array}\right.$$

(7)

where Lᵢ and Uᵢ correspond to the lower and upper limits for the i-th response, respectively, and rᵢ is the assigned weighting factor, ensuring that ∑rᵢ = 1.

This optimization methodology effectively reconciles competing performance criteria such as density, flow test, and L-box compressive and tensile strengths while integrating their relative significance. The outcome is a single optimal solution that reflects the best overall performance for the self-compacting concrete under investigation.

3. Results and Discussion

3.1. Bulk Density

Figure 3 illustrates the evolution of density across the mixtures studied, highlighting the influence of the type and combination of supplementary powders. The results illustrate that the mixture incorporating pure limestone powder (1L) has a higher density than those containing pure marble powder (1M and 1M*), with an observed increase of up to 5 kg/m³. This increase is mainly attributed to the finer particle size of limestone powder, which enhances packing efficiency by reducing interparticle voids. The smooth surface texture and angular morphology of limestone particles further facilitate better packing, leading to a denser matrix [63].

Binary mixtures, comprising combinations of limestone and marble powders (for example, 1/2L1/2M*, 1/2L1/2M, and 1/2M1/2M*), display an average density of approximately 2480 kg/m³. Within this category, mixtures containing a higher proportion of limestone powder consistently achieve higher densities, highlighting the superior ability of limestone to optimize particle arrangement and minimize void spaces. On the contrary, ternary mixtures exhibit an average density of around 2477 kg/m³. However, even within ternary formulations, mixtures with limestone powder consistently demonstrate a clear advantage in density. This observation can be related to the distinctive physical properties of limestone powder, such as its higher SSA and smoother particle morphology, which collectively contribute to more effective compaction and reduced porosity [64].

A detailed comparison of the densities of the ternary, binary, and single-powder mixtures (comprising only marble or limestone powder) indicates that the ternary systems exhibit lower densities, with reductions of up to 4–10 kg/m³. This reduction can be attributed to the increased heterogeneity that arises from the incorporation of powders with different particle size distributions. In single-powder mixtures, uniform granulometry facilitates optimal particle packing, leading to higher bulk densities. On the contrary, the mixing of powders with distinct granulometric profiles introduces irregularities in particle arrangement, thereby increasing the void content and reducing the overall density of the composite material. This effect is more pronounced in ternary mixtures, where the interaction of three powders further disrupts the packing efficiency.

3.2. Fresh-State Properties

Figure 4 shows the results of the slump flow test for the mixes studied. The results indicate that concretes that incorporate limestone powder exhibit a significantly higher slump flow compared to those that contain marble powder with particle sizes below 80 and 125 μm, with increases reaching up to 8%. This improved workability can be attributed to the smoother surface texture and more uniform morphology of limestone powder, which reduce interparticle friction and improve the flowability of the concrete mix [65]. On the contrary, binary and ternary mixes containing marble powder demonstrate a relatively consistent average slump flow of approximately 66 cm, with a marginal increase in workability observed after the incorporation of marble powder. This modest improvement is mainly due to the fine particle size of the marble powder, which promotes more efficient particle packing and slightly reduces internal friction within the mix [66,67].

However, the angular morphology of the marble powder particles contributes to additional resistance to flow, counteracting the benefits of their partial smoothness. These findings emphasize the critical influence of particle morphology and size distribution on the rheological properties of concrete mixtures. In particular, the results highlight the complementary role of limestone and marble powders as supplementary materials that can optimize the workability of concrete formulations while maintaining consistent performance in binary and ternary mixes [68,69,70]. Boukhelkhal et al. [42] observed a similar effect, where replacing cement with MP at rates ranging from 0% to 20% led to an increase in slump flow values. This can be attributed to the lower density of marble powder compared to cement, resulting in a higher paste volume, reducing interparticle friction between aggregates and, consequently, improving the fluidity and cohesiveness of the concrete.

The study by Belaid et al. [41] demonstrated that the incorporation of MP in ternary systems enhances the workability of self-compacting concrete (SCC). These findings are consistent with previous research on mortars and concretes incorporating slag and metakaolin as well as with the present results, further substantiating the influence of supplementary cementitious materials on the rheological behavior of cementitious systems [71,72]. Gritsada Sua-iam et al. [73] evaluated the flow behavior of SCC incorporating limestone powder (LS) and rice husk ash (RHA). Their results indicated a slight reduction in slump flow for mixtures containing these mineral additions compared to those without, attributed to the higher surface area of RHA and LS, which increases water demand. Additionally, the characteristics of the particles play a crucial role since LS exhibits a smoother texture and a more spherical shape than RHA, which influences rheological properties [74]. These findings align with the present study, strengthening the impact of supplementary cementitious materials on the flowability of SCC.

