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Article

Optimization and Modeling of 7-Day Ultra-High-Performance Concrete Comprising Desert Sand and Supplementary Cementitious Materials Using Response Surface Methodology

by
Hussein Hamada
1,2 and
Farid Abed
2,*
1
Department of Architecture, Al-Qalam University College, Kirkuk 36001, Iraq
2
Department of Civil Engineering, College of Engineering, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
*
Author to whom correspondence should be addressed.
Buildings 2024, 14(7), 2058; https://doi.org/10.3390/buildings14072058
Submission received: 5 June 2024 / Revised: 2 July 2024 / Accepted: 4 July 2024 / Published: 5 July 2024
(This article belongs to the Special Issue Advances in Modeling and Characterization of Cementitious Composites)
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Abstract

:
This research employs response surface methodology (RSM) to optimize and model ultra-high-performance concrete (UHPC) formulations, integrating desert sand and varying proportions of supplementary cementitious materials (SCMs), specifically fly ash (FA) and ground granulated blast furnace slag (GGBS). By investigating the influence of desert sand and SCM contents, the study aims to discern their impact on the workability and 7-day compressive strength of UHPC. Employing a central composite design (CCD), thirteen separate mixes were formulated. Key responses, namely workability and compressive strength, were evaluated. The developed models underscore the enhancement in UHPC performance through the partial replacement of cement with SCMs. Notably, an optimal combination of 75% desert sand and 30% SCMs resulted in a workability of 69.4 mm and a 7-day compressive strength of 46.01 MPa. The findings emphasize the potential for eco-friendly concrete in the construction industry, also prompting further exploration into long-term strength and higher SCM concentrations.

1. Introduction

The development of ultra-high-performance concrete (UHPC) has emerged as a pivotal solution to the escalating demands for enhanced compressive strength and superior workability in critical infrastructure projects [1,2]. UHPC offers a multitude of advantages, enabling the construction of lighter structures with innovative designs at a reduced cost compared to traditional concrete, while also minimizing resource consumption [1,3]. Central to the performance of UHPC is the judicious selection of materials in its production, with researchers defining it as a novel cement-based material containing fine and ultrafine aggregates, reinforced with steel fibers, and characterized by high ductility and strength [4].
Distinguished by its density resulting from the absence of coarse aggregate, UHPC significantly reduces heterogeneity, thereby enhancing overall performance [5]. However, the conventional preparation of UHPC involves a high cement content, typically around 1000 kg/m3, owing to the extensive use of fine sand in lieu of coarse aggregate [6]. This high cement content introduces challenges such as elevated costs and environmental concerns associated with substantial CO2 emissions [1,7]. These issues necessitate the exploration of sustainable alternatives, with supplementary cementitious materials (SCMs) like fly ash (FA) and ground granulated blast furnace slag (GGBS) having potential as replacements for cement. Desert sand also demonstrates great potential for replacing river sand. Fly ash and GGBS have been shown to improve the workability of concrete [8]. Arora et al. [9] achieved higher compressive strength by combining fine and coarse aggregates, while Karim et al. [10] substituted masonry sand for quartz sand. Others have explored the use of SCMs like GGBS and FA [11], steel fibers [12], and even locally available materials optimized through statistical design methods [13].
Several investigations of UHPC have been conducted in the last few years to replace OPC with various industrial waste materials, like fly ash and slag [14,15]. The strength of UHPC can be significantly influenced by mixing and curing methods. Traditionally, a steam curing method is used in precast UHPC to achieve rapid strength development. However, this method is often impractical at construction sites, presenting a significant challenge for projects requiring UHPC casting on-site. Many researchers have focused on determining the compressive strength of UHPC under standard curing conditions [16,17]. Furthermore, understanding the early compressive strength of UHPC and the factors affecting its development is crucial for some construction projects, yet there are few studies on this topic. Recently, Abdellatief et al. [18] developed eco-friendly UHPC using waste materials like fly ash, GGBS, silica fume, and metakaolin, and examined its effect on the properties of UHPC. They replaced cement with different amounts of FA (20–30%), GGBS (30–50%), or MK (15–25%) with a silica fume content of 15%. They observed that the highest strength was achieved with the addition of 15%MK as cement replacement.
Very limited studies have examined the effects of desert sand and supplementary cementitious materials (SCMs) on the workability and compressive strength of UHPC [19,20]. Lately, response surface methodology (RSM) as a statistical model has been extensively used in the construction material area to simulate and predict their properties and attain multi-objective optimization. Abdellatief et al. [21] investigated the effect of steel fibers and fly ash on the strength of UHPC using RSM. They tested workability, density, and compressive strength for twenty mixtures designed using central composite design (CCD) inside RSM software. However, the replacement of fine aggregate by desert sand (0–100%) alongside SCMs was not addressed. There is a lack of research on their impact at early curing ages. Also, few studies examined the effect of SCMs on the workability and strength of UHPC using RSM, and no study investigated the combined effect of SCMs and desert sand on the UHPC properties using RSM. Therefore, this study seeks to fill this gap by optimizing the workability and 7-day compressive strength of UHPC using a central composite design (CCD) within the framework of RSM. The research evaluates the influence of key input variables–desert sand as fine aggregate, and a combination of fly ash (FA) and ground granulated blast-furnace slag (GGBS) as SCMs on critical output responses such as workability and 7-day compressive strength. By employing the CCD technique, this study aims to uncover the optimal mix of UHPC incorporating desert sand, FA, and GGBS, with the overarching goal of achieving high-performance UHPC that also addresses economic and environmental considerations.
The current research study is mainly focused on the evaluation of the compressive strength and workability of UHPC made of desert sand and SCM. The aim was limited to 7 days due to the limitation of the cost and the testing machine capacity at that time. The authors are currently proposing extended research to investigate the long-term performance of UHPC such as 28-, 56-, and 360-day compressive strengths, as well as durability properties like sulfate and acid attacks, permeability, and shrinkage.

