1 Introduction

1.1 RPC’s characteristics, uses, and limitations

Over the past several years, technological breakthroughs have resulted in the development of new types of concrete. Reactive Powder Concrete (RPC) stands out for its remarkable mechanical and durability properties. Furthermore, the correct fiber dosage produces a cementitious composite with outstanding flexural and uniaxial tensile strengths [1,2,3]. These special cementitious composites perform better than regular or high-strength concretes owing to their capillary-free cementitious matrix with a denser microstructure [4]. The fine-grained mixture in this high-tech concrete has a particle size limit of 1 mm. By eliminating the coarse aggregate, RPC demonstrates an enhanced uniformity of its microstructure. Notably, this resulted in a reduction of the Interstitial Transition Zone (ITZ) between the paste and aggregates, thereby improving the mechanical properties of the material. Hence, compared to traditional coarse-grained concrete, the inner microstructure of RPC is much more homogeneous and denser. These properties result in a material with better durability due to the stress uniformity over its matrix [5, 6]. Thus, RPC has grown in popularity in building engineering over the last few decades. For example, it was successfully employed in precast components, shear walls, bridge engineering, railway infrastructure, petroleum and natural gas sector usage, architectural facades, radiation shielding, strengthening and rehabilitation, wind farm towers, and offshore applications [7,8,9,10,11].

Regrettably, the lack of design standards and norms, improper knowledge of this concrete nature and production engineering, its elevated carbon footprint per cubic meter, features of locally accessible cement, and expensive pricing limit the application of this cementitious material beyond early research activities. Moreover, owing to its low water and high binder dosages, RPC is prone to shrinkage, of particular concern is autogenous shrinkage. Therefore, it is still required a complete review and remediation of these back draws [7, 12].

Thus, most recent initiatives have attempted to address these shortcomings and restrictions to RPC’s applicability. The development of more environmentally friendly and cheaper materials has been a focus of several research fields that aim to replace cement, silica fume (SF), quartz powders, and manufactured quartz sand with greener products [13, 14]. For instance, recent research has demonstrated that rice ash, slag, oil fluid catalytic cracking waste, and waste glass may replace some of the conventional constituent materials in these ultra-high-strength concretes, resulting in lower costs and carbon footprints [15,16,17].

Moreover, cement quality is another issue. These ultra-high-strength cementitious composites require low tricalcium aluminate (celite-phase) cement, which is hard to source in developing countries [18]. Cement's high celite component is harmful to achieve that ultra-high strength, as this phase hydrates briefly to create ettringite, leaving less water to hydrate alite phase and form calcium silicate hydrate gel mainly responsible for the concrete’s mechanical features. This is especially relevant due to RPC’s extremely low water–binder ratio. Second, it increases concrete water requirements and capillary porosity, thus reducing resistance. It also impacts cement-superplasticizer (SP) incompatibility, which is a key factor for achieving the aforementioned RPC’s outstanding properties [6, 19].

1.2 Waste glass and its use in the concrete industry

Glass production contributes significantly to greenhouse gas emissions. Despite the fact that recycling may help the environment, glass is landfilled three times more in the US than it is recycled [20]. In 2017, an estimated amount of 11.4 million tons of municipal solid glass waste was generated in the US. Unfortunately, only 26% of the waste material was recycled, whereas the majority (8.4 million tons) was dumped in landfills [20]. In Colombia, where the local cement was used in this study, the waste glass proportion as a fraction of total garbage generated falls to 13% [21]. Therefore, 87% of this garbage is being disposed of in landfills.

Nevertheless, several studies have recently proved the feasibility of substituting pozzolanic components and aggregates using glass waste in the concrete industry [22,23,24]. Recycled glass powder has excellent pozzolanic characteristics as a cementitious material [15]. Furthermore, waste glass offers additional benefits compared to other industrial wastes utilized as a pozzolan. First, it is supplied from smaller, regional facilities rather than massive steel mills and power plants (e.g., slag and fly ash). Hence, it is likely to be found practically in any metropolitan area. In this regard, waste glass has a more comprehensive supply than these other industrial wastes [20]. Secondly, its chemistry was incredibly constant and devoid of hazardous components [25]. Furthermore, depending on its particle size, it has comparable pozzolanic capabilities. As a result, milled waste glass’s pozzolanic capacity may permit cement replacement rates equivalent to those of typical pozzolanic byproducts [20, 26]. In addition, because milled waste glass particles have nearly low porosity and minimal water absorption, their application to concrete minimizes the amount of cement and chemical admixture required [7, 27]. Finally, since glass powders are made from post-consumer rubbish, utilizing them in concrete production will have equal environmental advantages to using those typical industrial byproducts [20, 26]. In literature, various published investigations [9, 28,29,30] have shown this waste material’s effectiveness as concrete aggregate. However, the addition of Waste Glass Aggregate (WGA) to concrete reduces its mechanical properties and presents the risk of Alkali-Silica Reaction (ASR) [31]. As a result, it should be thoroughly researched when using WGA.

