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mathematics Article Statistical Approach for the Design of Structural Self-Compacting Concrete with Fine Recycled Concrete Aggregate 1 , 2 2 3 Víctor Revilla-Cuesta * , Marta Skaf , Ana B. Espinosa , Amaia Santamaría and Vanesa Ortega-López Department of Civil Engineering, University of Burgos, 09001 Burgos, Spain; vortega@ubu.es Department of Construction, University of Burgos, 09001 Burgos, Spain; mskaf@ubu.es (M.S.); aespinosa@ubu.es (A.B.E.) Department of Mechanical Engineering, University of the Basque Country, 48013 Bilbao, Spain; amaia.santamaria@ehu.es * Correspondence: vrevilla@ubu.es; Tel.: +34-947-497117 Received: 9 November 2020; Accepted: 6 December 2020; Published: 9 December 2020 Abstract: The compressive strength of recycled concrete is acknowledged to be largely conditioned by the incorporation ratio of Recycled Concrete Aggregate (RCA), although that ratio needs to be carefully assessed to optimize the design of structural applications. In this study, Self-Compacting Concrete (SCC) mixes containing 100% coarse RCA and variable amounts, between 0% and 100%, of ﬁne RCA were manufactured and their compressive strengths were tested in the laboratory for a statistical analysis of their strength variations, which exhibited robustness and normality according to the common statistical procedures. The results of the conﬁdence intervals, the one-factor ANalysis Of VAriance (ANOVA), and the Kruskal–Wallis test showed that an increase in ﬁne RCA content did not necessarily result in a signiﬁcant decrease in strength, although the addition of ﬁne RCA delayed the development of the ﬁnal strength. The statistical models presented in this research can be used to deﬁne the optimum incorporation ratio that would produce the highest compressive strength. Furthermore, the multiple regression models oered accurate estimations of compressive strength, considering the interaction between the incorporation ratio of ﬁne RCA and the curing age of concrete that the two-factor ANOVA revealed. Lastly, the probability distribution predictions, obtained through a log-likelihood analysis, ﬁtted the results better than the predictions based on current standards, which clearly underestimated the compressive strength of SCC manufactured with ﬁne RCA and require adjustment to take full advantage of these recycled materials. This analysis could be carried out on any type of waste and concrete, which would allow one to evaluate the same aspects as in this research and ensure that the use of recycled concrete maximizes both sustainability and strength. Keywords: self-compacting concrete (SCC); recycled concrete aggregate (RCA); RCA content optimization; robustness; analysis of variance (ANOVA); compressive strength prediction; characteristic compressive strength; distribution ﬁtting 1. Introduction The varied environmental impacts of the construction sector are often of great magnitude [1], extending to resource-intensive materials [2], widely used in this sector, such as concrete and bituminous mixtures [3]. The recovery of waste sub-products for use in construction materials is now a widely accepted solution to this problem [4], to reduce these impacts [5], and to minimize dumping in landﬁll sites [6]. Waste with pozzolanic properties that can substitute clinker [7] is speciﬁed in European Mathematics 2020, 8, 2190; doi:10.3390/math8122190 www.mdpi.com/journal/mathematics Mathematics 2020, 8, 2190 2 of 24 standard EN 197-1 [8]. Replacing Natural Aggregates (NAs) with waste sub-products [9] is, likewise, a valid strategy, if the eect of each particular waste is evaluated [10] in order to get a correct mix design of the construction material [11]. The most used by-products are Recycled Concrete Aggregate (RCA) [12]; slag, both in concrete [13] and asphalt mixes [14]; rubber [15]. There are three main characteristics of RCA. Firstly, its angular shape, due to the crushing process. Secondly, the presence of adhered mortar, which causes lower wear resistance, a greater water absorption, and the appearance of Interfacial Transition Zones (ITZs) of poor quality [16]. Finally, the presence of altered and potentially contaminated cement particles within the ﬁnest fraction [17]. Self-Compacting Concrete (SCC) is a high ﬂowability concrete in the fresh state, characterized by its slump ﬂow and viscosity [18]. The slump-ﬂow test measures the ease with which the concrete will pour, while the viscosity index is related to the speed of ﬂow [19]. The addition of RCA, in general, worsens both aspects, due to its angular shape [20], which hinders the ﬂow of aggregate particles within the paste [21], and its high water absorption, which decreases the eective water-to-cement (w/c) ratio [22]. This last aspect can be compensated by increasing the water content [23]. Another possible solution is to use RCA with a high ﬁne particle proportion, although it implies a decrease in concrete strength [24]. The most important property of concrete in the hardened state, including SCC, is its compressive strength [25], to which most structural calculations refer [26,27]. The standardized strength is referred to as the characteristic strength, and it can be used for a theoretical estimate of the modulus of elasticity or the tensile strength [28]. This strength is obtained through the statistical treatment of a large number of experimental data, all of which are necessary as this material is not homogeneous and can be aected, for example, by irregular aggregate distributions [28,29]. Most of the statistical models developed to predict the compressive strength of vibrated concrete with NA show that the quantities of the mix components and the w/c ratio are the key aspects that inﬂuence this strength [30,31]. The characteristics of the NA and their gradation have much less inﬂuence [32]. However, the characteristics and amount of waste are key factors in the compressive strength of the recycled concrete. In principle, the replacement of NA by RCA, in any fraction, decreases the compressive strength of SCC [33], due to the presence of contaminants and ITZs with poor adhesion [34]. However, a lower water content can yield higher strengths than those obtained with NA, by decreasing the eective w/c ratio [35], although the ﬂowability of the SCC will worsen [36]. A literature review of over 60 studies on vibrated concrete, conducted by Portuguese researchers [30], showed this trend (lower strength when increasing the RCA content). The same trend has also been observed in SCC [37]. Statistical studies of compressive strength in non-recycled SCC are very scarce and focus on the validity of Artiﬁcial Neural Networks and multivariate models that can predict compressive strength as a function of the composition of the mix [27,38]. The acceptability of these procedures has been demonstrated, but their disadvantage is that they only evaluate strength at the standard age of 28 days [39]. In relation to recycled concrete, regardless of its type, the inﬂuence of dierent cement components has been statistically evaluated [40], as well as the good ﬁt of normal probability distribution to the compressive strength if coarse RCA is used [41]. Correct statistical studies allow one to predict both the compressive strength when a certain waste is used and the optimal amount to add of this waste. With this kind of analysis, it is possible to adapt the strength of concrete to the requirements of each structural application [42]. Nevertheless, there is a lack of research that statistically evaluates the strength behavior of recycled concrete and the eect of the waste used. Therefore, this study aims to ﬁll this gap of knowledge in the ﬁeld of concrete. Previous research has demonstrated the good performance of coarse RCA [21,37], so the sustainable SCC designed included 100% of coarse RCA. Therefore, the study focused on the eect of dierent percentages of RCA in the ﬁne fraction (0, 25, 50, 75, and 100%). Both the ﬂowability and the compressive strength of the mixes were analyzed. Moreover, an experimental procedure was designed to discard the eect of the water content [35] and the curing conditions [43], and then isolate the eect of the ﬁne RCA content. Mathematics 2020, 8, 2190 3 of 24 The novelty of this study lies in the extensive laboratory work carried out and the statistical analysis of the compressive strength afterwards. This analysis is quite signiﬁcant and allows us to study some aspects that the traditional descriptive analysis does not cover: Evaluating the eect of RCA at each age and the signiﬁcance of the dierences in the strength of concrete made with dierent RCA ratios. This way, it is possible to detect whether the same performance can be expected with dierent waste contents, and to deﬁne the optimum ratios from the strength point of view. Developing models to estimate the compressive strength of SCC with RCA. The eect of the residue is dierent at each age and the interaction between these two parameters, age and RCA content, must be considered when developing these models. Analyzing if the predicted values of the compressive strength according to the existing structural design regulations are suitable for recycled SCC. Therefore, this study allows us to obtain relevant conclusions regarding how the analysis of SCC with RCA should be carried out. This analysis includes the evaluation of the signiﬁcance of the eect of RCA, the estimation of the strength, and the analysis of the existing regulations for the design of this type of concrete. These aspects are important for the generalization and standardization of the analysis of the SCC produced with RCA. In addition to the particular conclusions reached for the material studied, another scope of this research is the development of the study procedure, which is described in detail. Therefore, it could be replicated in any type of concrete manufactured with any alternative material. With this type of analysis, the use of sustainable materials in real structures is closer. 