2. Experimental Program

2.1. Materials

In this study, type I ordinary Portland cement (OPC) served as the primary binder material, possessing a specific gravity of 3.15. To mitigate the environmental impact and saving cost associated with cement production, industrial by-products, namely FA and GGBS, were employed as partial replacements for cement. Different replacement levels of FA and GGBS were incorporated. Table 1 and Table 2 provide the chemical compositions and physical properties of the cement, FA, and GGBS used in this research, respectively. The desert sand was collected from the Sharjah desert in the United Arab Emirates. The particle size distribution of the fine and coarse aggregates is depicted in Figure 1. The fine particle size of desert sand was passed at 100% in large sieves. Quartz sand, with consistent proportions and two particle sizes (0.5 mm and 1–5 mm), was introduced into the concrete mix with the primary objective of filling gaps among other mixture components and enhancing particle packing [9]. For improved workability and consistency of the UHPC, the superplasticizer Viscocrete 3425 was employed at a dosage of 0.7% of the binder weight. Twisted steel fibers, constituting 1% of the binder material weight, were utilized to reinforce the UHPC. A deliberately high water/binder ratio of 0.23 was adopted to achieve the desired workability of the concrete mixtures. This elevated water/binder ratio was specifically chosen to accommodate the use of desert sand, which necessitates additional water for optimal workability [10].