Several ultra-high-strength concrete projects have assessed the practicability of employing waste glass as a cement and filler [9, 28,29,30]. In this area, Vaitkevicius et al. [15] examined the utilization of WGP in these concretes’ microstructure, demonstrating that it accelerates cement hydration under heat treatment. Additionally, Soliman and Tagnit-Hamou [32] examined ultra-fine WGP’s partial replacement for SF. It was found that 30–50% of the SF can be replaced with ultra-fine WGP, leading to a compressive strength of 100–170 MPa under standard curing conditions and over 200 MPa under thermal curing conditions. Further, Abellan-García et al., studied WGP in this field extensively [7, 18, 27]. Various binder materials, including fluid catalytic cracking catalyst residue, rice husk ash, and fly ash, have been evaluated to determine whether the WGP can be used in ternary and quaternary cement blends. A significant synergistic effect was achieved by the partial substitution of limestone and recycled glass powder for cement and SF. Compared to the control mixture, a system containing these powders achieved compressive strengths of over 150 MPa without special curing and lower cement, SF, and SP concentrations. Furthermore, Jaramillo-Murcia et al. [33] found that high-packing density designed concrete made with limestone powder (LSP) and WGP had durability comparable to the control mixture without waste components. Additionally, Tagnit-Hamou and Soliman [34] showed that ultra-high-strength concrete containing WGP had minimal mechanical abrasion, nearly no chloride-ion penetration, and excellent freeze–thaw resistance. The limestone and recycled glass reduced SF and concrete drying shrinkage [7, 27].

Pertaining to using WGA, Tagnit-Hamou et al. [34, 35] found promising results employing it as they found that in combination with WGP, large typical ultra-high-strength and high-density packing typical concrete components can be replaced, attaining compressive strengths of over 100 MPa and up to 177 MPa under standard curing conditions [34]. However, the study [35] examines WGA with quartz sand replacement ratios of up to 100% while preserving a quartz powder quantity of 240 kg/m3. This research found an optimal WGA mean particle diameter of 275 microns to achieve compressive strengths from 130 to 170 MPa under ordinary curing. The study in [35] used 39.5% recycled glass in RPC-type concrete, the highest to date. ASTM C1260 [36]’s maximum expansion in this concrete was roughly a third of the “innocuous behavior” criteria (0.1%). The authors explained the insignificant ASR expansion value using WGA particles less than 1 mm. The smaller WGA particle size increases the pozzolanic reaction preventing the ASR issue. Undoubtedly, the high SF dosage also influenced the decision to select the pozzolanic reaction [22]. However, it is important to note the SF commercial process, which represents a significant portion of the overall cost of RPC [37, 38].

1.3 Importance, aim, and scope of the study

Although RPC research has made significant strides recently, there have been enormous concerns about health, cost, and carbon footprint. For instance, a carcinogenic danger is posed by manufactured quartz-based RPC [39]. Therefore, their replacement with recovered waste glass would vastly enhance the industrialization process from a health and safety point of view. The comprehensive replacement of these two quartz-based products reduces RPC overall price by two means. First, since the cost of these materials is more than that of recycled glass. Second, by utilizing locally accessible waste glass in RPC production, shipping expenses are decreased [35, 40]. The reutilization of waste-based components in cementitious materials has gained significant attention in recent years due to its potential to contribute to sustainability. The use of such components, including recovered glass, can decrease the utilization of virgin raw materials, reduce waste disposal, and lower energy consumption during the production process. In addition, the use of waste-based components can result in lower carbon emissions and environmental impacts, thus promoting a more sustainable approach to the development and use of cementitious materials.

Nonetheless, the inquiry for the optimum usage of waste glass in the concrete mixture must be mindful of the potential ASR, which has detrimental effects on concrete [31, 41]. Additionally, low-celite-phase cement is difficult to find commercially, especially in developing countries. Thus, these nations cannot duplicate the study published with ideal cement with low-celite-phase content; therefore, local cement must be considered. Most cases are reported in 1.2 and employed low tricalcium aluminate cement [7, 15, 18, 27, 34, 35]. This cement contrasts sharply with that employed in the present research, which had about 12% celite-phase (common value for commercially available cement in many developing countries).

Consequently, this research aims to design and produce an RPC that achieves a compressive strength of over 120 MPa with the highest amount of waste glass in its mixture proportion, and the lowest high-celite-phase cement and silica fume dosages.

2 Research methodology and materials

2.1 RPC-making raw materials’ characterization

Table 1 summarizes the physical and chemical characteristics of the RPC-making raw materials used in this research.

Table 1 The physicochemical characteristics of granular RPC-making raw materials
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To complete the characterization of the granular components used in the development of the RPC, we performed several X-ray diffractions (XRD) and scanning electron microscope (SEM) experiments. Figures 1 and 2 show the findings of XRD and SEM tests, respectively.