2. Materials CEM I 52.5 R was used, according to EN 197-1 [8], in all mixtures, with a clinker content of 95% and a density of 3.12 Mg/m . The mix water was taken from the mains water supply of the city of Burgos, Spain. Proper use of chemical admixtures is essential to achieve self-compacting properties [44]. In this study, a plasticizer gave the concrete a high level of ﬂowability. In addition, a viscosity regulator was also added, so that the concrete retained its ﬂowability for longer. Previous studies of this research group have shown the validity of these admixtures in proportions between 2% and 2.2% by weight of cement [35]. The mixes were developed with three dierent types of aggregates: RCA—supplied by a local Construction and Demolition Waste (CDW) management company (IGLECAR S.L.) based in Burgos. This waste came from crushing 45 MPa strength prefabricated elements, rejected due to aesthetic manufacturing defects. The initial granulometry, 0/31.5 mm, was sieved into three fractions: ﬁne RCA 0/4 mm, coarse RCA 4/12.5 mm, and RCA > 12.5 mm. The ﬁrst two fractions were used and the third was discarded and posteriorly re-crushed. Rounded siliceous sand 0/4 mm—used in the region to elaborate SCC. Limestone ﬁller—with a size below 0.063 mm and high purity (CaCO3 content above 98%), to provide the ﬁnest particle size fraction [45]. The physical properties of these aggregates, shown in Table 1, were in line with other similar investigations [46]: the presence of adhered mortar reduced the density and increased the water absorption of the RCA in comparison with the NA [47]. The content of particles of less than 0.125 mm in size was higher in the RCA, a very relevant aspect for the ﬂowability of the SCC, as can be seen in Figure 1 and Table 2. Mathematics 2020, 8, x FOR PEER REVIEW 4 of 24 Table 1. Physical properties of the aggregates. Mathematics 2020, 8, 2190 4 of 24 Coarse Fine Regulation Siliceous Sand Limestone Filler Test RCA RCA [8] 0/4 mm < 0.063 m 4/12.5 mm 0/4 mm Table 1. Physical properties of the aggregates. Saturated-Surface-Dry 2.42 2.37 2.58 2.77 Regulation Coarse RCA Fine RCA Siliceous Limestone Filler (SSD) density (Mg/m Test ) [8] 4/12.5 mm 0/4 mm Sand 0/4 mm < 0.063 m Water absorption 24 h (%) EN 1097-6 6.25 7.36 0.25 0.54 Saturated-Surface-Dry (SSD) 2.42 2.37 2.58 2.77 Water absorption 10 min density (Mg/m ) 5.28 6.03 0.18 0.37 EN 1097-6 Water absorption 24 h (%) 6.25 7.36 0.25 0.54 (%) Water absorption 10 min (%) 5.28 6.03 0.18 0.37 Figure 1. Aggregates’ sieve analysis. Figure 1. Aggregates’ sieve analysis. Table 2. Gradation of the aggregates (EN 933-1 [8]). Size Coarse RCA 4/12.5 mm Siliceous Sand 0/4 mm Fine RCA 0/4 mm Table 2. Gradation of the aggregates (EN 933-1 [8]). 16 100.0 100.0 100.0 Size Coarse RCA 4/12.5 mm Siliceous Sand 0/4 mm Fine RCA 0/4 mm 8 63.1 99.7 100.0 4 4.5 89.2 99.4 16 100.0 100.0 100.0 2 0.7 68.1 74.3 8 63.1 99.7 100.0 1 0.5 52.8 52.7 4 4.5 89.2 99.4 0.5 0.4 31.6 34.0 2 0.7 68.1 74.3 0.25 0.3 7.5 18.4 1 0.5 52.8 52.7 0.125 0.2 1.8 9.4 0.063 0.2 0.0 4.8 0.5 0.4 31.6 34.0 0.01 0.0 0.0 0.0 0.25 0.3 7.5 18.4 Fineness modulus 6.3 3.5 3.1 0.125 0.2 1.8 9.4 0.063 0.2 0.0 4.8 3. Experimental Procedure 0.01 0.0 0.0 0.0 Fineness modulus 6.3 3.5 3.1 As large proportions of ﬁne aggregate are required by SCC [48], its performance is very sensitive to the presence of residues within that fraction [33]. For this reason, this study evaluated the eect 3. Expe of ri adding mental ﬁne PrRCA ocedu on re the compressive strength of SCC with 100% coarse RCA at dierent ages, while minimizing the inﬂuence of other variables such as water content and curing conditions. To do As large proportions of fine aggregate are required by SCC [48], its performance is very sensitive so, the following experimental procedure was developed: to the presence of residues within that fraction [33]. For this reason, this study evaluated the effect of Having an optimal SCC with 100% NA in the ﬁne fraction and 100% RCA in the coarse fraction, adding fine RCA on the compressive strength of SCC with 100% coarse RCA at different ages, while the NA content was replaced by 25, 50, 75, and 100% ﬁne RCA. The mixtures were labelled SA0, minimizing the influence of other variables such as water content and curing conditions. To do so, SA25, SA50, SA75, and SA100, in which the acronym “SA” and the following number refer to the following experimental procedure was developed: “Statistical Analysis” and to the percentage of ﬁne RCA, respectively. In each mix, all the aggregates, except the ﬁller, were pre-soaked for 24 h, which managed to • Having an optimal SCC with 100% NA in the fine fraction and 100% RCA in the coarse fraction, maintain the eective w/c ratio constant (at a value of 0.45) in all the mixes. As RCA water the NA content was replaced by 25, 50, 75, and 100% fine RCA. The mixtures were labelled SA0, SA25, SA50, SA75, and SA100, in which the acronym “SA” and the following number refer to “Statistical Analysis” and to the percentage of fine RCA, respectively. Mathematics 2020, 8, x FOR PEER REVIEW 5 of 24 Mathematics 2020, 8, 2190 5 of 24 • In each mix, all the aggregates, except the filler, were pre-soaked for 24 h, which managed to absorption can be very prolonged over time [49], this long pre-soaking time (24 h) was chosen to maintain the effective w/c ratio constant (at a value of 0.45) in all the mixes. As RCA water achieve absorption c complete an be very pro stabilizatioln onged over t of water absorption. ime [49], t Thus, his long pre the eect -soof akthe ing t variable ime (24“water h) was chos content” en in the experiment was eliminated. In addition, the behavior of the RCA may be optimized with to achieve complete stabilization of water absorption. Thus, the effect of the variable “water this content” in procedur te, he exper although ime it nt was e requires prior liminated. In preparation addi ofti the on, the b aggregates ehavi and or of it the is notR economically CA may be proﬁtable [50]. optimized with this procedure, although it requires prior preparation of the aggregates and it is not economically profitable [50]. The mixing process consisted of a single stage, ﬁrst adding the aggregates after drying their • The mixing process consisted of a single stage, first adding the aggregates after drying their surface (SSD conditions) [50], then the cement, and ﬁnally the water with the admixtures dissolved. surface (SSD conditions) [50], then the cement, and finally the water with the admixtures The concrete, 60 L per mix, was mixed in a horizontal-axis mixer for 1 min. dissolved. The concrete, 60 L per mix, was mixed in a horizontal-axis mixer for 1 min. When the mixing process was ﬁnished, the fresh state tests were carried out (Table 3) and • When the mixing process was finished, the fresh state tests were carried out (Table 3) and 32 32 cylindrical 10 20 cm specimens were made for the compressive-strength test. Thirty minutes cylindrical 10 × 20 cm specimens were made for the compressive-strength test. Thirty minutes after mixing, the slump-ﬂow test was repeated with the rest of the concrete mass, to evaluate the after mixing, the slump-flow test was repeated with the rest of the concrete mass, to evaluate the evolution of ﬂowability over time [49]. evolution of flowability over time [49]. The specimens were left in their molds for 22 h under laboratory conditions: at a temperature and • The specimens were left in their molds for 22 h under laboratory conditions: at a temperature a humidity level of 20 C and 60%, respectively. Subsequently they were demolded and, 23 h and a humidity level of 20 °C and 60%, respectively. Subsequently they were demolded and, 23 after the mixing process, were placed in a wet chamber (temperature of 20 2 C and humidity of h after the mixing process, were placed in a wet chamber (temperature of 20 ± 2 °C and humidity 95 5%), until the time of testing. of 95 ± 5%), until the time of testing. At ages 24 1 h (1 day), 168 1 h (7 days), 672 1 h (28 days), and 2160 1 h (90 days), • At ages 24 ± 1 h (1 day), 168 ± 1 h (7 days), 672 ± 1 h (28 days), and 2160 ± 1 h (90 days), from the from the manufacturing of the mixes, 8 specimens were subjected to the compressive-strength manufacturing of the mixes, 8 specimens were subjected to the compressive-strength test, EN test, EN 12390-3 [8], obtaining the data for the statistical analysis. With these precise moments of 12390-3 [8], obtaining the data for the statistical analysis. With these precise moments of time, time, the eect of the variable “curing conditions” on the strength of SCC was eliminated: all the the effect of the variable “curing conditions” on the strength of SCC was eliminated: all the mixtures were tested at exactly the same age and after they had been in the same humidity and mixtures were tested at exactly the same age and after they had been in the same humidity and temperature conditions for the same time. temperature conditions for the same time. Table 3. In-fresh state tests on each mix. Table 3. In-fresh state tests on each mix. Test Regulation [8] Test Regulation [8] Slump-flow EN 12350-8 Slump-ﬂow EN 12350-8 V-funnel EN 12350-9 V-funnel EN 12350-9 2-bar 2-bar L-box L-box EN 12350-10 EN 12350-10 Sieve Sieve segregation segregation EN 12350-11 EN 12350-11 Fresh density EN 12350-6 Fresh density EN 12350-6 Air content EN 12350-7 Air content EN 12350-7 Some images of the most outstanding steps of the experimental plan are shown in Figure 2. On Some images of the most outstanding steps of the experimental plan are shown in Figure 2. On the the other hand, the dosage of each mix is shown in Table 4. As the aggregate was pre-soaked, the other hand, the dosage of each mix is shown in Table 4. As the aggregate was pre-soaked, the amount amount of water added to each concrete mixture was the same. of water added to each concrete mixture was the same. Figure 2. Highlights of the experimental plan: coarse RCA pre-soaked (left), slump-ﬂow test of mix Figure 2. Highlights of the experimental plan: coarse RCA pre-soaked (left), slump-flow test of mix SA50 (middle), and specimen tested for compressive strength (right). SA50 (middle), and specimen tested for compressive strength (right). Mathematics 2020, 8, 2190 6 of 24 Table 4. Mix design (kg/m ). Material SA0 SA25 SA50 SA75 SA100 Cement 320 320 320 320 320 