2.2. Proportions of Mix and Preparation of Samples

The mix design for UHPC employing RSM comprised thirteen mixtures initially, of which five mixtures sharing similar proportions were consolidated into a total of nine unique combinations. The inclusions of FA and GGBS as SCMs aimed at enhancing UHPC properties based on findings from existing literature [22,23]. The reference mix, serving as a baseline, consisted solely of cement. The carefully determined binder materials/fine aggregates ratio of 0.83 and a water/binder ratio of 0.23 were established through iterative experimental tests. The sample preparation and mixing process followed a systematic procedure as follows.
Firstly, the dry mix of fine aggregates, including crushed sand, desert sand, and quartz sand, underwent a three-minute mixing cycle to achieve homogeneity. Subsequently, binder materials such as cement, GGBS, and FA were added, and an additional three-minute mixing phase ensued to eliminate any agglomerated particles and enhance overall homogeneity. The addition of water occurred gradually, with 50% added to wet the binder materials, followed by the remaining 50% added with a superplasticizer (SP) over two minutes. Mixing continued until the UHPC mix achieved complete homogeneity. The incorporation of steel fibers and a subsequent two-minute mixing phase ensued. The resulting concrete was then poured into molds with slump values ranging from 60 to 90 mm. These molds were placed in an environment with a relative humidity of 75 ± 3% and a room temperature of 28 ± 3 °C for a curing duration of 24 h. The concrete samples were further submerged in a water tank until the testing date.
Utilizing RSM software in construction materials facilitated the derivation of an optimum concrete mix design. An analysis of variance (ANOVA) was concurrently employed to uncover the potential relationships between the various variables, specifically the SCMs and desert sand. Equation (1) illustrates the regression model within the RSM framework [24]. The difference between the second and third terms in this equation is that the second term represents the linear relationship between each independent variable and the response variable. The third term represents the quadratic relationship of independent variables with the response variable, capturing the curvature effect.
Y = β0 + ∑k,i=1 βi xi + (∑k,i=1 βii xi) + ∑k−1,i=1 ∑n j βij xi xj + e
Here, Y is the concrete property, xi and xj are the factors (SCMs and desert sand), k represents the parameters involved in this study, β is the coefficient of regression, and e is the random error.
RSM helps in identifying the relationship between the variables and the response, allowing for the optimization of the response by adjusting the variables. A regression model is a type of statistical model used to predict the value of a dependent variable based on one or more independent variables. In the context of RSM, regression models are used to fit a polynomial equation to the experimental data. Regression models, especially linear and quadratic models, are relatively simple to understand and interpret. The use of the regression model in RSM provides a powerful tool for optimizing the properties of UHPC made with desert sand and SCMs. Its simplicity, flexibility, and strong predictive capabilities make it an ideal choice for this type of study, ensuring that the mixture designs are both effective and economically viable.
The ranges and levels of all the factors (variables) examined, specifically SCMs and desert sand, can be seen in Table 3. The percentage of desert sand used in this study ranged between 25 and 75%, while the percentage of SCMs used in this study ranged between 10 and 30%.
Design-Expert v.7 is a popular software used for response surface methodology (RSM). It facilitates the creation and analysis of response surface models, includes tools for fitting linear, quadratic, cubic, and higher-order models, and provides visualization tools such as 3D surface plots, contour plots, and perturbation plots. Multi-objective optimization using methods such as desirability functions enabled within RSM provided solutions for finding the best combination of variables to achieve optimal responses. Furthermore, RSM performs statistical analysis to assess the significance of factors and interactions, and then provides graphical tools for visualizing the effects of factors on responses.
In this study, the Design-Expert® software tool version 13, was utilized to analyze the data obtained from the CCD and perform multi-objective optimization. Thirteen experimental runs were suggested for the two numerical factors [21]. The proportions of the UHPC mix employed in this study are outlined in Table 4. The model was formed according to the values obtained from the results of experiments. The prediction of mathematical equations was created based on Equation (1). The expected outcomes (properties) were evaluated as a task of the proportions of desert sand (%) and SCMs (%). The response average was applied to develop the expected model of all responses. The experiential relationship between the factors (desert sand and SCMs) and the response (workability and 7-day compressive strength) is described by a second-order polynomial, as shown in Equations (2) and (3), as follows:
Workability = +65 − 7.91A + 6.66B − 1.25AB + 3.44 A2 + 3.44 B2
Compressive strength = +38.73 − 9.10A − 3.59B − 0.265AB + 6.16A2 + 14.08B2

2.3. Experimental Design and Statistical Analysis

In the experimental study, the RSM software was employed to design UHPC mixtures. The primary rationale for opting for RSM was to minimize the number of experimental iterations, utilizing techniques such as CCD [25,26]. RSM facilitates the development of relationships between variables and responses, allowing for the creation of an efficient model that addresses variable interactions and determines optimal solutions while minimizing experimental efforts. CCD, a key RSM tool, is characterized by three clusters of design points.
The initial phase of this research involved a series of parametric analyses to identify the optimal independent variables. The outcomes underscored the importance of reducing Portland cement content in the UHPC matrix while maximizing desert sand content to achieve desirable responses. These conditions directly impact workability and compressive strength, the key focuses of this study. The overarching objective is to decrease cement content through the use of SCMs, specifically GGBS and FA, in the production of UHPC, aiming for cost-effectiveness and environmentally friendly concrete. Consequently, a sequence of investigations were conducted to pinpoint the suitable range for these added variables. Table 3 presents the maximum and minimum coded and actual values of the influencing factors, including SCMs and desert sand, which are further detailed in Table 4.

3. Results

As shown in Table 4, thirteen UHPC mixtures have been created using RSM. Out of the thirteen mixtures designed, five mixtures are similar in quantities, and the experimental runs were reduced to nine only. In the next subsections, the results obtained from the experimental runs, including the workability and 7-day compressive strength of UHPC, are presented.
The number of tests in an experimental design significantly affects the results and their reliability. Increasing the number of tests generally improves the statistical power of the experiment, allowing for a more precise estimation of the model parameters and a better understanding of the relationships between factors and responses.

