Improvement and predictive modeling of the mechanical performance of waste fire clay blended concrete

Özkılıç, Yasin Onuralp; Zeybek, Özer; Karalar, Memduh; Çelik, Ali İhsan; Althaqafi, Essam

doi:10.1515/rams-2025-0114

Full Article

1

Introduction

The increasing demand for sustainable building materials in today’s world has brought waste management and the reduction of environmental impacts to the forefront in the construction industry [1]. In particular, the use of alternative raw materials in concrete production offers significant potential for reducing natural resource consumption and converting waste into valuable products [2,3]. Additionally, environmentally friendly safety measures and sustainability concepts are gaining increasing importance on a global scale, although they vary depending on local conditions. In this context, new supply approaches aimed at re-evaluating by-products obtained from various production processes are being developed. Concrete is one of the most widely used basic construction materials in building and infrastructure projects worldwide. Current data indicate that approximately 2.8 billion m³ of concrete is consumed annually worldwide [4,5]. This high consumption rate results in a significant portion of construction and demolition waste consisting of concrete waste. In this context, the use of various industrial wastes in green concrete production offers both economically advantageous and effective solutions for waste management [6,7,8,9]. Globally, large amounts of concrete waste are generated each year, and the primary strategies developed to address this issue include reuse, recycling, and recovery. Among these strategies, the reuse of concrete waste in the form of aggregates stands out. However, the current rate of recycled aggregate use in concrete production remains at insufficient levels. Previous studies have demonstrated that different types of demolition waste materials can be successfully used as coarse aggregates for environmentally friendly concrete production. Extensive research has been conducted, particularly on the use of waste brick, ceramic, marble, glass, and others as recycled aggregates [10,11,12,13]. Khaloo [14] reported that crushed clinker clay can be used as the coarse aggregate instead of natural aggregates and that the resulting concrete has lower density and compressive strength (CS), 7% lower than that of concrete made with natural aggregates. In another study, the consumption of new and clean crushed clays as coarse aggregates in concrete was investigated by Khalaf [15]. In this study, the concrete samples were made by utilizing four modified forms of fired clay. It has been determined that the CS of the crushed clay aggregate concrete is 15% lower in strength than the normal aggregate concrete. In parallel with the CS, the flexural strength (FS) of the concrete with crushed clay aggregate was also determined to be 8% lower than the concrete with normal aggregate. Zheng et al. [16] compared the effects of waste fire clay (WFC) and concrete aggregates on the performance of hardened concrete and noted that recycled concrete aggregates generally exhibit a higher performance than those of non-recycled aggregates. For this purpose, C25 and C50 of concrete were examined, attained by using varying water/cement percentages. Five different replacement amounts – 0, 25, 50, 75, and 100% – were indicated in each concrete grade. Upon conclusion of this research, it was determined that, overall, the concrete incorporating used concrete aggregate exhibited enhanced productivity compared to the concrete containing used clay aggregate. A comparison of the current investigative findings with the results in the literature, for hardened concrete including recycled clay or concrete aggregate, was conducted. Studies in this field indicate that coarse aggregates produced from fired clay can be used in concrete production with certain limitations [17,18,19,20,21,22,23,24,25,26,27,28]. Moreover, there are studies which use waste WFC in the construction of the structural membrane level [29,30,31]. However, there are only a limited number of studies in the literature that have thoroughly investigated the effects of varying WFC content on the mechanical properties of concrete. Additionally, there is a lack of modeling approaches to predict the engineering performance of concrete WFC.

Concrete is the most widely used construction material worldwide and is responsible for the generation of large amounts of construction and demolition waste. From the perspective of sustainability and reducing environmental impacts, the reuse and recycling of waste materials are of great importance. Although the literature has demonstrated that WFC-based aggregates can be used in the production of environmentally friendly concrete, it has also been noted that these applications may result in the loss of certain mechanical performance. In particular, research on the effects of WFC on concrete properties is limited, and knowledge in this area remains insufficient. Additionally, the lack of studies on predicting the mechanical properties of concrete containing WFC using empirical models or advanced prediction methods is a significant gap in the literature. In this context, the current research aims to fill these gaps by comprehensively investigating the effects of different WFC replacement ratios on the mechanical performance of concrete and developing empirical and ARX-based prediction models based on experimental data. The details of the study and the findings obtained are presented in the following sections.

2

Materials and methods

WFC was used to replace fine aggregate (FA) and cement in order to obtain eco-friendly concrete. About 10, 20, 30, 40, and 50% of WFC concentrations were used for this purpose. To produce concrete, CEM 1 32.5 cement was used. The water-to-cement ratio was set to be 0.46. The percentage of cement to total aggregate was 34%. In the design mixture, superplasticizers were not utilized. Figure 1 shows the flow chart of the study.