Filler 180 180 180 180 180 Water 135 135 135 135 135 Coarse RCA 4/12.5 mm 525 525 525 525 525 Fine RCA 0/4 mm 0 275 550 825 1100 Siliceous sand 0/4 mm 1200 900 600 300 0 Plasticizer 2.20 2.20 2.20 2.20 2.20 Viscosity regulator 4.40 4.40 4.40 4.40 4.40 Approximate weight (kg) 2333 2332 2326 2325 2318 Approximate volume (m ) 1.00 1.00 1.00 1.00 1.00 Eective w/c ratio 0.45 0.45 0.45 0.45 0.45 4. In-Fresh Behavior The results of these tests (Table 5) were in line with expectations, as stated in the introduction: the decrease in ﬂowability, due to the addition of RCA, can be compensated by the increase in the water content, in this case by pre-soaking [50]. Thus, only the eect of ﬁne RCA was evaluated, with aggregate water absorption having no inﬂuence. Table 5. Results of in-fresh state tests. Test SA0 SA25 SA50 SA75 SA100 Viscosity, t slump-ﬂow test (s) 4.20 4.80 5.40 6.00 7.20 Slump ﬂow (mm) 675 680 690 700 710 Viscosity, t slump-ﬂow test 4.40 5.00 5.60 6.20 7.40 after 30 min (s) Slump ﬂow after 30 min (mm) 650 660 665 675 680 Viscosity, V-funnel test (s) 6.60 9.00 11.20 13.80 16.20 Passing ability, L-box test H /H 0.86 0.86 0.88 0.90 0.91 2 1 Sieve segregation (%) 1.65 1.51 1.32 1.07 0.85 2.35 2.29 2.24 2.19 2.15 Fresh density (Mg/m ) Air content (%) 3.80 3.90 4.20 3.95 4.05 A very dierent eect of the residue was observed in relation to slump ﬂow and viscosity according to a descriptive analysis: The ﬁne RCA slightly increased the ﬂowability (slump-ﬂow and L-box tests) [24]. Mixture SA100 showed a 4.7% higher slump ﬂow than mixture SA0, and the improvement in the L-box test was 5.8%. The addition of ﬁne RCA resulted in an increase in viscosity [49]. The results for mixture SA100 in the slump-ﬂow (t ) and in the V-funnel tests were, respectively, 28.6% and 70.8% higher than the results for mixture SA0. This behavior can be explained by the content of particles smaller than 0.125 mm of ﬁne RCA, which was higher than that of the NA (see the ﬁneness modulus in Table 2, and Figure 1). As the entire NA fraction 0/4 mm was replaced simultaneously by ﬁne RCA, it was not done size-by-size, the proportion of cement paste was greater when this waste was added. Therefore, the aggregate particles were evenly interspersed and dragged within the paste in the mixtures with ﬁne RCA. This led to the increase in the slump ﬂow [21]. However, this higher proportion of cement paste also resulted in a more viscous consistency and slower movement [33]. Sieve segregation was reduced as the ﬁne RCA content increased due to the increase in viscosity and its higher water absorption [19]. Mathematics 2020, 8, 2190 7 of 24 After 30 min of the end of the mixing process, the overall decrease in slump ﬂow was 4%, and t increased by 3%. The pre-soaking of the aggregates caused the water absorption by the aggregate to be minimal, thus favoring an optimum temporary conservation of self-compactability [50]. No clear inﬂuence of the ﬁne RCA on the air content was observed, which was mainly controlled through the use of admixtures [51]. Nevertheless, other studies have stated that admixtures do not control the air content of the mix [52] and that it increases as the ﬁne RCA content increases [33]. The fresh density of SCC decreased when replacing NA by RCA, due to its lower density [49]. The descriptive analysis can be completed with the one-factor ANalysis Of VAriance (ANOVA). By this statistical procedure it can be determined whether the eect of the factor (in this case, ﬁne RCA content) is signiﬁcative if the variances of the mixes are similar [53]—an aspect that is checked with two hypothesis tests explained in detail in Section 5.6. The results of this analysis are the p-value and the homogeneous groups. The eect of the factor will be signiﬁcant when the p-value is lower than the chosen signiﬁcance level (in this case the most usual one, 5% [41]). On the other hand, the homogeneous groups indicate the factor values that provide signiﬁcantly equal results. The results obtained from the ANOVA carried out for the fresh state tests performed (all mixes exhibited a similar variance) are collected in Table 6 and show that: The behavioral dierences obtained between mixtures with dierent percentage of ﬁne RCA regarding the passing ability and the air content were not signiﬁcative. Any variation in RCA content signiﬁcantly aected both viscosity, which increased when adding ﬁne RCA, and fresh density, which decreased with the addition of ﬁne RCA. No homogeneous groups were obtained. Slump ﬂow and resistance to segregation were signiﬁcantly equal for 0–50% and 75–100% ﬁne RCA contents. The increase in ﬁnes content experienced by SCC mixtures with the addition of RCA increased ﬁlling ability (slump ﬂow) and resistance to segregation, thus compensating for the eect of the irregular shape of RCA. Table 6. One-factor ANOVA of the fresh properties. Test p-Value Homogeneous Groups Viscosity t slump-ﬂow test 0.0000 None Slump ﬂow 0.0202 SA0, SA25 and SA50; SA75 and SA100 Viscosity t slump-ﬂow test after 30 min 0.0000 None Slump ﬂow after 30 min 0.0418 SA0, SA25 and SA50; SA75 and SA100 Viscosity V-funnel test 0.0000 None Passing ability L-box test H /H 0.3827 All 2 1 Sieve segregation 0.0119 SA0 and SA25; SA75 and SA100 Fresh density 0.0281 SA75 and SA100 Air content 0.1898 All 5. Compressive Strength: Statistical Analysis and Strength Prediction This section includes the statistical procedure carried out to evaluate the eect that the addition of dierent amounts of ﬁne RCA will have on the compressive strength of SCC at dierent curing ages. Thanks to the experimental procedure designed (Section 3), the remaining variables that might potentially inﬂuence compressive strength (water content and curing conditions) were completely discarded [43]. This section includes the steps performed sequentially to obtain conclusions and which could be applied to any type of waste or concrete. 5.1. Stages of the Statistical Analysis Eight 10 20 cm cylindrical specimens were subjected to a compressive-strength test at 1, 7, 28, and 90 days (Table 7) for each mix. All these values were required for applying all the statistical procedures collected in this paper [41], main novelty regarding previous similar studies [54]. Mathematics 2020, 8, 2190 8 of 24 Table 7. Compressive strength (MPa) values by mix and by age. Age SA0 SA25 SA50 SA75 SA100 47.05; 47.84; 38.36; 42.31; 31.45; 30.64; 21.30; 24.62; 22.85; 22.88; 50.13; 47.76; 35.43; 35.46; 30.77; 32.25; 24.35; 27.74; 22.92; 21.82; 1 day 44.87; 48.04; 37.48; 40.20; 30.64; 33.28; 25.12; 25.48; 21.78; 21.98; 44.02; 48.62 40.61; 42.02 32.58; 33.21 23.88; 22.38 22.64; 22.24 60.32; 50.69; 56.29; 51.96; 45.85; 45.36; 33.55; 34.89; 34.29; 33.17; 55.97; 58.21; 53.17; 54.47; 48.29; 46.21; 32.75; 34.11; 32.41; 35.31; 7 days 58.13; 62.23; 58.97; 52.73; 40.28; 40.34; 34.93; 34.01; 33.83; 32.57; 59.49; 52.73 50.00; 55.32 43.71; 46.91 33.33; 34.99 35.37; 32.20 64.51; 58.77; 56.21; 54.92; 49.31; 52.01; 41.30; 37.77; 37.78; 36.78; 58.13; 62.37; 56.59; 57.20; 46.03; 50.66; 36.46; 41.87; 38.78; 38.81; 28 days 52.85; 65.91; 55.11; 58.10; 49.42; 50.91; 41.19; 37.27; 37.49; 38.26; 59.53; 65.86 58.07; 57.13 47.19; 49.43 40.56; 36.49 40.02; 35.83 56.11; 57.42; 60.43; 55.97; 54.23; 45.29; 42.62; 38.27; 39.73; 39.91; 64.35; 67.65; 58.66; 60.37; 51.15; 53.08; 41.95; 37.24; 39.05; 43.13; 90 days 48.32; 49.60; 57.43; 63.15; 52.33; 46.87; 41.92; 44.48; 42.63; 40.83; 65.24; 62.31 61.28; 65.74 55.33; 48.91 43.25; 45.03 41.67; 38.62 The statistical analysis was performed with the above values. The aspects under evaluation were: The robustness of the measurements (Section 5.2). The normality of the compressive strength (Section 5.3). The conﬁdence intervals of the compressive strength and its dispersion (Section 5.4). The inﬂuence of the age and the percentage of ﬁne RCA (Sections 5.5 and 5.6). The estimation of the compressive strength (Section 5.7). The determination of the characteristic strength (Section 5.8), which is the main property of concrete in any structural design. A signiﬁcance level of 5% was also used throughout this analysis ( = 0.05), as in the analysis of the properties in the fresh state, which is very common and widely accepted in this type of studies [41]. 5.2. Robustness A robustness analysis will detect anomalous data, which are results that are not in harmony with the other measures. The absence of such data is fundamental to the application of any statistical procedure, as they will aect the signiﬁcance of the analysis. Two approaches were followed to assess the existence of anomalous data (outliers): They can be visually detected within the box and whiskers plot (outliers are the data that are not within the limits of the diagram, deﬁned by the whiskers). The comparison between the traditional indicators (arithmetic mean and standard deviation) and the robust indicators (median, trimmed mean 5%, winsorized mean, winsorized standard deviation, and Sbi), which are not aected by the presence of this type of data. In the absence of anomalous data, both types of indicators have very similar values. In this study, the existence of anomalous data would indicate inappropriate breakage of specimens and, above all, a lack of homogeneity of the RCA in use: an eventual increase in the content of ﬁne fractions (<1 mm) would cause notably lower strengths (anomalous data). All the indicators commented upon for each mixture, at each age are shown in Table 8, while Figure 3 shows the box and whiskers graphs at 1 and 28 days. It can be seen that the traditional and robust indicators presented very similar values, and the box and whiskers graphs showed no outliers. It can therefore be stated that the data agreed with each other and that no anomalous data were present, so all the data were incorporated in the analysis. Furthermore, the results show the great homogeneity Mathematics 2020, 8, x FOR PEER REVIEW 9 of 24 Mathematics 2020, 8, 2190 9 of 24 homogeneity in the compressive-strength behavior of all the mixtures that were produced, a fundamental aspect when this waste is used [33]. Therefore, the distribution of fine RCA was uniform in the compressive-strength behavior of all the mixtures that were