The filling capacity of mixtures containing a single type (see Figure 5) of powder demonstrates a trend that contrasts distinctly with the results from the slump-flow test. Although the slump flow test reveals slightly superior flowability in mixtures containing limestone powder, the fill capacity shows the opposite trend. Specifically, mixtures incorporating marble powder exhibit a modest increase in filling capacity compared to those with limestone powder, with an improvement of up to 5%. This discrepancy can be attributed to the unique characteristics of the powder particles. Marble powder, with its angular particle morphology, facilitates more effective interlocking, thus improving packing density and enhancing fill capacity [41]. In contrast, limestone powder, with its smoother and more rounded particles, reduces internal friction, leading to better flowability, but offers less efficient particle packing. Consequently, while limestone powder improves the slump flow by minimizing friction between the particles, marble powder improves the filling capacity by better occupying the spaces between the particles, thus increasing the overall packing density.

3.3. Hardened State Properties

Figure 6 provides a summary of the compressive strength results obtained for the various concrete mixes, considering the substitution rate and the type of material used. Mixes containing marble filler with an SSA of 330 m²/kg (1M*) demonstrated a notable increase in compressive strength compared to those produced with marble filler with 390 m²/kg of SSA or limestone powder. This improvement can be attributed to the fineness achieved in the milling process. Although fillers exhibit an SSA significantly higher than that of cement, excessive fineness can induce particle agglomeration. Such agglomeration creates weak zones within the cementitious matrix, compromising mechanical performance. Quantitatively, concretes that incorporate marble filler with 330 m²/kg of SSA exhibit an increase in compressive strength of 10% to 19% compared to the other formulations tested.

Concrete mixes formulated with two types of fillers achieved an average compressive strength of 38 MPa. This performance is primarily related to the granulometric complementarity of the fillers used, particularly the limestone filler, which plays an exclusive physical role in the cement matrix. Although limestone fillers are chemically inert and do not participate in pozzolanic reactions, their contribution improves the compactness of concrete. Variations in particle size distribution facilitate optimal packing of interparticle voids, reducing capillary porosity and increasing the matrix density [75]. This structural densification also strengthens the interfacial transition zones, which are often critical to overall mechanical performance. Furthermore, the combination of fillers with different granulometries promotes a more uniform distribution of mechanical stresses under load, causing the onset of microcracking and improving the mechanical strength of the material. These findings underscore the importance of the physical role of inert fillers such as limestone in enhancing the mechanical and microstructural properties of concrete. They also highlight the need for an optimized granulometric approach to maximize concrete performance while using economically viable and sustainable materials.

The examined ternary mixes achieved an average compressive strength of 40 MPa, with the notable exception of the 1/6L2/3M1/6M* mix, which recorded a compressive strength of 34 MPa, a reduction of up to 20% compared to other ternary formulations. This significant decrease is likely attributed to the negative effects induced by a substitution rate exceeding 20%, particularly when high-fineness materials are included. The presence of ultra-fine particles promotes agglomeration, creating weak zones within the cementitious matrix and compromising the efficiency of the granular network, thus adversely affecting the overall mechanical performance [76].

These observations are consistent with the findings of Aidjouli et al. [43], who highlighted the detrimental impact of high substitution rates with ultra-fine fillers, especially in terms of reduced compactness and the formation of structural defects within the cementitious matrix. These results emphasize the critical importance of achieving an optimal granulometric balance to maximize concrete density while avoiding agglomeration phenomena. Furthermore, they underscore the necessity of precise control over substitution proportions and filler granulometric characteristics to maintain high mechanical performance in ternary mixes. Furthermore, some studies indicate that substituting up to 15% of cement with marble powder yields acceptable compressive strength while sometimes improving workability [77]. However, higher levels of substitution may adversely affect the hydration process, leading to a decrease in strength [78]. On the contrary, limestone powder has been extensively studied for its effects on SCC. The replacement of cement with limestone powder can improve the workability and flow characteristics of concrete due to its shape and distribution of particle size [79]. For example, a limestone powder content of about 10% has been reported to optimize the rheological properties of SCC while improving the compressive strength [80].