Pictures related to strength tests, slump, workability, and setting time of tests performed according to appropriate standards are provided in Figure 2. A slump test was conducted as stated by the ASTM C143 [32] standard. The slump test results for WFC percentage are presented in Figure 3 for the replacement of FA and cement. Five different WFC contents for replacing FA and cement were used to confirm the most efficient cost and optimal workability. The results showed that the slump values reduced as the water-to-fine aggregate ratio (WFC) increased for cement replacement. Additionally, the slump values increased as the WFC content increased for FA replacement.

3

Analysis of experimental tests and discussion

The primary objective of this study was to conduct a comprehensive analysis of various cement products that are composed of specific proportions of FA and cement coupled with WFC. As stated above, to attain this goal, the proportion of FA and cement combined with WFC was altered to 0, 10, 20, 30, 40, and 50% in concrete mixtures, and the influence of WFC was also measured. Following these investigations, the CS, splitting tensile strength (STS), and FS tests were performed. In addition, scanning electron microscopy (SEM) investigations were also conducted. Then, conclusions of the investigation are provided.

3.1

A comprehensive examination of CS’s impact

The primary goal of this study was to assess the susceptibility of a sample to fracture when subjected to external pressure. The required testing for each individual concrete instance was conducted following the requirements specified in ASTM C39 [33]. To achieve this objective, the dimensions of the test cube sections were chosen as 150 mm × 150 mm × 150 mm. In this investigation, samples including different proportions of FA and cement combined with WFC were tested under a longitudinal restriction load at a level determined in relation to specimen breaks. At this point, the compression ability was predicted, starting from the severe failure point, which was determined by the number of examples. As shown in Figure 4, the CS values were observed after a 28-day period. The samples were constructed with a 100% reference mix, various proportions of aggregate and cement, and reference aggregates, which were swapped with and without waste WFC. As shown in Figure 4, the concrete admixture’s CSs were larger than those of the stable concrete combinations devoid of waste WFC, when WFC was used as a minor aggregate substitute in a small WFC percentage. Alternatively, as observed in Figure 4, the CSs of concrete admixture with small WFC consumption as a replacement for cement were smaller than those of the steady concrete combinations, lacking waste WFC. It was realized that this rate is approximately 12%. As shown in Figure 4, when 10, 20, and 30% of aggregates were replaced with waste WFC, it was observed that the CSs of the concrete admixture improved by 6, 15, and 3.2%, respectively. However, after a 30% replacement of the aggregate, it was detected that the CSs of the concrete admixture reduced by 4.2 and 10%. When this comparison was made with the exchange of cement, subsequent results were observed. The reductions in the CSs of the concrete admixture were detected by 12.2, 25, 34, 46, and 68%. The numerical examination of the example results offered significant benefits of WFC (as aggregate replaced by waste WFC) to the CS of concrete by up to 20% replacement. Concrete waste’s physical and chemical constitution explains this condition. Increased firing temperatures cause the leftover concrete to react with the clay particles, forming new crystalline phases in the burned body [5]. As a final point, the strength of the WFC structure increases. In the literature, a significant decrease in CS was reported, while the concrete used the utilized clay aggregate as the replacement for natural coarse aggregate [34,35,36], ranging from 8 to 40%. Some of the investigations indicated that the removal of the floating elements could decrease the strength alterations between utilized and controlled concretes. In contrast, Zheng et al. [16] found that the primary decrease in the 28-day CS was only 7.2 and 9.6% for C25 and C50 utilized concrete when the natural coarse aggregate was 100% replaced with utilized concrete aggregate, and 11 and 13% for C25 and C50 utilized concrete when the natural coarse aggregate was 100% replaced with utilized clay aggregate. These values are significantly smaller than values stated in the available research. This highlights the significance of developing recycled aggregates, whose efficacy can be enhanced by having a similar size distribution in comparison to native aggregates [16].