Fig. 1
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The XRD results of: a waste glass, b LSP, c SF, and d cement

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Fig. 2
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Results of SEM analysis on a WGA; b WGP; c LSP; d SF; and e cement

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The XRD analysis of waste glass depicted in Fig. 1 (a) revealed the amorphous nature of this waste material. The result shown in Fig. 1 (b) indicated that calcite most of the LSP. Figure 1 (c) illustrates the XRD pattern of SF. This high silicon-oxide substance is entirely amorphous, as shown by the extraordinarily broad peak for SF. Figure 1 (d) represents the OPC’s mineralogical findings.

Figure 2 displays the SEM analyses of WGA, WGP, LSP, SF, and cement. These photos demonstrate that the diameter of spherical SF particles is less than 1 micron. The pictures of recycled glass items also reveal their flatted surface, paucity of porosity, and the presence of non-desired shape-factor particles (i.e., flat-shape and needle-shape), as remarked in red ellipses [See Fig. 2 (a) and (b)].

2.2 Mixture proportions

2.2.1 Selecting the superplasticizer

Three commercially available SPs were considered in this research. The selection of SPs was based on their effect on compressive strength and porosity measured on the concrete’s water absorption rate as per the ASTM C1403 [42]. Figure 3 presents a photo of the three SPs considered and an image of the test for measuring the water absorption rate.

Fig. 3
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a Commercially available SP; b water absorption test setup

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The commercial polycarboxylate-based superplasticizers considered in the present research can be found under the following brand labels; Plastol 7500 ultra, Sikacrete 2100, and Plastol Precast Plus (from left to right in Fig. 3a).

The evaluation of the absorption by capillarity of the concrete specimens was carried out using the procedure described in ASTM C1403 [42]. The compressive strength of the tested concrete and its respective absorption show a relationship in most cases. With this test, it was possible to determine the effect of some additives or components of the mixture on water repellency over time. In this particular case, it was intended to know the influence of the SP and cement used in the proposed mixture.

Following the ASTM C1403 [42] standard, three specimens per type were prepared, to be cured for 28 d, and then weighed and dried in the oven at a temperature of 110 ± 5 °C for a maximum 24 h. Subsequently, the samples were removed from the oven and cooled for 2 h (24 ± 8 °C and relative humidity less than 80%) to proceed with the test within 24 h. The cubes were once more weighed and measured at least three points on each side. The samples were placed in the container on the separators, leaving a minimum space between the underside of the specimens and the bottom of the container of 3.0 mm, as well as an immersion of 3.0 ± 0.5 mm [See Fig. 3 (b)]. The samples were weighed at 0.25 h ± 0.5 min, 1 h ± 2 min, 4 h ± 10 min, and 24 h ± 15 min immersed in the water. Before each weighing, the surface water of each specimen must be removed with a towel, and after the weighing, water must be added to the container to guarantee immersion of 6 mm. Then, the absorption (\({A}_{T}\) in g/cm2) was calculated using Eq. (1) for each measurement period T. The water absorption at total saturation (\({A}_{s}\)) was calculated using Eq. (2):

$${A}_{T}=\frac{{W}_{T}-{W}_{0}}{{L}_{1}{L}_{2}}$$
(1)
$${A}_{s}=\frac{{W}_{s}-{W}_{0}}{{L}_{1}{L}_{2}},$$
(2)

where:

\({W}_{T}\): The weight of a specimen (g) at the time (\(T\)) after immersion.

\({W}_{0}\): The specimen weight (g) at the beginning of the test.

\({W}_{S}\): The weight of a specimen (g) at 24 h after immersion.

\({L}_{1}\): The cubic cube’s average submerged surface length (mm).

\({L}_{2}\): The cubic cube’s average submerged surface width (mm).

2.2.2 Adjusting SF content to avoid ASR expansion

Several studies have proven that recycled glass is suitable for ultra-high-strength cementitious materials. Nonetheless, the risk of damaging ASR caused by waste glass’s high alkalinity and amorphous silica concentrations and cement hydration’s portlandite has restricted its usage in cement and concrete [23, 31, 35]. The literature review presented subsection 1.2. shows that in the reported cases of high-packing density concrete recycled glass has a maximum weight of 39.5%. This study reported the complete replacement of quartz sand for recycled glass, maintaining 223 kg/m3 of SF and 238 kg/m3 of quartz powder [35]. The ASR expansion of this dosage was evaluated by conducting a test based on ASTM C1260 [36], resulting in an insignificant expansion at 16 days [35].