Figure 7 presents the evolution of the tensile strength of various concrete mixtures as a function of the substitution rate and filler type. Mixes that incorporate marble powder with a specific Blaine surface area (SSA) of 330 m²/kg (1M*) exhibited superior tensile strength compared to those with finer marble powder (390 m²/kg SSA) or limestone filler. This enhancement is mainly attributed to an optimized particle size distribution, which improves matrix densification. While increased SSA enhances packing efficiency, excessive fineness promotes particle agglomeration, disrupting microstructural homogeneity and adversely affecting mechanical performance. In particular, formulations containing marble filler with 330 m²/kg SSA demonstrated a 5% to 12% increase in tensile strength compared to other mixtures.

Mixes that incorporate multiple fillers achieved an average tensile strength of 2.84 MPa, highlighting the beneficial synergies of granular interactions. Limestone filler, acting as an inert physical component, enhances matrix density by reducing capillary porosity. Optimized particle packing minimizes voids, strengthens interfacial cohesion, and improves stress distribution, thus mitigating microcrack propagation and enhancing overall mechanical performance.

Non-destructive tests were performed to assess the influence of the fillers on the rebound index of the mixes. The results, shown in Figure 8, show that the rebound index varies from 40 to 32, depending on the type and percentage of filler used. This observation mirrors the results obtained from the compression and tensile tests, highlighting a correlation between the composition of the mix and its mechanical properties measured by various tests. A significant correlation was observed between the rebound index and compressive strength, with a high coefficient of determination (R² = 0.98), as shown in Figure 9. These results are consistent with those obtained by other researchers, further demonstrating the reliability of this method [81,82].

3.4. Statistical Analysis

An in-depth statistical analysis of the data enabled an assessment of the impact of each factor (type and percentage of filler) on the results. Figure 10 describes the relationship between the experimental and predicted values of the responses studied. The models developed revealed high correlation coefficients: 0.94 for density, 0.98 for spreadability, 0.97 for filling capacity, 0.99 for compressive strength, and 0.97 for tensile strength (

Table 5. Summary of the ANOVA analysis fit to the responses studied.

	Density	Slump Flow	L-Box	CS	TS
R2	0.94	0.98	0.97	0.99	0.97
Adjusted R2	0.86	0.96	0.93	0.97	0.92
Root-Mean-Square-Error (RMSE)	1.24	0.31	0.01	0.56	0.04
Mean response	2480.34	66.17	0.85	38.66	2.96
Observations (or weighted sums)	10	10	10	10	10

). These results demonstrate the validity of the proposed models in predicting the effects of fillers on the properties of SCC. The high correlation coefficients indicate a close agreement between the experimental results and the predicted values, enhancing the confidence in their accuracy.

Furthermore, the analysis of variance (ANOVA) for each modeled response is presented in

Table 6. ANOVA analysis for the responses studied.

	Source	df	Sum of Squares	Mean Squares	F-Ratio
Density	Model	5.00	94.91	18.98	12.26
	Error	4.00	6.19	1.55	Prob. > F
	Uncorrected total	9.00	101.11		0.008
Slump flow	Model	5.00	19.37	3.87	39.69
	Error	4.00	0.39	0.10	Prob. > F
	Uncorrected total	9.00	19.76		0.0022
L-box	Model	5.00	0.0094	0.0019	25.58
	Error	4.00	0.0003	0.0001	Prob. > F
	Uncorrected total	9.00	0.0097		0.0017
CS	Model	5.00	82.55	16.51	53.15
	Error	4.00	1.24	0.31	Prob. > F
	Uncorrected total	9.00	83.79		0.0039
TS	Model	5.00	0.188	0.04	22.25
	Error	4.00	0.007		Prob. > F
	Uncorrected total	9.00	0.195		0.0013

. With a degree of freedom of 1 (df1 = P − 1 = 5), a degree of freedom of 2 (df2 = n − P = 4), and a 95% confidence interval, the critical value of the Fisher F-test is 6.26, where df is the degree of freedom, P the number of coefficients in the model, and n the number of experiments. The calculated F-values for density, spreadability, fill capacity, compressive strength, and tensile strength are 12.26, 39.69, 25.58, 53.15, and 22.24, respectively. These calculated F-values exceed the critical value of the Fisher’s F-test, indicating that the models obtained are valid. The p-values obtained for density (0.008), flow in the L-box (0.0022), compressive strength (0.0017), and tensile strength (0.0039 and 0.0013, respectively) indicate significant deviations from normality at a level of significance of 5% (α = 0.05). According to the Shapiro–Wilk test, a p-value below 0.05 leads to the rejection of the null hypothesis (H₀), which assumes that the dataset follows a normal distribution.