3.2

Detailed examination of the effect of STS

An estimation of relative STS of various concrete amount admixtures prepared with 100% reference and many quantities of utilized aggregates swapped by FA and cement with and without WFC is presented in Figures 5 and 6. As shown in Figure 6, the results of the STS test commonly follow a parallel trend to that of the CS. Compared with CS, STS of concrete also improves with the proportion of WFC up to a 20% replacement of aggregate, but at that point, it then decreases. As shown in Figure 6, when 10, 20, and 30% aggregates were swapped with waste WFC, it was observed that the STSs of the concrete admixture improved by 7.1, 9, and 4.3%, respectively. On the other hand, after a 30% partial replacement of aggregate, it was detected that the STSs of concrete admixture reduced by 6.5 and 12%. As shown in Figure 6, optimum values of STS are achieved at 20% WFC, where maximum STS distribution is observed. When this evaluation was compared with the cement swapped one, the following results were achieved. When the quantity of the WFC increased from 10 to 50%, it was observed that the values of STS decreased. It was discovered that the STSs of concrete admixture were reduced by 8.2, 22, 33, 48, and 63%. As mentioned above, numerical examination of example results offered the important benefits of WFC (as aggregates were interchanged with waste WFC) to the STS of concrete up to a 20% replacement. The connection of CS with STS is also shown in Figure 7. As shown in Figure 7, the model between the CS and STS is modeled as flat. In addition, as noted in Figure 7, the regression analysis defines a strong association for CS compared to STS, with an R ² value of more than 89% for aggregate replacement and 98% for cement replacement.

3.3

Detailed investigation of the influence of flexural performance tests

The strength of instances exposed to flexural stress might be considered as the tensile strength of WFC, as shown in Figure 8. In contrast, the FS is generally larger than the indirect STS. Flexure strength was determined in investigational samples. The observed strengths ranged between 7.8 and 9.8 MPa for aggregates replaced with FA and 5.4 and 7.8 MPa for aggregates replaced with cement. In Figure 9, FS is discovered by means of the altered percentages of waste WFC. As mentioned above, aggregate for 10, 20, 30, 40, and 50% was exchanged with waste WFC, and the FSs of the concrete admixture were improved by 11.5, 25.6, 18, 12.8, and 7.7%. A numerical investigation of sample results revealed the significant contributions of WFC to the FS of concrete, as aggregates were swapped with waste WFC, up to a 20% replacement rate. In contrast, while this evaluation is related to the replacement of cement, the following results were detected. It was discovered that the FSs of concrete admixture were reduced by 2.6, 6.8, 13, 26, and 44%. The deduction of the FS of the instances is presented in Figure 9. The results found here are compatible with the studies in the literature. This is because of the pozzolanic internal curing influences of the fine recycled aggregates from crushed bricks, encouraging the progress of mortar strength [37]. Like the compressive ability of concrete, FS was also improved as the replacement percentage of WFC, where aggregate was swapped with waste WFC, increased up to 20%, but declined thereafter. This is because the extra water content increases with the replacement percentage of waste WFC, resulting in an improved efficient water cement percentage, which is a vital influence on the strength of mortar [37].

4

Empirical proposed models for mechanical properties

The main objectives of this part are twofold. The relationships between the mechanical properties of concrete produced with recycled materials were investigated by considering different design treatments. To estimate CS, STS, and FS, an empirical model was developed based on our test results and different investigations conducted by researchers.

4.1

Evaluation of capacities of concrete with waste WFC

To compare the investigational performance of concrete using materials with those expected via mechanical procedures, ACI 318 and Eurocode 2 (EC2) were used to estimate the FS and the elastic modulus based on the values of CS. ACI 318 suggests the following sequent equations: (1) $f_{r} = 0.62 \sqrt{f_{c}^{'}},$ {f}_{\text{r}}=0.62\sqrt{{f}_{\text{c}}^{\text{'}}}, (2) $E_{c} = 4,700 \sqrt{f_{c}^{'}} .$ {E}_{\text{c}}=\mathrm{4,700}\sqrt{{f}_{\text{c}}^{^{\prime} }}.

EC2 recommends the following sequent equations: (3) $f_{rctm, fl} = max 1.6 - \frac{h}{100}) f_{ctm}, f_{ctm}),$ {f}_{\text{rctm},\text{fl}}=\text{max}\left(\left(1.6-\frac{h}{100}\right){f}_{\text{ctm}},{f}_{\text{ctm}}\right), (4) $E_{c} = 22 {\frac{f_{cm}}{10})}^{0.30} .$ {E}_{\text{c}}=22{\left(\frac{{f}_{\text{cm}}}{10}\right)}^{0.30}.