produced, a fundamental aspect in all of them. when this waste is used [33]. Therefore, the distribution of ﬁne RCA was uniform in all of them. Table 8. Both traditional and robust indicators of the compressive strength in MPa of the mixtures. Table 8. Both traditional and robust indicators of the compressive strength in MPa of the mixtures. Winsorized Mix and Arithmetic Trimmed Winsorized Standard Winsorized Median Standard Sbi Mix and Arithmetic Trimmed Winsorized Standard Age Mean Mean 5% Mean Deviation Median Standard Sbi Age Mean Mean 5% Mean Deviation Deviation Deviation SA0-1d 47.29 47.80 47.32 47.29 1.98 1.98 1.97 SA0-1d 47.29 47.80 47.32 47.29 1.98 1.98 1.97 SA0-7d 57.22 58.17 57.31 57.22 3.89 3.89 3.86 SA0-7d 57.22 58.17 57.31 57.22 3.89 3.89 3.86 SA0-28d 60.99 60.95 61.17 60.99 4.53 4.53 4.40 SA0-28d 60.99 60.95 61.17 60.99 4.53 4.53 4.40 SA0-90d 58.88 59.87 58.97 58.88 7.24 7.24 7.22 SA0-90d 58.88 59.87 58.97 58.88 7.24 7.24 7.22 SA25-1d 38.98 39.28 39.00 38.98 2.73 2.73 2.68 SA25-1d 38.98 39.28 39.00 38.98 2.73 2.73 2.68 SA25-7d 54.11 53.82 54.07 54.11 2.78 2.78 2.70 SA25-7d 54.11 53.82 54.07 54.11 2.78 2.78 2.70 SA25-28d 56.67 56.86 56.68 56.67 1.21 1.21 1.19 SA25-28d 56.67 56.86 56.68 56.67 1.21 1.21 1.19 SA25-90d 60.38 60.40 60.33 60.38 3.12 3.12 3.02 SA25-90d 60.38 60.40 60.33 60.38 3.12 3.12 3.02 SA50-1d 31.85 31.85 31.84 31.85 1.12 1.12 1.09 SA50-1d 31.85 31.85 31.84 31.85 1.12 1.12 1.09 SA50-7d 44.62 45.61 44.66 44.62 2.96 2.96 3.00 SA50-7d 44.62 45.61 44.66 44.62 2.96 2.96 3.00 SA50-28d 49.37 49.43 49.41 49.37 1.96 1.96 1.90 SA50-28d 49.37 49.43 49.41 49.37 1.96 1.96 1.90 SA50-90d 50.90 51.74 50.96 50.90 3.57 3.57 3.56 SA50-90d 50.90 51.74 50.96 50.90 3.57 3.57 3.56 SA75-1d 24.36 24.49 24.34 24.36 1.96 1.96 1.93 SA75-1d 24.36 24.49 24.34 24.36 1.96 1.96 1.93 SA75-7d SA75-7d 34.07 34.07 34.06 34.06 34.09 34.09 34.07 34.07 0.83 0.83 0.830.83 0.800.80 SA75-28d 39.11 39.17 39.11 39.11 2.33 2.33 2.29 SA75-28d 39.11 39.17 39.11 39.11 2.33 2.33 2.29 SA75-90d 41.85 42.29 41.92 41.85 2.77 2.77 2.71 SA75-90d 41.85 42.29 41.92 41.85 2.77 2.77 2.71 SA100-1d 22.39 22.44 22.39 22.39 0.49 0.49 0.48 SA100-1d 22.39 22.44 22.39 22.39 0.49 0.49 0.48 SA100-7d 33.64 33.50 33.63 33.64 1.26 1.26 1.25 SA100-7d 33.64 33.50 33.63 33.64 1.26 1.26 1.25 SA100-28d 37.97 38.02 37.97 37.97 1.30 1.30 1.27 SA100-28d 37.97 38.02 37.97 37.97 1.30 1.30 1.27 SA100-90d 40.70 40.37 40.68 40.70 1.66 1.66 1.65 SA100-90d 40.70 40.37 40.68 40.70 1.66 1.66 1.65 Figure 3. Box plot for all mixes: (a) 1 day; (b) 28 days. Figure 3. Box plot for all mixes: (a) 1 day; (b) 28 days. 5.3. Normality 5.3. Normality Data normality was validated with three hypothesis tests: the Chi-square test, the Saphiro–Wilk Data normality was validated with three hypothesis tests: the Chi-square test, the Saphiro–Wilk test, with which the histogram and the quartiles of each variable were, respectively, compared with test, with which the histogram and the quartiles of each variable were, respectively, compared with those corresponding to a normal distribution, and the Z-asymmetry test, which evaluates the symmetry those corresponding to a normal distribution, and the Z-asymmetry test, which evaluates the of the data. All these tests have as their null hypothesis that the data sample will follow a normal symmetry of the data. All these tests have as their null hypothesis that the data sample will follow a distribution, which is rejected if its p-value (Table 9) is lower than the signiﬁcance level (in this normal distribution, which is rejected if its p-value (Table 9) is lower than the significance level (in study, 0.05). this study, 0.05). Table 9. p-value for the normality tests of the compressive strength of each mixture at each age. Mix and Age Chi-Square Test Shapiro–Wilk Test Z-Asymmetry Test SA0-1d 0.1247 0.5203 0.5877 SA0-7d 0.7769 0.6493 0.5339 Mathematics 2020, 8, 2190 10 of 24 Table 9. p-value for the normality tests of the compressive strength of each mixture at each age. Mix and Age Chi-Square Test Shapiro–Wilk Test Z-Asymmetry Test SA0-1d 0.1247 0.5203 0.5877 SA0-7d 0.7769 0.6493 0.5339 SA0-28d 0.1247 0.4483 0.5632 SA0-90d 0.1247 0.4297 0.6801 SA25-1d 0.2570 0.3616 0.8480 SA25-7d 0.9856 0.9923 0.7139 SA25-28d 0.4815 0.4258 0.7394 SA25-90d 0.7769 0.9630 0.7219 SA50-1d 0.2570 0.1483 0.9021 SA50-7d 0.4815 0.2399 0.5156 SA50-28d 0.2570 0.6155 0.5733 SA50-90d 0.9856 0.6942 0.6539 SA75-1d 0.7769 0.9187 0.9218 SA75-7d 0.1247 0.3958 0.7797 SA75-28d 0.0245 0.0731 0.9760 SA75-90d 0.2570 0.2869 0.4457 SA100-1d 0.1247 0.1089 0.8789 SA100-7d 0.1247 0.2888 0.7316 SA100-28d 0.4815 0.9913 0.8830 SA100-90d 0.7769 0.6304 0.7558 It is known that the strength of non-recycled concrete conforms to a normal distribution [28]. If the RCA concretes also complied with this distribution, then similar calculation procedures would be applicable [28,29]. It may be observed that the p-value of these three tests was higher than 0.05, so the compressive strength of each mixture at each age followed a normal distribution. Nevertheless, there was an exception: at 28 days, mix SA75 presented an incompatible histogram with the normal distribution (Chi-square test) at a conﬁdence level of 95%, although it was compatible with that distribution at a signiﬁcance level of 0.01. This discrepancy was due to the concentration of the experimental results in two small intervals (around 37 MPa and 41 MPa), with no intermediate values (see Table 7). A signiﬁcance level of 0.01 was therefore used for mixture SA75 at 28 days throughout the rest of the study. 5.4. Conﬁdence Intervals The conﬁdence intervals for the arithmetic mean and the absolute and the relative standard deviation (Table 10 and Figure 4) inform us of the values between which a variable is found for a certain level of conﬁdence. Thus, it can be ascertained whether, for example, an overlap is possible between the strengths obtained in the concretes with dierent percentages of ﬁne RCA. Mathematics 2020, 8, 2190 11 of 24 Table 10. Conﬁdence intervals for mean and standard deviation of compressive strength for each mixture and age. Relative Conﬁdence Conﬁdence Interval Conﬁdence Interval Interval of the Standard Mix and Age Standard Deviation Arithmetic Mean (MPa) Deviation from the (MPa) Arithmetic Mean (%) SA0-1d (45.63; 48.95) (1.31; 4.04) (2.77; 8.54) SA0-7d (53.97; 60.48) (2.57; 7.92) (4.49; 13.84) SA0-28d (57.20; 64.78) (2.30; 9.22) (3.77; 15.12) SA0-90d (52.83; 64.92) (4.78; 14.73) (8.12; 25.02) SA25-1d (36.71; 41.26) (1.80; 5.55) (4.62; 14.24) SA25-7d (51.79; 56.44) (1.84; 5.67) (3.40; 10.48) SA25-28d (55.66; 57.68) (0.79; 2.46) (1.39; 4.34) SA25-90d (57.77; 62.99) (2.07; 6.36) (3.43; 10.53) SA50-1d (30.91; 32.79) (0.74; 2.29) (2.32; 7.19) SA50-7d (42.15; 47.09) (1.96; 6.02) (4.39; 13.49) SA50-28d (47.73; 51.01) (1.30; 3.99) (2.63; 8.08) Mathematics 2020, 8, x FOR PEER REVIEW 11 of 24 SA50-90d (47.91; 53.88) (2.36; 7.27) (4.64; 14.28) SA75-1d (22.72; 26.00) (1.29; 3.99) (5.30; 16.38) SA75-7d (33.38; 34.76) (0.55; 1.69) (1.61; 4.96) SA75-7d (33.38; 34.76) (0.55; 1.69) (1.61; 4.96) SA75-28d (36.23; 41.99) (1.37; 6.19) (3.50; 15.83) SA75-28d (36.23; 41.99) (1.37; 6.19) (3.50; 15.83) SA75-90d (39.53; 44.16) (1.83; 5.64) (4.37; 13.48) SA75-90d (39.53; 44.16) (1.83; 5.64) (4.37; 13.48) SA100-1d (21.98; 22.80) (0.32; 1.00) (1.43; 4.47) SA100-1d (21.98; 22.80) (0.32; 1.00) (1.43; 4.47) SA100-7d (32.59; 34.70) (0.84; 2.57) (2.50; 7.64) SA100-7d (32.59; 34.70) (0.84; 2.57) (2.50; 7.64) SA100-28d (36.88; 39.06) (0.86; 2.65) (2.26; 6.98) SA100-28d (36.88; 39.06) (0.86; 2.65) (2.26; 6.98) SA100-90d SA100-90d (39.31; 42.08)(39.31; 42.08) (1.10; 3.37) (1.10; 3.37) (2.70; 8.28) (2.70; 8.28) 1 1 The confidence intervals of the mixture SA75 at 28 days have been obtained for a confidence level of 99%. The conﬁdence intervals of the mixture SA75 at 28 days have been obtained for a conﬁdence level of 99%. Figure 4. Graph of the conﬁdence intervals of the arithmetic mean. Figure 4. Graph of the confidence intervals of the arithmetic mean. The arithmetic mean conﬁdence intervals showed several relevant aspects (see Figure 4): The arithmetic mean confidence intervals showed several relevant aspects (see Figure 4): In almost all mixtures, the 28-day and 90-day conﬁdence intervals overlapped, with their strengths • In almost all mixtures, the 28-day and 90-day confidence intervals overlapped, with their developing mainly during the ﬁrst 4 weeks. The 7-day and 28-day conﬁdence intervals also strengths developing mainly during the first 4 weeks. The 7-day and 28-day confidence intervals overlapped in two mixes, SA0 and SA25, showing that, in principle, the increase in the content of also overlapped in two mixes, SA0 and SA25, showing that, in principle, the increase in the this residue caused a slower development of strength. content of this residue caused a slower development of strength. Comparing the conﬁdence intervals of dierent mixtures with each other, it was found that they • Comparing the confidence intervals of different mixtures with each other, it was found that they overlapped in mixtures SA0 and SA25, as well as in mixtures SA75 and SA100, at 7, 28, and 90 days. overlapped in mixtures SA0 and SA25, as well as in mixtures SA75 and SA100, at 7, 28, and 90 Therefore, the strength of mix SA25 might be greater than the strength of mix SA0 at any of these days. Therefore, the strength of mix SA25 might be greater than the strength of mix SA0 at any ages, despite the higher ﬁne RCA content of the ﬁrst one. This behavior of mixture SA25 was of these ages, despite the higher fine RCA content of the first one. This behavior of mixture SA25 was mainly due to the higher fines content of fine RCA compared to NA (see Figure 1), which produced a “filler effect” that increased the expected compressive strength of SCC. On the other hand, mixtures SA75 and SA100 also did not show a significant difference in their compressive strength. Therefore, it seems, in principle, that strength can increase, despite a small increase in fine RCA. The standard deviation confidence intervals show the dispersion of the compressive strength. At early ages (1 and 7 days), there was no clear trend in the dispersion of results with respect to the fine RCA content, although at older ages (28 and 90 days), the dispersion decreased as the percentage of fine RCA increased. Therefore, in spite of the contaminants present in the RCA, the concretes that contain fine RCA can show a homogeneous behavior. 