Independent variables, namely filler types and addition rates, were incorporated into JMP Pro software (version 17). All proposed models were constructed using a mixture design approach. Polynomial equations were developed to predict density, spreadability, filling capacity, compressive strength after 28 days, and tensile strength across a wide range of mixtures. These models include addition rates of up to 20% relative to the cement mass and include the use of three types of fillers.

$${\mathrm{Y}}_{\mathrm{D}\mathrm{e}\mathrm{n}\mathrm{s}\mathrm{i}\mathrm{t}\mathrm{y}}=2475.81\mathrm{L}+2481.18\mathrm{M}+2485.79\times {\mathrm{M}}^{\mathrm{*}}+\mathrm{L}\times \mathrm{M}\times 3.14+\mathrm{L}\times {\mathrm{M}}^{\mathrm{*}}\times -15.95+\mathrm{M}\times {\mathrm{M}}^{\mathrm{*}}\times 3.14$$

(8)

$${\mathrm{Y}}_{\mathrm{S}\mathrm{l}\mathrm{u}\mathrm{m}\mathrm{p}\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{w}}=65.34\mathrm{L}+62.87\mathrm{M}+68.55\times {\mathrm{M}}^{\mathrm{*}}+\mathrm{L}\times \mathrm{M}1\times 11.10+\mathrm{L}\times {\mathrm{M}}^{\mathrm{*}}\times -3.95+\mathrm{M}1\times \mathrm{M}2\times 2.30$$

(9)

$${\mathrm{Y}}_{\mathrm{L}-\mathrm{b}\mathrm{o}\mathrm{x}}=0.84\mathrm{L}+0.84\times \mathrm{M}+0.79\times {\mathrm{M}}^{\mathrm{*}}+\mathrm{L}\times \mathrm{M}\times 0.24+\mathrm{L}\times {\mathrm{M}}^{\mathrm{*}}\times 0.016+\mathrm{M}\times {\mathrm{M}}^{\mathrm{*}}\times 0.14$$

(10)

$${\mathrm{Y}}_{\mathrm{C}\mathrm{S}}=43.30\mathrm{L}+43.40\times \mathrm{M}+35.05\times {\mathrm{M}}^{\mathrm{*}}+\mathrm{L}\times \mathrm{M}\times -35.91+\mathrm{L}\times {\mathrm{M}}^{\mathrm{*}}\times 3.05+\mathrm{M}\times {\mathrm{M}}^{\mathrm{*}}\times 1.25$$

(11)

$${\mathrm{Y}}_{\mathrm{T}\mathrm{S}}=3.01\mathrm{L}+3.21\mathrm{M}+2.80\times {\mathrm{M}}^{\mathrm{*}}+\mathrm{L}\times \mathrm{M}\times -1.75+\mathrm{L}\times {\mathrm{M}}^{\mathrm{*}}\times 0.23+\mathrm{M}1\times {\mathrm{M}}^{\mathrm{*}}\times 0.17$$

(12)

The influence of the factors studied, particularly the type and fineness of the fillers, on the properties of fresh and hardened concrete is clearly demonstrated in Figure 11. With the addition of limestone powder, an initial decrease in density is observed, followed by an increase up to an addition rate of 0.33, and then a reduction in spreadability and filling capacity. The compressive and tensile strength decreases to an addition rate of 0.4, after which an increasing trend is observed. For marble powder of specific surface area (SSA) 390 kg/m³, an increase in density is observed up to addition rates of 0.33 and 0.67, followed by a decrease in spreadability and filling capacity. These properties decrease to an addition rate of 0.4, after which there is an improvement in compressive and tensile strength.