3.1. Workability

The assessment of UHPC workability involved testing the slump, and the outcomes are depicted in Figure 2. The incorporation of desert sand, particularly in higher proportions, markedly reduced the workability of the concrete [27,28]. The reduction in workability is conspicuous with escalating levels of desert sand in lieu of natural sand. This decline can be attributed to the fine particle size and spherical shapes characterizing desert sand, which significantly increase its specific surface area [29]. Consequently, the need for an additional paste amount arises to achieve improved workability.
The slump values for the UHPC mix ranged from 60 to 90 mm. To enhance the workability of the concrete mixtures, particularly with high desert sand content, a high water/binder ratio of 0.23 was employed. The incorporation of SCMs in the concrete mix significantly improved workability, as evidenced in Mix 6 (M6). Conversely, Mixes 1 (M1) and 8 (M8), characterized by high dun sand content and low SCM content, exhibit the lowest slump values. These findings align with the results reported by Dawood and Jaber [30], who observed a reduction in concrete workability with higher levels of desert sand. This reduction is attributed to the spherical shape and fine particle sizes of desert sand, necessitating additional water for lubrication within the cement matrix [30].
However, these results differ from those reported by Al-Harthy et al. [31], who noted an increase in concrete workability with a higher desert sand content. This variance might be attributed to the influence of ball bearings moving more easily than angular-shaped particles. Nevertheless, it is worth noting that an excess of 50% desert sand led to a decrease in workability.

3.2. Compressive Strength

A total of 54 cubes with dimensions of 100 mm × 100 mm × 100 mm were prepared to assess the 7-day compressive strength, as depicted in Figure 3. Among the concrete mixes, M10 exhibited the highest 7-day compressive strength, reaching 76.45 MPa. This notable strength can be attributed to the incorporation of 10% SCMs and 25% desert sand. However, it is noteworthy that the high content of desert sand in the concrete mix could potentially contribute to a decrease in compressive strength. Conversely, Mix M1, featuring 85.35% desert sand and 20% SCMs, attained the lowest strength value at 7 days, measuring 34.85 MPa. The diminished compressive strength in this case may be linked to the spherical shape and fine particle sizes of desert sand, necessitating additional water during the casting process.
Figure 3 illustrates the 7-day compressive strength of UHPC mixtures based on the RSM-adopted mix design. Notably, the incorporation of a lower proportion of desert sand contributed to an enhancement in the compressive strength of UHPC, particularly evident in Mixes M6 and M10. This finding aligns with the results reported by Al-Harthy et al. [31], who observed a general reduction in concrete compressive strength with an increase in desert sand content. The decrease in strength is attributed to the heightened surface area of desert sand, necessitating an increased amount of grout to effectively coat the aggregate surface. Another reason for reducing compressive strength is the lack of steam or heat curing in the concrete lab at that time, thus using water curing to treat the concrete samples. This agrees with the studies by Aydin et al. [32] and Hamada et al. [33], which reported that the compressive strength of UHPC decreases if treated using water curing. In general, desert sand is more abundant and less expensive compared to river sand or crushed sand. However, its suitability and processing requirements (e.g., washing, sieving) can impact costs. SCMs like fly ash and GGBS are often by-products of industrial processes and may be cheaper than traditional cement. However, transportation and processing costs can vary depending on the source and location.