Reducing glass particle size promotes pozzolanic behavior in recycled glass concrete, preventing ASR growth [41, 43]. Waste glass particles under 1 mm behave as a pozzolanic concrete component, interacting with portlandite to form C-S–H gel instead of ASR gel [26, 35]. The low water–binder (w/b) value also reduces interior moisture, preventing ASR gel formation [35]. The most effective way to prevent ASR is to use a certain amount of high-pozzolanic concrete-making ingredients, which causes the pozzolanic reaction to occur first [22, 23]. For numerous reasons, the pozzolanic reaction avoids ASR: (i) it generates C–S–H gel on the glass surface to shield its amorphous silica against Na + and K + reactions [22, 44]; (ii) the pozzolanic process lower OH- ions and reduce pH, preventing ASR below 13 [22]; (iii) the pozzolanic reaction produces C–S–H gel unattached silicon oxide ions on the surface that capture and combine alkali cations [45], preventing ASR. On one hand, avoiding ASR gel formation is important since this study aims to create an RPC with the highest waste glass content. On the other hand, as SF represents a high percentage of the total cost of RPC [46, 47], determining the minimum SF dosage to avoid is crucial, thereby not jeopardizing the material's viability for developing countries’ applications.

Therefore, once the SP is selected, the next stage will determine the quantity of SF needed to prevent ASR in RPC. Table 2 lists three SF dosage levels, expressing the proportion of the RPC-making components as a function of the cement weight. The lowest amount of SF (i.e., 100 kg/m3) was chosen based on several recent studies conducted in Colombia, where this research was carried out [13, 16, 27, 48]. The maximal SF dosage (223 kg/m3) matches with the mixture proportion presented in [35] with trifling ASR expansion. Thus, the current experiment also considered the mean value of 161.5 kg/m3.

Table 2 Concrete mixture designs to assess ASR vs SF dosage
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Table 2 shows mixture designs with 100, 161.5, and 223 kg/m3 SF. For these three mixture proportions, the ASR expansion was measured using ASTM C1260 [36]. These experiments used normal prismatic molds (20 × 20 × 275 mm), as RPC had no coarse aggregate. Three samples were selected for each mixed design. Demolding prompted length and mass measurements. Before measuring longitudinal length and weight at “zero,” the specimens were immersed in NaOH at 80 ± 2 ºC. After saturation in NaOH, weight and longitude fluctuations were measured daily for 16 days.

2.2.3 Statistical techniques for mixture adjustments

Once the SP was selected and the SF dosage was fixed, the RPC other component’s proportion can be determined for each design point. For this purpose, Central Composite Design [CCD, a type of design of experiments (DoE)] was used in this research. CCD is a powerful and widely used statistical tool that allows researchers to explore complex response surfaces and optimize the input variables to achieve the desired response. CCD was employed to investigate the key parameters’ effects on the RPC’s mechanical and durability properties, including cement content, water-to-cement ratio, and superplasticizer. CCD has several advantages over other experimental designs, such as its ability to model the curvature of the response surface, the ability to estimate the optimal values of the input variables, and the ability to assess the interaction effects between the input variables. Using CCD, efficient and systematical evaluation of the effects of multiple variables on the response variables, would have been difficult and time-consuming to accomplish using traditional experimental methods. In addition, CCD allowed us to generate a mathematical model that describes the relationships between the input variables and the response variables, which can be used to predict the response variables for any combination of input variables within the range of the experimental design. This model provides valuable insights into the mechanisms governing the properties of the RPC and can be used to optimize the RPC mixture design [13, 16, 27, 48].

The steps followed in the statistical framework for DoE used for the CCD are illustrated below. The experimental design’s cement, water, and SP ratios were controlled by various factors. One of the main factors in reaching the improved characteristics of RPC is its particles’ high packing density. The modified Andreasen & Andersen (MAA) theory defined the remaining raw materials. This packing theory was used to achieve a highly compacted cementitious matrix the MAA curve [Eq. (3)] was used to specify the additional raw materials for RPC using a \(q\) value of 0.264, as determined in [38, 49].

$$P\left(D\right)=\frac{{D}^{q}-{{D}_{min}}^{q}}{{{D}_{max}}^{q}-{{D}_{min}}^{q}},$$
(3)

where \(P(D)\) denotes the weight percentage of the total weight of the granular RPC-making components smaller than \(D\). \(D\) stands for the grain size, while \({D}_{\mathrm{max}}\) and \({D}_{\mathrm{min}}\) denote the largest and smallest particle sizes, respectively. CCD is typically employed to create a second-order regression approach for each response without requiring a complete factorial experiment. It has various benefits, such as estimating the quadratic influence of each factor taken into consideration on the response and identifying the relationships between components and pointing out the optimal set of the considered input variables [50,51,52] at the lowest cost. This experiment included extended center and axial points to increase variable dominance and estimate the quadratic terms [53]. For each design factor considering, these axial points, often referred to as beginning points, indicate new extreme values (low and high). A three-level, k-factor CCD has the following structure: 2 k + 2 k + c runs, where k is the number of variables to be taken into consideration. As a result, 2 k stands for the factorial points of the design, which are those points that are ± 1 unit from the design’s center and, in the case of a k = 3 design, are situated at the cube’s vertices, as illustrated in Fig. 1. A distance of α from the design’s center denotes the axial (or star) points of the design. The value of α depends on the number of experimental runs in the CCD. Six beginning points are identified for a k = 3 design, as shown in Fig. 1. All levels of C are set to code level 0, representing a repetition of the center point. As they are replicated to increase the experiment's precision, the number of these key runs in the design depends on a few necessary characteristics [13, 54]. The major points of the design are situated in the cube’s center, as seen in Fig. 1. These central runs are replicated to increase the experiment’s precision, and the number of them in the design depends on specific attributes [13, 54]. The major points of the design are situated in the cube’s center (Fig. 1).