5.5. Pearson Correlations A correlation between two variables is a number between −1 and 1 that shows the linearity of the relationship between them. If there are more than two variables, the correlations are obtained by pairs of variables ignoring the others. The closer the absolute value is to 1, the greater the linearity, while if the sign is positive or negative it indicates whether the relationship is increasing (if one variable increases, so too is the other) or decreasing. Mathematics 2020, 8, 2190 12 of 24 mainly due to the higher ﬁnes content of ﬁne RCA compared to NA (see Figure 1), which produced a “ﬁller eect” that increased the expected compressive strength of SCC. On the other hand, mixtures SA75 and SA100 also did not show a signiﬁcant dierence in their compressive strength. Therefore, it seems, in principle, that strength can increase, despite a small increase in ﬁne RCA. The standard deviation conﬁdence intervals show the dispersion of the compressive strength. At early ages (1 and 7 days), there was no clear trend in the dispersion of results with respect to the ﬁne RCA content, although at older ages (28 and 90 days), the dispersion decreased as the percentage of ﬁne RCA increased. Therefore, in spite of the contaminants present in the RCA, the concretes that contain ﬁne RCA can show a homogeneous behavior. 5.5. Pearson Correlations A correlation between two variables is a number between 1 and 1 that shows the linearity of the relationship between them. If there are more than two variables, the correlations are obtained by pairs of variables ignoring the others. The closer the absolute value is to 1, the greater the linearity, Mathematics 2020, 8, x FOR PEER REVIEW 12 of 24 while if the sign is positive or negative it indicates whether the relationship is increasing (if one variable increases, so too is the other) or decreasing. In this study, the variables considered were compressive strength, age, and percentage of fine In this study, the variables considered were compressive strength, age, and percentage of ﬁne RCA. It is clear that the correlation between compressive strength and age is positive and, according RCA. It is clear that the correlation between compressive strength and age is positive and, according to existing studies [49], is negative between this strength and the percentage of fine RCA. However, to existing studies [49], is negative between this strength and the percentage of ﬁne RCA. However, the absolute value, indicated in the correlation symmetric matrix (Figure 5), shows that the effect of the absolute value, indicated in the correlation symmetric matrix (Figure 5), shows that the eect of the the percentage of fine RCA on the compressive strength was 83% ((0.75–0.41)/0.41·100) greater than percentage of ﬁne RCA on the compressive strength was 83% ((0.75–0.41)/0.41100) greater than the the effect of the passing of time. The compressive strength was mainly conditioned by the residue eect of the passing of time. The compressive strength was mainly conditioned by the residue content content of the SCC. of the SCC. Figure 5. Pearson correlation matrix. Figure 5. Pearson correlation matrix. 5.6. Eect of Age and Percentage of Fine RCA on Compressive Strength 5.6. Effect of Age and Percentage of Fine RCA on Compressive Strength The eect of each factor (age and ﬁne RCA percentage) can be separately analyzed when the other The effect of each factor (age and fine RCA percentage) can be separately analyzed when the factor takes a particular value, rather than neglecting it (as in correlations). An example would be the other factor takes a particular value, rather than neglecting it (as in correlations). An example would eect of the percentage of ﬁne RCA at the age of 7 days or the eect of age, if the percentage of ﬁne be the effect of the percentage of fine RCA at the age of 7 days or the effect of age, if the percentage RCA was 50%. of fine RCA was 50%. The usual statistical procedure for this analysis is the one-factor ANOVA, which was also used in The usual statistical procedure for this analysis is the one-factor ANOVA, which was also used the statistical analysis of the fresh properties. In this case, this statistical test states as its null hypothesis in the statistical analysis of the fresh properties. In this case, this statistical test states as its null that there is no eect of the factor (age or ﬁne RCA percentage) on the variable (compressive strength), hypothesis that there is no effect of the factor (age or fine RCA percentage) on the variable providing a p-value that indicates whether to accept or to reject the null hypothesis. ANOVA must (compressive strength), providing a p-value that indicates whether to accept or to reject the null be applied to independent measurements (in our case, each compressive strength value was from hypothesis. ANOVA must be applied to independent measurements (in our case, each compressive a dierent specimen and was therefore independent). Likewise, the variances of the variable must strength value was from a different specimen and was therefore independent). Likewise, the variances of the variable must be significantly equal for each value of the factor under analysis, which was evaluated with two hypothesis tests, Cochran test and Bartlett test, the null hypothesis of which is that the variances are equal (Table 11). Table 11. p-value for both the Cochran test and the Bartlett test. Factor Analyzed Condition p-Value Cochran Test p-Value Bartlett Test 0% fine RCA 0.0262 0.0210 25% fine RCA 0.5981 0.1360 Age 50% fine RCA 0.1348 0.0369 75% fine RCA 0.2585 0.0435 100% fine RCA 0.2547 0.0445 1 day 0.0629 0.0023 7 days 0.0617 0.0021 Fine RCA percentage 28 days 0.0006 0.0026 90 days 0.0008 0.0036 These tests on the age factor showed that the variance was significantly equal in all cases except for 25% fine RCA, at a significance level of 5%. For this reason, the one-factor ANOVA with a Mathematics 2020, 8, 2190 13 of 24 be signiﬁcantly equal for each value of the factor under analysis, which was evaluated with two hypothesis tests, Cochran test and Bartlett test, the null hypothesis of which is that the variances are equal (Table 11). Table 11. p-value for both the Cochran test and the Bartlett test. Factor Analyzed Condition p-Value Cochran Test p-Value Bartlett Test 0% ﬁne RCA 0.0262 0.0210 25% ﬁne RCA 0.5981 0.1360 Age 50% ﬁne RCA 0.1348 0.0369 75% ﬁne RCA 0.2585 0.0435 100% ﬁne RCA 0.2547 0.0445 1 day 0.0629 0.0023 7 days 0.0617 0.0021 Fine RCA percentage 28 days 0.0006 0.0026 90 days 0.0008 0.0036 These tests on the age factor showed that the variance was signiﬁcantly equal in all cases except for 25% ﬁne RCA, at a signiﬁcance level of 5%. For this reason, the one-factor ANOVA with a signiﬁcance level of 1% was applied, except for 25% ﬁne RCA, for which the signiﬁcance level of 5% was maintained. For the ﬁne RCA percentage factor, the low p-values of the Bartlett test prevented the use of the one-factor ANOVA, regardless of the level of signiﬁcance. Therefore, the Kruskal–Wallis test was used, which is similar to the one-factor ANOVA, although it requires no equal variances, as it is a robust procedure. Both procedures allow homogeneous groups to be obtained, i.e., those factor values (age or ﬁne RCA percentage) for which there is no signiﬁcant dierence in the value of the variable (compressive strength). In this study, the homogeneous groups would indicate at which ages the compressive strength of a mixture (speciﬁc ﬁne RCA percentage) no longer varies and for which ﬁne RCA percentages the compressive strength is statistically the same (at a speciﬁc age). The results of this analysis are shown in Table 12. Table 12. Results of ANOVA analysis and Kruskal–Wallis test. ANOVA/Kruskal–Wallis Factor Analyzed Condition Homogeneous Groups p-Value 0% ﬁne RCA 0.0001 Ages 7, 28 and 90 25% ﬁne RCA 0.0002 Ages 7 and 28 Age 50% ﬁne RCA 0.0001 Ages 28 and 90 75% ﬁne RCA 0.0003 Ages 28 and 90 100% ﬁne RCA 0.0006 None Age of 1 day 0.000000248 SA75 and SA100 Age of 7 days 0.000000662 SA0 and SA25; SA75 and SA100 Fine RCA percentage Age of 28 days 0.000000492 SA0 and SA25; SA75 and SA100 Age of 90 days 0.00000171 SA0 and SA25; SA75 and SA100 1 2 One-factor ANOVA with a signiﬁcance level of 1% except for 25% ﬁne RCA, which was used at 5%. Kruskal–Wallis test with a signiﬁcance level of 5%. The results of the ANOVA/Kruskal–Wallis test were consistent with the above-mentioned studies [33] and with the correlations: both factors, age and fine RCA percentage, influenced the compressive strength. The homogeneous groups confirmed the trends shown by the confidence intervals: The compressive strength development of the SCC was slower as the ﬁne RCA content increased. The compressive strength of mixture SA0 was statistically identical at 7, 28, and 90 days, while this strength for mixtures SA50 and SA75 was statistically dierent at 7 days and was the same at later ages (28 and 90 days). Mixture SA100 showed dierent strengths at all ages. Mathematics 2020, 8, 2190 14 of 24 In contrast, the factor ﬁne RCA percentage showed that the compressive strengths of mixtures SA75 and SA100 were statistically equal, as they were in mixtures SA0 and SA25, at both 7 and 90 days. It can therefore be stated that the eect on the compressive strength of the ﬁne RCA content can statistically be divided into three groups with the same strength: low percentage (0–25%), medium percentage (50%), and high percentage (75–100%). Therefore, according to the statistical results obtained, in this study the optimal amount of ﬁne RCA would be 25–50% from the strength point of view, depending on the level of self-compactability and sustainability required for the mixture. Nevertheless, if the beneﬁcial eect of the higher ﬁnes content of RCA is to be maximized, the incorporation of ﬁne RCA in SCC should be less than 25%. Finally, the interaction between the factors (age and percentage of ﬁne RCA), i.e., whether the eect of one factor is dierent depending on the value of the other factor, can be assessed by means of a two-factor ANOVA. Since a p-value of 0.0034 was obtained, the interaction between both factors was signiﬁcant (at any conﬁdence level). A result indicating that no generalization is possible and that the eect of ﬁne RCA on compressive strength should in particular be studied for each age and each ﬁne RCA percentage, which is the approach followed in this section. This interaction also conditions the estimation of compressive strength as a function of RCA content and age, as explained in the next section. 