3.3. Statistical Analysis and Modeling

RSM has been adopted to obtain a suitable connection among the factors (desert sand and SCM proportions) and the properties (workability and compressive strength) of UHPC. An analysis of variance (ANOVA) was adopted to evaluate the results from the quadratic prediction model, as presented in Table 5.
Table 5 details the ANOVA results for the responses, affirming the significance of all models. The consistently low p-values, obtained at a 95% confidence level, remain below 0.05 for the acquired data. Simultaneously, Table 6 presents the models’ validation, specifically concerning workability and compressive strength. The ANOVA-derived outcomes instill confidence in the reliability of the models, as indicated by the elevated coefficients of determination (R2). For workability and compressive strength, the R2 values are commendably high, at 0.9663 and 0.9495, respectively. Additionally, the predicted R2 values for workability and compressive strength are 0.7605 and 0.6410, respectively. These metrics collectively highlight the robustness and credibility of the models in accurately approximating response effectiveness.
As indicated in Table 6, all models can be deemed effective. The relative impact of desert sand and SCM contents on response development is delineated by the perturbation plots, as depicted in Figure 4. The expected values, juxtaposed with the actual values obtained from the experiments, are illustrated in Figure 5. Notably, the curve (green line) corresponding to desert sand percentage represented by (A) appears to exhibit a more pronounced effect than the curve (blue line) associated with the SCM percentage (B) in the outcomes of the responses. As shown in Figure 4, desert sand has somewhat the same effect as SCMs on the workability, while desert sand has a higher effect than that of SCMs on the 7-day compressive strength of UHPC. This effect is mostly due to the filling effect of desert sand that can increase the compactness of the concrete sample.
Figure 5 presents the predicted values versus actual values for the workability and 7-day compressive strength of UHPC. Notably, the predicted values in the case of workability closely align with the actual values, outperforming the prediction accuracy observed in the case of compressive strength.
Furthermore, the significance of the model can be elucidated through two plots, both 2D and 3D, generated by the statistical analysis. In these plots, desert sand is denoted as A, while SCMs are indicated as B. The interplay of these two plots reveals the dynamics of response development, specifically in terms of workability and compressive strength. Furthermore, the effects of the experimental results of desert sand and SCMs on the responses are visually depicted in both 2D and 3D surface response plots, as illustrated in Figure 6 and Figure 7, respectively.
The maximum slump value, reaching 90 mm in Mix M6 made of 25% desert sand and 30% SCMs, aligns with findings from a recent study by Yan et al. [34]. They reported that a lower desert sand content tends to increase the slump value of a concrete mix, while higher desert sand amounts lead to a reduction in the slump value. This effect is primarily attributed to the heightened water demand and fine particle sizes of desert sand [35]. The significant water absorption by desert sand, necessitated by its high surface area, results in decreased slump values. In contrast, the use of 85.35% desert sand and 20% SCMs in Mix M1 achieved the lowest slump value, measuring 60 mm. Furthermore, the high compressive strength observed in Mix M10, reaching 76.45 MPa at day 7, was attained by utilizing 25% desert sand and 10% SCMs.

4. Optimization

It is difficult to obtain the optimum result for each property separately inside the same area. Thus, multi-objective optimization is considered the best way to determine the best solution that serves all responses together. After evolving and confirming ANOVA simulations for the studied properties (workability and compressive strength), the top probable responses were designated using a multi-objective optimization method. The optimization process for multi-objective simultaneous improvement is initiated after a thorough examination of the inserted factors to discern the optimal outcomes. Utilizing the CCD technique within the RSM software, the aim is to determine the optimal results for desert sand content ranging from 25% to 75%.
The weighted sum method (WSM) is selected for multi-objective optimization to determine the optimal performance of UHPC. This method is chosen for its simplicity and effectiveness in handling multiple objectives to identify the performance criteria for UHPC. The weighted sum method provides a clear and straightforward approach to optimize multiple performance criteria for UHPC. By systematically assigning weights and normalizing objectives, this method ensures a balanced and comprehensive optimization process. Table 7 outlines the lower and upper limits of each factor, emphasizing the significance of each factor and its impact on concrete properties. Variations in variable levels can enhance one quantified property while exerting a passive effect on another property. Consequently, a multi-criteria approach was embraced to address the challenges associated with optimizing various properties simultaneously. In this study, the CCD technique was employed to optimize all responses concurrently.
Certainly, the responses, namely workability and 7-day compressive strength, were transformed into individual desirability (di) values, devoid of dimension, spanning 0 for a wholly undesirable response to 1 for an entirely desirable response. This conversion facilitates the amalgamation of results derived from all properties, allowing for the optimization of both concrete properties to attain the optimal outcomes. The desirability variations for all responses have been obtained and visually presented in Figure 8 and Figure 9 illustrating the graphical slopes for the investigated optimized responses. The graphical ramps for the optimized workability and compressive strength are illustrated in Figure 9. It can be detected that the multi-objective optimization of factors is 75% desert sand as desert sand proportion rate and 30% SCM content as a cement replacement. The optimum values of workability and 7-day compressive strength were 69.8 mm and 46.01 MPa, respectively. In this study, all the factors and responses were recognized with the same significance related to the study goal, as shown in Table 7.
Also, the workability and 7-day compressive strength were simultaneously optimized. Desert sand and SCM contents were the factors used in this study. The importance was 4 from 1 to 5 for factors and responses as shown in Table 7. The factors desert sand and SCMs are represented by the variables. The desirability function of factors ranged from 0 (not desired) to 1.0. (desired), as shown in Figure 10. The optimum selection was projected to contribute considerably in completing the required goal when the desirability value close to one.
Figure 10 reveals the desirability index of desert sand and SCMs resulting from multi-objective optimizations. Notably, the optimal values for workability and compressive strength are 69.4 mm and 46.02 MPa, respectively, yielding a combined desirability of 0.558. The optimized outcomes indicate that the combination of 75% desert sand and 30% SCMs achieves the desired value of 0.558.