In the present investigation, a CCD with k = 3 was used with the following structure: (i) four central runs; (ii) eight factorial design runs; and (iii) six initial design runs placed away from the design’s center. An alpha value of 1.789 was selected which is in agreement with [13, 16, 38]. The three variables taken into account are the cement dosage (kg/m3, factor 1), the water–binder ratio (factor 2), and the SP [PCA (vol.), factor 3]. Table 3 lists the variables taken into account by the CCD, along with their ranges. The cement values for codifications − 1 and 1 were established per previous research [13, 16, 38]. However, those values in the water-to-binder ratio and superplasticizer content had to be adjusted experimentally a step before. This had to be so due to the strong interaction of the superplasticizer with the alkaline nature of the recycled glass, used in quantities higher than previously experimented by the authors due to, in the case of the present investigation, all the aggregate being replaced by recycled glass. This produces that around fifty percent of the total dosage in mass was recycled glass, and, as can be observed in Table 1, both recycled glasses contained more than 11% of Na2O, thereby considerably augmenting the alkalinity of the mixture in comparison with typical mixtures that employed quartz sand.

Table 3 The variation intervals of the CCD input factors
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Once the factorial points of the design are established, the center and star points can be easily computed (Fig. 4).

Fig. 4
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Schema CCD with F1, F2, and F3 as input parameters

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2.3 Mixing, pouring, curing, and testing

The proportions of each type of mixture are determined at each point of the design. There is a defined mixing procedure for each because the time required to mix the components depends on the design point. The interactions between them are influenced by the ratios of the granular components, water, and SP. In Fig. 5, the mixing procedure is illustrated. It starts mixing the at the slowest possible speed water and SP for 1 min, then the powders (cement, SF, calcium carbonate, and recycled glass) are added at the same first speed for another 1-min and finally, after this mixing time, the speed is changed to intermedium and when the fluid aspect is reached the pasta is finished. Depending on how much paste is used, this process can take various times. It is therefore possible to reach this stage in only 1 min for designs that contain less cement and higher volumes of water and SP. Comparatively, the ones with a greater percentage of cement and lower volumes of water and SP took up to 5 min to set. We then blended the paste at high speed for 3 min. A further minute was then spent mixing the recycled glass sand at the slowest possible speed until it was completely incorporated. The mixture was then blended for 5 min—three at medium speed and two at the highest speed. Following the accomplishment of the blending process, the RPC was poured into 50 mm cube side molds while being lightly vibrated (for one minute). Then plastic sheets were used to wrap the molds, which were kept in the lab after that. After 24 h of pouring, the cube-shaped specimens were removed the mold. Then, until the trial day, it was cured in a pool at 20 ºC. Compressive testing was conducted as per ASTM C109 [55]. Three samples were tested at each age (1, 7 and 28 days) by a universal testing machine (1000 kN capacity). Figure 6 illustrates the mixing procedure, the covered specimens after pouring, and the 50 mm side cubes for compressive strength tests.

Fig. 5
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Schematic diagram of mixing procedure

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Fig. 6
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Mixing procedure, specimens covered with plastic sheets after pouring, and 50 mm side cubes for the compressive test

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2.4 Multicriteria optimization

A quadratic polynomial regression model was fitted to predict each of the responses taken into consideration after the tests suggested by the CCD were completed. The response models are used for the independent steps of (i) factor interaction analysis using the response surface methodology (RSM) and (ii) multi-objective optimization of the RPC with a high volume of recycled glass after the response models have been validated. To perform multiparameter optimization, this study used Derringer et al. [56], represented in Eq. 4, global desirability function as a basis. In this instance, \({r}_{i}\) denotes the level of relevance of each function outcome \({d}_{i}\), and \(n\) denotes the total number of optimization responses. The relevance of individual desirability in overall optimization increases as the considered \({r}_{i}\) value rises. Individual desirability functions (\({d}_{i}\)) range from 0 for an entirely undesirable response to 1 for an entirely desired result. Combining several criteria is also ideal in every case for a \(D\) value of about 1. As a result, in this case, the response values are reasonably close to the goal values. Moreover, if any one outcome is outside the desirable range, the total function will be equal to zero. Applying mixed design variables or responses may be the goal of a numerical optimization technique.

$$ OD\; = \;\left( {d_{1}^{r1} \times d_{2}^{r2} \times d_{3}^{r3} \times \ldots \times d_{n}^{rn} } \right)^{{\frac{1}{{\sum {ri} }}}} \; = \;\left[ {\Pi_{i = 1}^{rn} } \right]^{{\frac{1}{{\sum {ri} }}}} . $$
(4)

\(OD\) stands for overall desirability, properly considering all criteria, \(n\) for the number of responses during optimization, and \({r}_{i}\) for the relative weight of each desirability, function criteria (\({d}_{i}\)). The answer is either more relevant or less relevant, as indicated by the \({r}_{i}\) values. In the present work, \({r}_{i}\) value was fixed as 0.25 for all the considered responses in the multicriteria optimization. Individual desirability functions (\({d}_{i}\)) range from 0 to 1, where 0 represents a completely undesirable response and 1 is a completely wanted one. The global synthesis of the different criteria is ideal for a value of OD close to 1. Therefore, the response metrics are relatively close to the desired ones. The entire equation becomes zero if any answer or variable falls outside the desirable range. The purpose of using numerical optimization would be to combine design with numerical optimization [57].