5.7. Compressive Strength Regression Simple regression models were developed as a function of the compressive strength and its dependence on two variables: age and percentage of ﬁne RCA. A process similar to one-factor ANOVA was performed: each mixture (dierent ﬁne RCA percentages) was studied at each age, as the interaction between both factors was signiﬁcative. Table 13 shows, for each situation, the two models with the best ﬁt with their coecient R2. The variables used are CS (mean values of Compressive Strength, in MPa), FRP (Fine RCA Percentage, in percentage), and A (Age, in days). These were ﬁtted with the arithmetic mean of the compressive strength for each ﬁne RCA percentage and age (see Table 8). The best-ﬁt models are shown in Figure 6 (compressive strength as a function of age) and Figure 7 (compressive strength as a function of ﬁne RCA percentage). Table 13. Best-ﬁt models of compressive strength as a function of the ﬁne RCA percentage and age. Dependent Condition Model Equation (A 1 Day; FRP = 0–100%) Coecient R Variable CS = 1/(0.0167 + 0.0045/A) 0.9793 0% ﬁne RCA CS = exp(4.0931 0.2377/A) 0.9728 CS = 1/(0.0170 + 0.0087/A) 0.9910 25% ﬁne RCA CS = exp(4.0700 0.4101/A) 0.9826 CS = 1/(0.0200 + 0.0115/A) 0.9904 Age 50% ﬁne RCA CS = exp(3.9062 0.4507/A) 0.9795 CS = (621.75 + 260.606Lg(A))ˆ0.5 0.9932 75% ﬁne RCA CS = 25.2318 + 3.9337Lg(A) 0.9779 CS = 1/(0.0256 + 0.0192/A) 0.9861 100% ﬁne RCA CS = (553.028 + 257.627Lg(A))ˆ0.5 0.9833 CS = exp(3.8495 0.0079FRP) 0.9830 Age of 1 day CS = (229.177 182.027FRPˆ0.5 )ˆ0.5 0.9816 CS = (3307.49 24.2083FRP)ˆ0.5 0.9402 Age of 7 days Fine RCA CS = 58.173 0.2688FRP 0.9396 percentage CS = (3715.6 24.9521FRP)ˆ0.5 0.9597 Age of 28 days CS = 61.542 0.2544FRP 0.9584 CS = 1/(0.0158 + 0.00009FRP) 0.8957 Age of 90 days CS = exp(4.1303 0.0044FRP) 0.8941 Mathematics 2020, 8, x FOR PEER REVIEW 14 of 24 5.7. Compressive Strength Regression Simple regression models were developed as a function of the compressive strength and its dependence on two variables: age and percentage of fine RCA. A process similar to one-factor ANOVA was performed: each mixture (different fine RCA percentages) was studied at each age, as the interaction between both factors was significative. Table 13 shows, for each situation, the two models with the best fit with their coefficient R2. The variables used are CS (mean values of Compressive Strength, in MPa), FRP (Fine RCA Percentage, in percentage), and A (Age, in days). These were fitted with the arithmetic mean of the compressive strength for each fine RCA percentage and age (see Table 8). The best-fit models are shown in Figure 6 (compressive strength as a function of age) and Figure 7 (compressive strength as a function of fine RCA percentage). Table 13. Best-fit models of compressive strength as a function of the fine RCA percentage and age. Dependent Coefficient Condition Model Equation (A ≥ 1 Day; FRP = 0–100%) Variable R = 1/(0.0167 + 0.0045/) 0.9793 0% fine RCA = exp(4.0931 − 0.2377/) 0.9728 = 1/(0.0170 + 0.0087/) 0.9910 25% fine RCA = exp (4.0700 − 0.4101/) 0.9826 = 1/(0.0200 + 0.0115/) 0.9904 Age 50% fine RCA = exp (3.9062 − 0.4507/) 0.9795 = (621.75 + 260.606 · ( ))^0.5 0.9932 75% fine RCA = 25.2318 + 3.9337 · () 0.9779 = 1/(0.0256 + 0.0192/) 0.9861 100% fine RCA = (553.028 + 257.627 · ( ))^0.5 0.9833 = exp (3.8495 − 0.0079 · ) 0.9830 Age of 1 day = (229.177 − 182.027 · ^0.5 )^0.5 0.9816 = (3307.49 − 24.2083 · )^0.5 0.9402 Age of 7 days Fine RCA = 58.173 − 0.2688 · 0.9396 percentage = (3715.6 − 24.9521 · )^0.5 0.9597 Age of 28 days = 61.542 − 0.2544 · 0.9584 Mathematics 2020, 8, 2190 15 of 24 = 1/(0.0158 + 0.00009 · ) 0.8957 Age of 90 days = exp (4.1303 − 0.0044 · ) 0.8941 Figure 6. Best-ﬁt models of compressive strength as an age function: (a) mix SA0, also valid for mixtures Figure 6. Best-fit models of compressive strength as an age function: (a) mix SA0, also valid for Mathematics 2020, 8, x FOR PEER REVIEW 15 of 24 SA25, SA50 and SA100; (b) mix SA75. mixtures SA25, SA50 and SA100; (b) mix SA75. Figure 7. Best-ﬁt models of compressive strength as a ﬁne RCA percentage function: (a) 1 day; (b) 7 days; Figure 7. Best-fit models of compressive strength as a fine RCA percentage function: (a) 1 day; (b) 7 (c) 28 days; (d) 90 days. days; (c) 28 days; (d) 90 days. With all the above, it is observed that the simple regression provides an optimal adjustment of the With all the above, it is observed that the simple regression provides an optimal adjustment of compressive strength, reaching R coecients of 99%. However, four aspects should be highlighted: the compressive strength, reaching R coefficients of 99%. However, four aspects should be highlighted: 2 A good ﬁt was obtained for both the age and the percentage of ﬁne RCA, although better R coecients were obtained for the function of the age. • A good fit was obtained for both the age and the percentage of fine RCA, although better R The coefficients w adjustment ere obtain according ed to fothe r the functi percentage on of of the ﬁne agRCA e. worsened with the age of the concrete: • the The adj longer ustme the time nt accord that had ing telapsed o the percent sincea the ge of concr fine ete RCA worsene was mixed, d the with the less reliable age of the concret the estimate e of : its the longer th compressive e time that had elapsed strength. since the concrete was mixed, the less reliable the estimate of its compressive strength. The adjustment of the compressive strength by age was robust: the best-ﬁt model was unchanged • The adjustment of the compressive strength by age was robust: the best-fit model was when the percentage of ﬁne RCA varied, only the coecients (a, b) changed. For all mixtures, unchanged when the percentage of fine RCA varied, only the coefficients (a, b) changed. For all except mix SA75, the best-ﬁt model followed Equation (1). mixtures, except mix SA75, the best-fit model followed Equation (1). y= = (1) (1) a + • When the compressive strength was fitted to the percentage of fine RCA, the best-fit model varied with age (there were three different models, for four different ages). This makes it difficult to obtain a valid overall model. It can therefore be concluded that in order to predict the compressive strength of an SCC made from fine RCA using single-variable models, the best option was to do so as a function of age (for each specific percentage of fine RCA). This approach achieves greater stability and accuracy. Obtaining a multiple regression model is very useful, since it allows the strength of all the mixtures to be predicted (different percentages of fine RCA) at any age by means of a single expression. Firstly, the simplest linear model was evaluated, as shown in Equation (2). It presented a poor fit (coefficient R of 78%), which is explained by the large width of the confidence intervals of all its coefficients (Table 14) and the low correlation between the different variables (Figure 5). Therefore, and secondly, from the combination of the simple regression models with a better fit, a more complex multiple model was developed, as indicated in Equation (3), reaching a correlation coefficient of 96.5%. It can be seen that this model, unlike the simple regression models, has a much more complex formulation with four terms: an independent term, two terms that each depend on a variable (age and percentage of fine RCA) and a fourth summand that reflects the effect of the Mathematics 2020, 8, 2190 16 of 24 When the compressive strength was ﬁtted to the percentage of ﬁne RCA, the best-ﬁt model varied with age (there were three dierent models, for four dierent ages). This makes it dicult to obtain a valid overall model. It can therefore be concluded that in order to predict the compressive strength of an SCC made from ﬁne RCA using single-variable models, the best option was to do so as a function of age (for each speciﬁc percentage of ﬁne RCA). This approach achieves greater stability and accuracy. Obtaining a multiple regression model is very useful, since it allows the strength of all the mixtures to be predicted (dierent percentages of ﬁne RCA) at any age by means of a single expression. Firstly, the simplest linear model was evaluated, as shown in Equation (2). It presented a poor ﬁt (coecient R of 78%), which is explained by the large width of the conﬁdence intervals of all its coecients (Table 14) and the low correlation between the dierent variables (Figure 5). Therefore, and secondly, from the combination of the simple regression models with a better ﬁt, a more complex multiple model was developed, as indicated in Equation (3), reaching a correlation coecient of 96.5%. It can be seen that this model, unlike the simple regression models, has a much more complex formulation with four terms: an independent term, two terms that each depend on a variable (age and percentage of ﬁne Mathematics 2020, 8, x FOR PEER REVIEW 16 of 24 RCA) and a fourth summand that reﬂects the eect of the interaction between both variables (discussed above interact inion the b two-factor etween bot ANOV h var A). iab The les ( variables discussed involved above in in t both he t models wo-factar or A e the Nsame OVA)as . The in the va simple riables rinvolved egression in (CS, botFRP h models , and A), are t whose he same valid as iranges n the siar mp e le A r egression 1 day and (CS, F FRPR = P0–100%. , and A), Figur whose v e 8 a shows lid range thes estimated are A ≥ 1 da values y and FR compar P = 0– ed10 to0%. the F experimental igure 8 showvalues s the esof tim both ated models, values