5. Conclusions and Recommendations

This study aimed to advance the development of an eco-friendly UHPC by incorporating SCMs (FA and GGBS) as partial cement replacements and desert sand as partial substitutes for fine aggregate. The investigation delved into the replacement levels of SCMs (10–30%) and desert sand (25–75%), and their impacts on the workability and compressive strength of UHPC, employing the CCD method within RSM. The key conclusions from this study are drawn as follows.
  • The incorporation of SCMs improved the workability of UHPC, while the use of desert sand significantly reduced workability, especially with high content in Mix M1, achieving the lowest slump value of 60 mm only due to the high-water absorption and porosity of desert sand particles.
  • A low replacement level of cement by SCMs enhanced the 7-day strength of UHPC, achieving 76.45 MPa for Mix (M10), and this attributed to its filling effect and pozzolanic reactivity, contributing to the production of additional C-S-H gels crucial for hardened concrete. However, a high amount of desert sand led to a notable reduction in UHPC strength.
  • Optimal strength was achieved for UHPC containing 10% SCMs and 25% desert sand, while the lowest strength was observed for UHPC with 20% SCMs and 85.35% desert sand.
  • The study employed RSM to evaluate the impact of SCMs and desert sand replacement levels on UHPC responses at 7 curing days. The R2 values for workability and compressive strength were 0.966 and 0.949, respectively. The optimal UHPC composition was identified by RSM as 30% SCMs and 75% desert sand.
Incorporating desert sand and SCMs in UHPC can notably reduce the environmental impact of concrete production. These materials enhance UHPC’s mechanical and durability characteristics. Nevertheless, regional variations in desert sand properties necessitate standardization and quality control for consistent performance. Efficient management of their transportation and storage is crucial for large-scale projects. Extensive field trials and long-term studies are needed to fully understand UHPC behavior with these materials under various conditions. The results presented in this paper are specific to 7-day curing periods. Future research should explore the effects of supplementary cementitious materials (SCMs) and desert sand on the strength of concrete at later ages. Additionally, investigations into other mechanical and durability properties are necessary to develop a highly sustainable and durable eco-friendly UHPC.

Author Contributions

Data collection, methodology, and writing the main draft by H.H., reviewing, formal analysis, funding, and proofreading by F.A. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the American University of Sharjah, FRG19-L-E23.

Data Availability Statement

Data will be available upon reasonable request.