In Eqs. , 6 and 7, we show the individual form of the desired response of each response for the three maximization, minimization, and range cases, respectively. Where S is a superior limit, \(I\) is an inferior limit for a response, and impi represents the importance of the considered response. Different \(im{p}_{i}\) values can change the shape of the individual desirability for each target. The \(im{p}_{i}\) value usually varies between 0.1 and 10 [57]. The higher the value of \(im{p}_{i}\), the greater the importance of the response \(i\) in the goal.

$$d= \left\{\begin{array}{c}1 {R}_{i}\le I\\ { \left[\frac{S-{R}_{i}}{S-I}\right]}^{{imp}_{i}} I<{R}_{i}<S\\ 0 {R}_{i}\ge S\end{array}\right.$$
(5)
$$d= \left\{\begin{array}{c}0 {R}_{i}\le I \\ { \left[\frac{{R}_{i}-L}{S-L}\right]}^{{imp}_{i}} I<{R}_{i}<S\\ 1 {R}_{i}\ge S\end{array}\right.$$
(6)
$$d= \left\{\begin{array}{c}0 {R}_{i}\le I \\ 1 I<{R}_{i}<S\\ 0 {R}_{i}\ge S\end{array}\right..$$

\({d}_{i}\) is a linearly variable [57] with a \(im{p}_{i}\) value of 1. The objectives of each response to take into consideration during the optimization process are presented below. For the compressive strength \(I=\) 120 MPa, \(S=\) 165, and the objective is to maximize. In the case of the cement content, \(I=\) 700 kg/m3, \(S=\) 800 kg/m3, and the objective is to minimize. For the water–binder ratio,\(I=\) 0.145, \(S=\) 0.165, and the objective is to maintain it in range. In the latter, the I value is based on a previous experimental test, as with a low value of w/b there would not be enough water to hydrate the cement and the compressive strength drops significantly. For the PCA, the \(I\) value is fixed at 1.70%, while the S value equals to 2.50%. In this case, the objective is to minimize given the high weight that the SP has in the final cost of the RPC.

3 Results and discussion

3.1 Mixture proportions definition

3.1.1 Selection of superplasticizer

The results of the evaluation of the three commercially available SPs are presented in Table 4 and Fig. 7. It is important to note that the mixture proportion considered to assess the effect of each SP corresponds to that with the highest factorial value of the design for F1, F2, and F3 (See Table 4). The A&A mod curve was used for adjusting the rest of the components. Table 5 summarizes the results on the values of total absorption by capillarity (As) for each type of SP at the ages of 28 d and 90 days.

Table 4 As values for each type of SP at the ages of 28 d and 90 days
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Fig. 7
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Compressive test findings at 28 and 90 days for SP selection

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Table 5 ASR expansion measurements for D-1 mixture (%)
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As can be seen in Table 4 and Fig. 7, the lowest values of capillary absorption and the highest compressive strength are obtained for SP B, which is why it is selected for the following phases of the investigation. These findings show the importance of the selection of the SP for the development of RPC-type concrete. This is especially relevant when types of cement with a high tricalcium aluminate content are used, as is the case in the present investigation [57, 58].

3.1.2 Adjusting the SF dosage

Tables 5, 6, 7 show the expansion measurements of ASR for the D-1, D-2, and D-3 mixture proportions described in Table 2. Figure 6 demonstrates that the SF concentration has a significant effect on the ASR expansion measured values.

Table 6 ASR expansion measurements for D-2 mixture (%)
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Table 7 ASR expansion measurements for D-3 mixture (%)
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It is still insufficient to prevent ASR growth in the presence of 100 kg/m3 of SF, even if all recycled glass particles have a size of less than 1 mm. The findings of this study are directly contrary to those of other researchers [26, 35, 59]. In their study, the researchers concluded that recycled glass performs similarly to pozzolanic materials with particle sizes less than one millimeter and does not expand as a result of ASR. The large amount of recycled glass used in the mixture proportions D-1, D-2, and D-3, which are about fifty percent of the total concrete weight, much larger than previously reported [26, 35, 59], may account for this phenomenon. Notably, these previous researches indicated SF concentrations of up to 223 kg/m3, which substantially help prevent the development of ASR gel [23, 46].