com clearly parsupporting ed to the exp the erihigher mental pr val ecision ues ofof bot the h models second, c model. learly supporting the higher precision of the second model. = 52.4322 − 0.2501 · + 0.1378 · , = 77.99% (2) CS = 52.4322 0.2501FRP + 0.1378A, R = 77.99% (2) = 26.7876 + − 0.2657 · + 0.0005 · · ( + 0.8373 ), 0.0233 CS = 26.7876 + 0.2657FRP + 0.0005A(FRP + 0.8373), R = 96.51% (3) (3) 0.0284 + 0.0233 0.0284 + = 96.51% Table 14. Main results for the model obtained by multiple linear regression (Equation (2)). Table 14. Main results for the model obtained by multiple linear regression (Equation (2)). Coecient R 0.7799 Coefficient R 0.7799 Conﬁdence interval for the independent term ( = 0.05) (47.0884; 57.7760) Confidence interval for the independent term (α = 0.05) (47.0884; 57.7760) Conﬁdence interval for FRP (ﬁne RCA percentage) coecient ( = 0.05) (0.3277;0.1726) Confidence interval for FRP (fine RCA percentage) coefficient (α = 0.05) (−0.3277; −0.1726) Conﬁdence interval for A (age) coecient ( = 0.05) (0.0560; 0.2156) Confidence interval for A (age) coefficient (α = 0.05) (0.0560; 0.2156) Figure 8. Relationship between observed values and estimated values of compressive strength: (a) Figure 8. Relationship between observed values and estimated values of compressive strength: (a) linear model; linear m (bo )del multiple ; (b) mr u egr ltiple ession regrpr ession propo oposed model. sed model. The proposed models are not intended to be general models that can be applied independently of The proposed models are not intended to be general models that can be applied independently the composition of the mixtures since, for example, the eect of adding dierent types or quantities of of the composition of the mixtures since, for example, the effect of adding different types or quantities cement, variations in the w/c ratio or dierent compressive strength of the original concrete of the RCA of cement, variations in the w/c ratio or different compressive strength of the original concrete of the RCA have not been evaluated. Nevertheless, this model can be useful to predict the behavior of SCC with a compressive strength of 40–60 MPa at 28 days, as shown in Figure 9. In this figure, the results obtained are compared with the values collected in the few existing investigations in which the elaboration of SCC with RCA was approached. At most, the difference between the experimental value and the value estimated by this model is less than 5–8 MPa. In addition, the estimated value is generally lower than the experimental one. This allows us to carry out a safe estimation of the compressive strength of this type of concrete. Mathematics 2020, 8, 2190 17 of 24 have not been evaluated. Nevertheless, this model can be useful to predict the behavior of SCC with a compressive strength of 40–60 MPa at 28 days, as shown in Figure 9. In this ﬁgure, the results obtained are compared with the values collected in the few existing investigations in which the elaboration of SCC with RCA was approached. At most, the dierence between the experimental value and the value estimated by this model is less than 5–8 MPa. In addition, the estimated value is generally lower than the experimental one. This allows us to carry out a safe estimation of the compressive strength of this Mathematics 2020, 8, x FOR PEER REVIEW 17 of 24 type of concrete. Figure 9. Validation of the model developed (Equation (3)) throughout other similar studies [4,24,54,55]. Figure 9. Validation of the model developed (Equation (3)) throughout other similar studies However, the main utility of this model is that it does allow us to establish some guidelines for [4,24,54,55]. the prediction of the compressive strength of recycled concrete; in this case SCC, which can serve as a starting However, point. the ma On in ut the ilit one y of t hand, his model the amount is that of it does recycled allow aggr us t egate o estaadded, blish some in this guide study linesﬁne for RCA the predictio (coarse n of the compressive streng RCA content was 100% for all th of recycled the mixes), concret has a signiﬁcant e; in this c inﬂuence ase SCC, on which can the compr ser essive ve as str a st ength arting and point. On the on must be consider e hand ed. , the On the amount of other hand, recy the cled e aggre ect ofgrate ecycled added aggr , inegate this study varies fine RCA with age (interaction), (coarse RCA which content makes was 10 it 0% necessary for all to the mixes introduce ), h aaterm s a siin gnthe ifica model nt inflthat uencre eﬂects on thit. e comp The models ressive developed strength and formust be considered. On the other hand non-recycled concrete do not reﬂect these , the effect o aspects, as f re NA cycled does agg not reg aate var ect theies w behavior ith age of concr (interete action) in this , which ma way [32]. kes it necessary to introduce a term in the model that reflects it. The models developed for non-recycled concrete do not reflect these aspects, as NA does not affect the behavior 5.8. Probability Distributions Fitting: Characteristic Strength of concrete in this way [32]. The characteristic strength of concrete is the compressive strength value for which the probability of 5.8. Probability Distributions Fitting: Characteristic Strength the actual compressive strength being lower is 5% at an age of 28 days, according to the standards [28,29]. This strength is used in structural design and its determination is made by adjusting the experimental The characteristic strength of concrete is the compressive strength value for which the values to the normal probability distribution and determining the 5% percentile [41]. However, probability of the actual compressive strength being lower is 5% at an age of 28 days, according to other probability distributions may be better ﬁtted to the experimental data. the standards [28,29]. This strength is used in structural design and its determination is made by In Section 5.3, the normality of the results was evaluated, concluding that the compressive strength adjusting the experimental values to the normal probability distribution and determining the 5% of each mixture at any age could be adjusted to a normal distribution, whose expression is shown in percentile [41]. However, other probability distributions may be better fitted to the experimental data. Equation (4). Nevertheless, a log-likelihood study indicated that the probability distribution that best In Section 5.3, the normality of the results was evaluated, concluding that the compressive strength of each mixture at any age could be adjusted to a normal distribution, whose expression is shown in Equation (4). Nevertheless, a log-likelihood study indicated that the probability distribution that best fitted the experimental data was the Weibull distribution, shown in Equation (5), except for the mix SA100, which was the gamma distribution, shown in Equation (6). In the normal distribution, µ and σ are the arithmetic mean and standard deviation of the experimental data, respectively. In the Weibull and gamma distribution, k and λ are the shape and scale parameters, respectively, i.e., the parameters of distribution fitting. All these parameters for each mixture are given in Table 15 for the 28-day compressive strength. Mathematics 2020, 8, 2190 18 of 24 ﬁtted the experimental data was the Weibull distribution, shown in Equation (5), except for the mix SA100, which was the gamma distribution, shown in Equation (6). In the normal distribution, and are the arithmetic mean and standard deviation of the experimental data, respectively. In the Weibull and gamma distribution, k and are the shape and scale parameters, respectively, i.e., the parameters of distribution ﬁtting. All these parameters for each mixture are given in Table 15 for the 28-day compressive strength. (u) ( ) ( ) Normal distribution : f x = p e du (4) 2 1 k1 k x x ( ) Weibull distribution : f (x) = e (5) k1 ( ) Gamma distribution : f (x) = e (6) (k 1)! Table 15. Adjustment parameters for the probability distributions of the 28-day compressive strength. Mix Normal Distribution Weibull/Gamma Distribution SA0 = 60.99; = 4.53 k = 17.97; = 62.89 SA25 = 56.67; = 1.21 k = 59.99; = 57.20 SA50 = 49.37; = 1.96 k = 32.80; = 50.21 SA75 = 39.11; = 2.33 k = 21.27; = 40.14 SA100 = 37.97; = 1.30 k = 964.75; = 25.41 In the mix SA100, the best-ﬁt distribution at 28 days was the gamma distribution. It is possible to determine the characteristic compressive strength of each mixture by obtaining the 5% percentile if the probability distributions are known. Table 16 shows the characteristic strength according to the normal distribution and the best-ﬁt distribution (Weibull or gamma) for each mixture. In addition, this table also shows the normalized value according to the Spanish Instruction of Structural Concrete EHE-08 [29], calculated by approximating the value obtained to the standard series (20, 25, 30, 35, 40, 45, 50, 55, 60, 70, 80, 90, and 100 MPa). Figure 10 shows the calculation of the 5% percentile for each mixture in the best-ﬁt distribution (Weibull or gamma). Table 16. Characteristic compressive strength of the mixes developed. Characteristic Characteristic Normalized Compressive Strength Compressive Strength Characteristic Mix According to According to Normal Compressive Strength Weibull/Gamma Distribution (MPa) (MPa) Distribution (MPa) SA0 53.54 53.31 50 SA25 54.68 54.44 50 SA50 46.15 45.86 45 SA75 35.28 35.11 35 SA100 35.83 35.98 35 Mathematics 2020, 8, x FOR PEER REVIEW 18 of 24 () · (4) Normal distribution: ( ) = · · · √· (5) Weibull distribution: ( ) = · · (·) Gamma distribution: ( ) = · · (6) ( )! Table 15. Adjustment parameters for the probability distributions of the 28-day compressive strength. Mix Normal Distribution Weibull/Gamma Distribution SA0 = 60.99; = 4.53 = 17.97; = 62.89 SA25 = 56.67; = 1.21 = 59.99; = 57.20 SA50 = 49.37; = 1.96 = 32.80; = 50.21 SA75 = 39.11; = 2.33 = 21.27; = 40.14 SA100 = 37.97; = 1.30 = 964.75; = 25.41 In the mix SA100, the best-fit distribution at 28 days was the gamma distribution. It is possible to determine the characteristic compressive strength of each mixture by obtaining the 5% percentile if the probability distributions are known. Table 16 shows the characteristic strength according to the normal distribution and the best-fit distribution (Weibull or gamma) for each mixture. In addition, this table also shows the normalized value according to the Spanish Instruction of Structural Concrete EHE-08 [29], calculated by approximating the value obtained to the standard series (20, 25, 30, 35, 40, 45, 50, 55, 60, 70, 80, 90, and 100 MPa). Figure 10 shows the calculation of the 5% percentile for each mixture in the best-fit distribution (Weibull or gamma). Table 16. Characteristic compressive strength of the mixes developed. Characteristic Compressive Normalized Characteristic Compressive Strength According to Characteristic Mix Strength According to Normal Weibull/Gamma Distribution Compressive Strength Distribution (MPa) (MPa) (MPa) SA0 53.54 53.31 50 SA25 54.68 54.44 50 SA50 46.15 45.86 45 MathematicsSA75 35.28 2020, 8, 2190 35.11 35 19 of 24 SA100 35.83 35.98 35 Mathematics 2020, 8, x FOR PEER REVIEW 19 of 24 Figure Figure 10. 