Here, f _r is defined as FS and E _c is defined as the static elastic modulus (N·mm⁻²). Furthermore, $f_{c}^{'}$ {f}_{\text{c}}^{^{\prime} } refers to the CS after 28 days of curing (N·mm⁻²) and f _ctm,fl to the FS sequent EC2. In the above equations, h is defined as the height of the specimen (mm), and f _ctm is defined as the mean of the FS gained using f _ctm = 0.3(f _ck)2/3, where f _ck are the investigational values obtained for the CS minus 8 MPa. The other equation was developed by Mansoor et al. [38] in Eq. (5). In this study, Mansoor et al. [38] presented the CS and FS results graphically. Based on investigative results, the subsequent experimental calculations are suggested between CS and FS. The results showed that the strength of combinations having waste clay powder is greater than that of the control combination. The maximum strength was observed in combination with 15% waste clay for both CS and FS of samples. This is because leftover clay powder reflects a naturally occurring pozzolan material, and silicon dioxide (SiO₂) reacts chemically with CaOH (an alkali that arises from cement hydration) to process a cementitious product that gives mortar its strength [39,40]. An additional cause is that fine particles of WFC can successfully fill the gaps, resulting in a denser concrete microstructure. (5) $f_{t} = 1 \times 10^{- 4} {(WFC %)}^{3} - 0.0093 {(WFC %)}^{2} + 0.2255 {(WFC %)}^{1} + 6.1848 .$ {f}_{\text{t}}=1\times {10}^{-4}\hspace{.25em}{(\text{WFC} \% )}^{3}-0.0093{(\text{WFC} \% )}^{2}+0.2255{(\text{WFC} \% )}^{1}+6.1848.

Creating empirical expressions to predict important outcomes according to the results of the experiment is one of the solution methods [41,42,43]. As observed in Figure 10, all the samples exist at higher values than the theoretical ones, and even these sequences have a higher assessment than the one attained, resulting in EC2. While Eq. (1) (provided by ACI) is utilized, the experimental values found for CS go beyond the empirical ones. Additionally, it is observed that while Eq. (3), provided by EC2, is utilized, the investigational values for CS surpass the empirical ones. In view of these consequences, the empirical values attained using the equations are not sufficiently conservative when WFC is used, and the examples are experimentally weaker than estimated. When using ACI equations, it is crucial to consider the variance. It is recommended that technical regulations explore the possibility of developing new equations for the FS in the creation of recycled concretes using WFC. These results are also supported by previous similar investigations [44].

In this study, according to investigational test results, the sequential experimental equations are offered between CS and FS, for the partial replacement of FA in Eq. (6) and cement replacement in Eq. (7). Furthermore, for STS, Eqs. (8) and (9) offer solutions for the partial replacement of FA and cement. In Figures 10 and 11, these equations are also presented. (6) $f_{t} = - 0.2232 {(WFC %)}^{2} + 1.6396 {(WFC %)}^{1} + 6.43,$ {f}_{\text{t}}=-0.2232{(\text{WFC} \% )}^{2}+1.6396{(\text{WFC} \% )}^{1}+6.43, (7) $f_{t} = - 0.0821 {(WFC %)}^{2} + 0.1007 {(WFC %)}^{1} + 7.76,$ {f}_{\text{t}}=-0.0821{(\text{WFC} \% )}^{2}+0.1007{(\text{WFC} \% )}^{1}+7.76, (8) $f_{t} = - 0.041 {(WFC %)}^{2} + 0.2277 {(WFC %)}^{1} + 1.9337,$ {f}_{\text{t}}=-0.041{(\text{WFC} \% )}^{2}+0.2277{(\text{WFC} \% )}^{1}+1.9337, (9) $f_{t} = + 0.0073 {(WFC %)}^{2} - 0.2145 {(WFC %)}^{1} + 2.3119 .$ {f}_{\text{t}}=+0.0073{(\text{WFC} \% )}^{2}-0.2145{(\text{WFC} \% )}^{1}+2.3119.

4.2

Assessment of current findings with existing investigations

Considering very limited existing investigations on concrete with WFC, it was used as either FA or cement replacement. Thus, two empirical models were developed to estimate the strength. Mechanical properties such as CS, STS, and FS for concrete with WFC have been collected from the literature [17,18,19,20,21,22,27,28,45,46]. The resistance values (f) of concrete with WFC were then normalized by plain concrete strengths (f′). Figures 12–17 show the normalized resistances as a function of WFC quantities.

As shown in Figures 12–14, the CS values containing WFC generally decrease after a certain value when WFC was used as an FA replacement. Hence, an empirical model was derived to account for these reductions in the resistances as follows: (10) $f = [1 + a_{1} \times (FCA) + a_{2} \times {(FCA)}^{2}] \times f',$ f={[}1+{a}_{1}\times (\text{FCA})+{a}_{2}\times {(\text{FCA})}^{2}]\times f^{\prime} , where f is the concrete strength values produced with WFC ((N·mm⁻²) (f _c = CS; f _s is the STS; f _f is the FS); a ₁ and a ₂ are coefficients given in Table 1; FCA is the WFC amounts (0 < FCA < 50); f′ is the strength values of the plain concrete.