3.1.3 Experimental design point definition

When the SP is selected, and the proportion of SF has been determined, the CCD design point may be precisely specified according to the procedure outlined in subsection 2.2. The proportions of the CCD design point mixture based on the cement weight are shown in Table 8. The results of the experiments conducted for each of the 18 points of the experimental design are presented in the next section in Fig. 6, 9 and 12.

Table 8 Proportions expressed as a function of cement (wt.) for CCD design points
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3.2 Analysis of the results on compressive strength

3.2.1 1-Day compressive strength

The compressive strength results after 1 day of curing are illustrated in Fig. 8.

Fig. 8
figure 8

RPC’s compressive strength at 24 h for each N-run of the experimental design

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The main effect plots which isolate the effect of each considered factor on the compressive strength at 24 h, are presented in Fig. 9.

Fig. 9
figure 9

Main effect plots to analyze the individual impact of each factor on the compressive strength in one day

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Figure 10 displays the three-dimensional RSM to analyze the effect of the considered RPC’s compressive strength after 24 h. To capture the effect of the cement’s dosage, F1’s factorials and center levels were considered, while the interaction between F2 and F3 is presented for each fixed value of F1.

Fig. 10
figure 10

Three-dimensional RSM for analyzing the interaction of factors F2 and F3 at fixed values of F1 on the RPC’s compressive strength at 24 h

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Figure 9 reveals a nonlinear relationship between the compressive strength at 1 day and the input variables. This figure also demonstrates that F2 and F3 (water–binder ratio and SP dosage) reduce the RPC's compressive strength after 24 h of curing. The adverse effect of increased water content on compressive strength is associated with the paste’s rising capillary porosity [47]. Concerning the impact of factor F3 on R1, several studies have shown that polycarboxylate has a detrimental effect on early strength development [60]. The ether-based polycarboxylate SP prevents the hydration of silicates (especially tricalcium silicate, C3S) and impacts the synthesis of ettringite [60]. Figure 9 and 10 illustrate the positive impact of cement dosage (factor F1) on the considered age strength. This is because cement is the principal source of hydrates that impart mechanical qualities to concrete of any age [61,62,63].

3.2.2 7-Day compressive strength

Figure 11 presents the average value with error for the compressive strength at seven days of each considered N-runs.

Fig. 11
figure 11

RPC’s compressive strength at seven days for each N-run of the experimental design

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For its part, Fig. 12 demonstrates the isolated effects of each considered factor on the RPC’s compressive strength at seven days.

Fig. 12
figure 12

Main effect plots to analyze the individual impact of each factor on the compressive strength after seven days of curing

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The interlinkage of the three considered factors is depicted in Fig. 13. As previously indicated, factor F1 favorably influenced the response. Yet, factors F2 and F3 have a detrimental influence on this response. In the case of HRWR admixture, multiple studies have demonstrated that the delay in cement hydration caused by the polycarboxylate’s capture of Ca + ions can affect the curing time by up to 14 days [7, 50], which explains the tendency and surface depicted in Fig. 12 and 13.

Fig. 13
figure 13

Three-dimensional RSM for analyzing the interaction of factors F2 and F3 at fixed values of F1 on the RPC’s compressive strength at 7 days

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3.2.3 28-Day compressive strength

The findings of the compressive strength at 28 days of each of the eighteen N-runs of the design are shown in Fig. 14, in which the average value and error can be appreciated.

Fig. 14
figure 14

RPC’s compressive strength at 28 days for each N-run of the experimental design

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As shown in Fig. 14, the achieved compressive strength is much lower than those reported in comparable studies. These low levels may be attributed to the following factors. First, the cement utilized in the present study contains almost 12% of tricalcium aluminate. While the reported in [13, 16, 49, 57] can be labeled as low-celite cement, which ranges between 1 and 3%. It is important to note that in developing countries such as Colombia, it is not possible to obtain cement which such a low tricalcium aluminate proportion [64]. The chemical phenomenon that explains this is based on the fact that this cement mineral phase is the one that first reacts with water to produce hydrated calcium aluminate tri-sulfate (AFt) [6]. The latter narrows the amount of water available to hydrate tricalcium silicate to create calcium silicate hydrate, which is much more advantageous for the mechanical performance of concrete than AFt [51, 52].

Second, as shown in Fig. 2 (a) and (b), the milling process produces a specific fraction of non-desired shape-factor ground waste glass particles in the WGP and the WGA. According to earlier research, the inclusion of glass particles with undesired form parameters reduces the RPC mechanical behavior [49, 53, 65]. Third, the smooth surface, together with no absorption of the glass particles, produces a weaker Interfacial Transition Zone (ITZ) amidst those and the paste resulting in lower bond strength and a reduction in the RPC mechanical features [31]. Finally, experimental works have demonstrated that the hydration reaction of calcium aluminates in ultra-high-strength concrete drives a significant increase in the micro-pores, adversely affecting the compressive strength [56].