Acknowledgments

The authors would like to thank and deepest gratitude to the American University of Sharjah for the support required to complete this work.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Particle size distribution of fine aggregates.
Figure 1. Particle size distribution of fine aggregates.
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Figure 2. Slumps of concrete mixtures containing different desert sands and SCM contents.
Figure 2. Slumps of concrete mixtures containing different desert sands and SCM contents.
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Figure 3. Compressive strengths of concrete containing different desert sands and SCM contents.
Figure 3. Compressive strengths of concrete containing different desert sands and SCM contents.
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Figure 4. Perturbation plots of (a) workability and (b) compressive strength of concrete.
Figure 4. Perturbation plots of (a) workability and (b) compressive strength of concrete.
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Figure 5. Predicted versus actual values of (a) workability and (b) 7-day compressive strength.
Figure 5. Predicted versus actual values of (a) workability and (b) 7-day compressive strength.
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Figure 6. The 2D design portable for the workability and 7-day compressive strength of UHPC.
Figure 6. The 2D design portable for the workability and 7-day compressive strength of UHPC.
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Figure 7. The 3D curve for the workability and 7-day compressive strength of UHPC.
Figure 7. The 3D curve for the workability and 7-day compressive strength of UHPC.
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Figure 8. Optimization of responses: (a) workability and (b) 7-day compressive strength.
Figure 8. Optimization of responses: (a) workability and (b) 7-day compressive strength.
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Figure 9. Ramp curves of factors and responses.
Figure 9. Ramp curves of factors and responses.
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Figure 10. The optimum amount of desert sand and SCMs.
Figure 10. The optimum amount of desert sand and SCMs.
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Table 1. Chemical compositions and physical properties of cement, FA, and GGBS.
Table 1. Chemical compositions and physical properties of cement, FA, and GGBS.
Binder Material SiO2Al2O3CaOFe2O3K2OP2O5TiO2ZnO
OPC112.9775.567.720.6910.3990.490.107
FA52.2627.332.559.932.390.4094.230.045
GGBS22.58.2164.951.640.3310.1811.270.485
Table 2. Physical properties of cement, GGBS, and FA.
Table 2. Physical properties of cement, GGBS, and FA.
Physical PropertyOPCGGBSFA
Specific gravity3.152.92.19
Fineness specific surface m2/kg374400474.2
Compressive strength mortar prism (MPa)25.7 5.1
Table 3. Limits of factors coded using RSM.
Table 3. Limits of factors coded using RSM.
Factors (Variables)CodeUnit−10+1
Desert sandA%255075
SCMsB%102030
Table 4. Mix design using Design-Expert software version 13.
Table 4. Mix design using Design-Expert software version 13.
RunSCMDesert SandCementSCM (FA+ GGBS)Natural SandDesert SandSteel FiberQuartz PowderWaterSP
12085.35800200175.81024.21020023070
220508002006006001020023070
334.1450658.6341.46006001020023070
420508002006006001020023070
510759001003009001020023070
630257003009003001020023070
730757003003009001020023070
85.8550941.558.56006001020023070
92014.648002001024.2175.81020023070
1010259001003009001020023070
1120508002006006001020023070
1220508002006006001020023070
1320508002006006001020023070
Table 5. ANOVA results of workability and compressive strength of UHPC.
Table 5. ANOVA results of workability and compressive strength of UHPC.
Source Sum of Square Df Mean Square F-Value p-Value Remarks
WorkabilityModel1007.205201.4440.16<0.0001Significant
A-Desert sand500.611500.6199.81<0.0001
B-Fly ash354.901354.9070.76<0.0001
AB6.2516.251.250.3012
A282.20182.2016.390.0049
B282.20182.2016.390.0049
Residual35.1175.02
Lack of Fit35.11311.70
Pure Error0.000040.0000
Cor Total1042.3112
Compressive strengthModel2277.435455.4926.330.0002Significant
A-Desert sand662.441662.4438.300.0005
B-Fly ash103.321103.325.970.0445
AB0.280910.28090.01620.9022
A2264.081264.0815.270.0058
B21379.0211379.0279.72<0.0001
Residual121.08717.30
Lack of Fit121.08340.36
Pure Error0.000040.0000
Cor Total2398.5112
Table 6. Validation of model for workability and compressive strength.
Table 6. Validation of model for workability and compressive strength.
Description Workability Compressive Strength
Standard deviation (SD)2.244.16
Mean 69.2351.19
R20.96630.9495
Predicted R20.76050.6410
Adjusted R20.94230.9135
Precision 19.153411.9580
Table 7. Lower and upper limits of individual factors.
Table 7. Lower and upper limits of individual factors.
NameGoalLower LimitUpper LimitImportance
A: Desert sandmaximize25754
B: SCMmaximize10304
Workabilitymaximize60904
Compressive strengthmaximize34.8576.454
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Hamada, H.; Abed, F. Optimization and Modeling of 7-Day Ultra-High-Performance Concrete Comprising Desert Sand and Supplementary Cementitious Materials Using Response Surface Methodology. Buildings 2024, 14, 2058. https://doi.org/10.3390/buildings14072058

AMA Style

Hamada H, Abed F. Optimization and Modeling of 7-Day Ultra-High-Performance Concrete Comprising Desert Sand and Supplementary Cementitious Materials Using Response Surface Methodology. Buildings. 2024; 14(7):2058. https://doi.org/10.3390/buildings14072058

Chicago/Turabian Style

Hamada, Hussein, and Farid Abed. 2024. "Optimization and Modeling of 7-Day Ultra-High-Performance Concrete Comprising Desert Sand and Supplementary Cementitious Materials Using Response Surface Methodology" Buildings 14, no. 7: 2058. https://doi.org/10.3390/buildings14072058

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