10. Graph Graph of the of the characteristic characteristic com compr pressive essive streng strength th for for the b the best-ﬁt est-fit d distribution istribution ((W Weibu eibull ll and and gamma): gamma):( ( aa )) SA0; ( SA0; (b b )) SA25; SA25; (( cc)) SA50; ( SA50; (d d)) SA75; ( SA75; (e e)) SA100 SA100.. The values obtained show that mixtures with larger quantities of ﬁne RCA can present the same The values obtained show that mixtures with larger quantities of fine RCA can present the same characteristic strength as others with a lower ﬁne content. Therefore, if structural calculations are to be characteristic strength as others with a lower fine content. Therefore, if structural calculations are to performed, each mix developed with these sorts of recycled aggregates must be separately studied. be performed, each mix developed with these sorts of recycled aggregates must be separately studied. The The cha characteristic racteristicstr strength ength of of concrete m concrete may ay not be not be a affected by the increased ected by the increased amounts of r amounts of reecover covered ed waste waste bec because, ause, as as shown shown in Table in Table 16, 16, mixes mixes w with ith 0 and 0 and 25% 25% ﬁne fine RCA RCA had t had the he same st same standar andard dized ized characteristic characteristicstr strength, ength, as asalso also did mi did mixtur xtures i es incorporating ncorporating 75 75 and and 100% f 100% ﬁne ine RCA. RCA. Finally Finall,y, both both EC-2 EC-2[ [ 28 28] ] and andEHE-08 EHE-08[ [2 29 9] ] estimate estimate cha characterist racteristic ic com compr pressiv essive e st str ren ength gth ((ffck, i , n in MPa MPa) ) ck by Equation (7) as a function of 28-day medium compressive strength (fc,m, in MPa, see Table 8). This by Equation (7) as a function of 28-day medium compressive strength (f , in MPa, see Table 8). c,m expression was only valid for mix SA0, underestimating the characteristic strength between 4 and 6 This expression was only valid for mix SA0, underestimating the characteristic strength between 4 and MPa for the rest of the mixtures that incorporate fine RCA (Table 17). This is due to the sharpest form 6 MPa for the rest of the mixtures that incorporate ﬁne RCA (Table 17). This is due to the sharpest of the adjusted probability distribution, so that the use of this expression would not allow us to form of the adjusted probability distribution, so that the use of this expression would not allow us to employ all the strength capacity of these mixtures, with the consequent economic loss. This is one of employ all the strength capacity of these mixtures, with the consequent economic loss. This is one of the reasons why the analysis of this article is fundamental in concrete for structural use. the reasons why the analysis of this article is fundamental in concrete for structural use. = −8 (7) f = f 8 (7) ck c,m Table 17. Comparison between the characteristic strength obtained by calculation and that obtained through the standards. Characteristic Compressive Strength: Characteristic Compressive Mix Distribution Fitting (MPa) Strength: Equation (7) (MPa) SA0 53 53 SA25 54 49 SA50 46 41 SA75 35 31 SA100 36 30 Mathematics 2020, 8, 2190 20 of 24 Table 17. Comparison between the characteristic strength obtained by calculation and that obtained through the standards. Characteristic Compressive Characteristic Compressive Mix Strength: Distribution Fitting (MPa) Strength: Equation (7) (MPa) SA0 53 53 SA25 54 49 SA50 46 41 SA75 35 31 SA100 36 30 6. Conclusions Throughout this article, the ﬂowability and the compressive strength of a Self-Compacting Concrete (SCC) made with Recycled Concrete Aggregate (RCA) have been analyzed. The compressive strength was also subjected to an extensive statistical analysis, which allowed us to evaluate dierent aspects than the traditional descriptive analysis. Regarding the ﬂowability, it was veriﬁed that it is possible to achieve SCC using high quantities of coarse and ﬁne RCA (up to 100% incorporation ratios). The higher proportion of ﬁne particles of the RCA (ﬁne fraction), compared to Natural Aggregate (NA), resulted in higher slump ﬂow and slower movement, which reduced the risk of segregation. Nevertheless, the most relevant conclusions are related to the statistical evaluation of compressive strength: The behavior of ﬁne RCA in relation to the compressive strength of SCC was homogeneous, as no discordant breaks occurred in any mixture at any age (anomalous data). The dispersion was reduced with higher contents of ﬁne RCA. The compressive strength of SCC in all the mixtures was properly ﬁtted to a normal probability distribution, although the Weibull and gamma distributions showed the best ﬁt. Characteristic compressive strength was underestimated when applying the standard estimation methods to mixtures with ﬁne RCA. The dispersion of the compressive strength values obtained in the mixtures with RCA led the variance of the dierent mixtures not to be considered statistically equal. Therefore, the analysis of the eect of RCA could not be carried out using the usual procedures and required unusual robust procedures such as the Kruskal–Wallis test, which is not inﬂuenced by the variance of the mixtures. The addition of ﬁne RCA, at a constant eective water-to-cement (w/c) ratio, reduced the compressive strength, being its inﬂuence greater than age. However, the addition of a larger amount of ﬁne RCA was not always associated with a signiﬁcant decrease in that strength: mixtures with low ﬁne RCA content (0 and 25%), and high content (75 and 100%) showed, respectively, the same strength in statistical terms. Therefore, the normalized characteristic compressive strength was also the same in each batch. Thus, according to the results of the ANalysis Of VAriance (ANOVA), the optimum RCA content in the concretes developed would be 25–50% from the strength point of view. The exact amount should be deﬁned by the assessment of ﬂowability, service requirements of the structure, and sustainability criteria. With respect to age, the addition of ﬁne RCA delayed the development of strength: for 0% ﬁne RCA, the compressive strength at 7, 28 and 90 days was statistically equal, while for 100% ﬁne RCA, the strength at each age was signiﬁcantly dierent. The interaction between age and percentage of ﬁne RCA makes the strength behavior of each mixture dierent. This implies that it is not possible to establish a clear generalization of the expected behavior of concrete with RCA: the eect of each RCA content must be studied in detail at each age. The most accurate and simplest techniques to estimate compressive strength were simple age-dependent regression models, while the models for predicting the compressive strength as Mathematics 2020, 8, 2190 21 of 24 a function of the ﬁne RCA percentage showed imprecisions at advanced ages. The multiple regression model that has been developed provided highly reliable estimations, although its formulation was more complex. The interaction between RCA content and age should be considered for an accurate estimation of compressive strength. This statistical approach towards the analysis of the compressive strength of an SCC containing coarse and ﬁne RCA is intended to show a useful way of both addressing the problems associated with recycled aggregate and of arriving at conclusions that facilitate its use in real structures and the prediction of its strength. This procedure could be applied to any type of waste, making the structural use of recycled concrete more feasible. Author Contributions: Conceptualization, V.R.-C., M.S. and V.O.-L.; methodology, V.R.-C. and V.O.-L.; software, V.R.-C.; validation, M.S., A.B.E. and A.S.; formal analysis, V.R.-C., A.B.E. and A.S.; investigation, V.R.-C. and A.B.E.; resources, M.S., A.S. and V.O.-L.; data curation, V.R.-C., M.S. and A.B.E.; writing—original draft preparation, V.R.-C.; writing—review and editing, M.S. and V.O.-L.; visualization, A.B.E. and A.S.; supervision, M.S. and V.O.-L.; project administration, M.S. and V.O.-L.; funding acquisition, M.S. and V.O.-L. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the following entities and grants: Spanish Ministry MCI, AEI, EU, and ERDF, grants FPU17/03374 and RTI2018-097079-B-C31; the Junta de Castilla y León and ERDF, grant BU119P17 awarded to research group UIC-231; Youth Employment Initiative (JCyL) and ESF, grant UBU05B_1274; the University of Burgos, grant Y135 GI awarded to the SUCONS group; the University of the Basque Country, grant PPGA20/26; the Basque Government research group IT1314-19. Conﬂicts of Interest: The authors declare no conﬂict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results. References 1. Sandanayake, M.; Zhang, G.; Setunge, S. Estimation of environmental emissions and impacts of building construction—A decision making tool for contractors. J. Build. Eng. 2019, 21, 173–185. [CrossRef] 2. Liang, W.; Dai, B.; Zhao, G.; Wu, H. 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Mathematics – Multidisciplinary Digital Publishing Institute
Published: Dec 9, 2020
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