Figures 15 and 16 show the isolated factor effect and the three-dimensional representation of the correlation between the examined components and the considered response, as determined using RSM analysis, respectively. In this instance, variables F1 and F3 boosted the RPC’s compressive strength at 28 days, but factor Y lowered it. The behavior of factors F1 and F2 has previously been outlined. In contrast, the connection between SP concentration and RPC’s compressive strength at 28 days changes significantly for younger ages. The latter phenomenon may be due to higher packing as hydration retardation subsides. Furthermore, the SP also increases the rheology of the material, which improves the mechanical strength of the material by reorganizing the particles more effectively [13, 57, 66].

Fig. 15
figure 15

Main effect plots to analyze the individual impact of each factor on the compressive strength at 28 days

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Fig. 16
figure 16

Three-dimensional RSM for analyzing the interaction of factors F2 and F3 at fixed values of F1 on the RPC’s compressive strength at 28 days

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3.3 Derriger–Suich optimization

The results of the algorithmic-based multicriteria optimization described in Sect. 2.4 are presented in Table 9.

Table 9 The Derringer–Suich based algorithmic results
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Table 10 presents the mixture proportion of the RPC obtained in the multicriteria optimization. The experimental validation of the RCP depicted in Table 10 obtained an average compressive strength value of 124.52 Mpa, with a standard deviation of 7.8 Mpa. These findings represent a mixture proportion of reactive powder concrete made from waste glass, the highest waste glass content recorded using cement readily accessible in the area. As a result, this dose may be replicated in poor nations in South America like Colombia. A significant decrease in the need for natural resources (such as quartz rock to create quartz powder and sand) and landfill space might result from the widespread use of recycled glass.

Table 10 Optimized RPC mixture proportion in kilograms per cubic meter
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4 Conclusions

This study aims to meet a greener RPC dosage with compressive strength over 120 Mpa while including more than 50% recycled glass in its composition. In this manner, recycled glass replaced quartz-based typical RPC-making materials. In addition, commercially accessible cement containing almost 12% aluminate tricalcium is used to make the approach replicable in developing nations. Experimental work was carried out to determine the concentration of SF that prevents ASR growth. The influence of the cement dosage, water–binder ratio, and high-range water reducer SP on the compressive strength at 1, 7, and 28 days were evaluated using a three-factor experimental design. Statistical tools like main effect plots and response surfaces were conducted to visually analyze each factor and its interlinkages. A multicriteria algorithmic-based optimization technique was applied to obtain an optimal dose with the desired compressive strength, maximum recycled glass content, and minimum cement and SP content. In this manner, both expenses and the environmental impact were decreased. The following conclusions are drawn from the results of this experimental study:

  1. (1)

    The selection of the appropriate SP is a key issue for the development of the RPC, as it affects the strength and porosity of the concrete. This issue is especially relevant when types of cement with high tricalcium aluminate contents are used since this enhances the incompatibility of the polycarboxylate cement system.

  2. (2)

    When working with recycled glass aggregates, the ASR reaction is an extremely important item. Contrary to previously published work on the subject, a reduction in particle size of less than one millimeter for waste glass is insufficient to prevent ASR growth. To avoid this potentially dangerous reaction, the fraction of the mixture examined for this investigation required a dose of 161.5 kg/m3 of SF.

  3. (3)

    The roughly 12% presence of the celite phase in the cement augments in the RPC's early strength, which may be attributed to the interaction of this cement mineral phase with the disposable gypsum and water to generate AFt. Due to the fact that this hydration process reduces the amount of water disposable for hydrating alite and belite phases, the high tricalcium aluminate concentration results in a decreased compressive strength at 28 days.

  4. (4)

    While previous research has proved that the alkalinity of waste glass facilitates the SP impact in this kind of cementitious material, the SP content required in the optimum mix when utilizing high-tricalcium-aluminate cement was more than that found for low-tricalcium-aluminate cement. This points out that the harmful effect of this mineral phase on the rheology weighs more than the beneficial effect of the glass alkalinity.

Conclusively, this research demonstrated the possibility of developing a new RPC mixture with a more than half-weight composition based on waste glass, representing a valuable contribution to reducing the carbon footprint of these cementitious materials.

However, although this study aimed to develop a novel green reactive powder concrete (RPC) with a compressive strength over 120 MPa while including more than 50% recycled glass in its composition, there are a few limitations to this study that need to be acknowledged. Firstly, this study only focused on the mechanical properties of RPC, and further studies are required to investigate other properties, such as rheology, durability and resistance to aggressive environments, and the interaction of this cementitious matrix with the fibers in fiber-reinforced RPC. Secondly, the current study only focused on one type of cement, and it is unclear whether the findings can be applied to other types of cement. Moreover, the use of high-celite cement was found to have a detrimental effect on the compressive strength of the RPC at 28 days. Finally, although the results of this study are promising, the use of waste glass in RPC production requires a consistent and reliable supply of high-quality waste glass. Therefore, future studies should explore the availability and cost-effectiveness of waste glass in different regions to promote the widespread use of this sustainable building material.