Regarding the addition of marble powder of SSA of 330 kg/m³, there is an increase in density up to an addition rate of 0.33. Spreadability and fill capacity increase up to an addition rate of 0.4, after which there is a decrease in compressive and tensile strength.

To optimize the results and define the desired mixes, a desirability function was applied. The density was maximized to achieve compact and dense concrete, while the spreadability and filling capacity were maximized to obtain a fluid concrete capable of easy flow. At the same time, compressive and tensile strengths were maximized to achieve more durable concrete. The results of this optimization are presented in

Table 7. The best four optimized SCC mixes.

	Mix 1	Mix 2	Mix 3	Mix 4
(A) L	0.214	0.059	0.132	0.177
(B) M	0.76	0.871	0.47	0.779
(C) M*	0.026	0.071	0.398	0.044
Slump flow (cm)	66.567	66.577	67.281	66.879
L-box	89.739	88.946	87.289	88.166
Density (min)	2484.932	2484.473	2486.336	2485.395
CS (MPa)	44.195	43.522	41.899	48.955
TS (MPa)	3.135	3.183	3.135	3.066
Desirability	1	0.994	0.956	0.793

.

An iso-response representation was developed using second-order polynomial models to visualize the variations in responses based on input variables such as filler type and its addition ratio (Figure 12). This graphical method provides a detailed view of areas where specific SCC properties, including density, spreadability, filling capacity, compressive strength, and tensile strength, reach the predicted levels by the model. It allows a comprehensive understanding of the complex relationships between factors influencing the performance of the material.

4. Conclusions

This study examined the properties of SCC by incorporating limestone and marble powders as partial cement replacements, using a mixture design methodology. Research comprehensively evaluated SCC properties, including fresh-state performance (slump flow, L-box test, and density) and mechanical characteristics (compressive strength, split tensile strength, and rebound hardness). The following conclusions can be drawn.

• Mixtures containing pure limestone powder (1L) achieve a density up to 5 kg/m³ higher than those incorporating pure marble powder (1M and 1M*), attributed to the finer granulometry and smoother morphology of limestone powder, which improves packing efficiency by reducing void spaces. Ternary mixtures have an average density of approximately 2477 kg/m³ but show density reductions of up to 4–10 kg/m³ compared to binary and single-powder mixtures;
• Mixtures incorporating limestone powder exhibit a significant improvement in slump flow, with an increase of up to 8%, reaching 69 cm, compared to marble powder mixtures, which show an average flow of 66 cm. This enhancement can be attributed to the finer particle size and smoother morphology of limestone, which reduce friction between particles and improve workability. In contrast, binary and ternary mixtures containing marble powder demonstrate only marginal improvements, with the angular particle morphology of marble powder contributing to increased resistance to flow;
• The fill capacity of the SCC ranged from 0.79 to 0.9, with mixtures containing marble powder achieving a fill capacity 5% higher than those incorporating limestone powder;
• The compressive strength of the concretes studied ranged from 34 to 45 MPa. However, mixtures containing marble powder with an SSA of 330 m²/kg exhibited a significant improvement in compressive strength, with increases ranging from 10% to 19% compared to other mixtures. Furthermore, concrete mixes incorporating a combination of fillers, particularly limestone and marble powders, achieved an average compressive strength of 38 MPa;
• The correlation between compressive strength and rebound index was effectively modeled using a first-order polynomial equation, with an R² value of 0.97, demonstrating a strong predictive relationship. This correlation highlights the potential of using rebound testing as a non-destructive method to estimate the compressive strength of concrete. The high value of R² indicates that the rebound index is a reliable indicator of concrete strength, offering a practical tool for quality control and in situ testing;
• The mixture design method was proven to be an effective tool for optimizing and analyzing the properties of SCC, enabling efficient investigation of the complex interactions between the input variables (fillers L, M, and M*) and their impact on the various responses. Statistical analysis of the results demonstrates that the polynomial equations obtained accurately predicted responses, with a p-value less than 0.05 and an R² value exceeding 0.94, indicating a strong correlation and high prediction precision.

Future work should focus on optimizing self-compacting concrete properties through response surface methodologies, evaluating long-term durability (compression, absorption, and flexural strength), and performing advanced microstructural analyses (SEM, XRD, etc.) to better understand the correlations between composition, porosity, and mechanical performance, ensuring enhanced sustainability and structural integrity.