Table 1

Coefficients used in Eq. (10)

Capacities (f)		a ₁	a ₂
Concrete with WFC as a partial replacement for FA	f _c	0.008	−0.0002
	f _s	0.009	−0.0002
	f _f	0.015	−0.0003

As shown in Figures 15–17, the resistance of concrete with WFC decreases when the amount of WFC increases in the mixture. Thus, a subsequent empirical model was proposed for the strength values: (11) $f = [1 + a_{3} \times (FCA)] \times f',$ f={[}1+{a}_{3}\times (\text{FCA})]\times f^{\prime} , where a ₃ is the coefficient given in Table 2.

Table 2

Coefficients used in Eq. (11)

Capacities (f)		a ₃
Concrete with WFC as a partial replacement for cement	f _c	−0.0080
	f _s	−0.0075
	f _f	−0.0055

As shown in Eqs. (10)–(11), the resistances of concrete can be determined as a function of the amount of WFC. Estimated strength values, based on proposed equations, are also presented in Figures 12–17.

Furthermore, an MIMO (multiple-input multiple-output) ARX model was also used for more precise prediction of the engineering properties (CS, STS, and FS). It can estimate the above-mentioned properties, taking multiple inputs into account. In this way, more detailed analysis was conducted to obtain these properties. Due to limited data in the cement replacement case, a model was developed for the FA replacement. Multiple data points from the concrete test specimens were collected to estimate the CS, STS, and FS. Six input parameters (cement [kg·m⁻³], WFC amount [kg·m⁻³], fine aggregate [kg·m⁻³], coarse aggregate [kg·m⁻³], water [kg·m⁻³], and age [day of specimen test]) and one output parameter, either CS (MPa) or STS (MPa) or FS (MPa), are used in the developed model. A polynomial model with identifiable coefficients (idpoly) was used in the discrete-time linear model. The above-mentioned mechanical properties were obtained as follows: (12) $A (z) y (k) = B (z) u (k) + e (k),$ A(z)y(k)=B(z)u(k)+e(k), where A(z) denotes the corresponding output parameters, y(k) is the corresponding output to be predicted, B(z) stands for input vector coefficients, u(k) is input variables, e(k) represents the prediction errors, and z and k are discrete time parameters. (13) $B (z) = [B_{1} (z) B_{2} (z) B_{3} (z) B_{4} (z) B_{5} (z) B_{6} (z)],$ B(z)={[}{B}_{1}(z)\hspace{.5em}{B}_{2}(z)\hspace{.5em}{B}_{3}(z)\hspace{.5em}{B}_{4}(z)\hspace{.5em}{B}_{5}(z)\hspace{.5em}{B}_{6}(z)], (14) $u (k) = \begin{matrix} u_{1} (k) \\ u_{2} (k) \\ u_{3} (k) \\ u_{4} (k) \\ u_{5} (k) \\ u_{6} (k) \end{matrix}] .$ u(k)=\left[\begin{array}{c}{u}_{1}(k)\\ {u}_{2}(k)\\ {u}_{3}(k)\\ {u}_{4}(k)\\ {u}_{5}(k)\\ {u}_{6}(k)\end{array}\right].

By using Eq. (12), the multiple-input single-output (MISO) ARX model for CS value can be constituted via the following A(z) and B(z) expressions: (15) $\begin{matrix} A (z) = 1 + 8.477 {(z)}^{- 1} + 6.027 {(z)}^{- 2} + 1.183 {(z)}^{- 3} - 4.238 {(z)}^{- 4} - 8.156 {(z)}^{- 5} - 5.374 {(z)}^{- 6} - 8.124 {(z)}^{- 7} - 4.428 {(z)}^{- 8} + 0.6344 {(z)}^{- 9} - 1.36 {(z)}^{- 10} + 2.317 {(z)}^{- 11}, \end{matrix}$ \begin{array}{c}A(z)=1+8.477{(z)}^{-1}+6.027{(z)}^{-2}+1.183{(z)}^{-3}-4.238{(z)}^{-4}-8.156{(z)}^{-5}-5.374{(z)}^{-6}-8.124{(z)}^{-7}-4.428{(z)}^{-8}+0.6344{(z)}^{-9}-1.36{(z)}^{-10}+2.317{(z)}^{-11},\end{array} (16) $\begin{matrix} B 1 (z) = - 0.1737 - 1.12 {(z)}^{- 1} - 0.4362 {(z)}^{- 2} + 0.1083 {(z)}^{- 3} + 0.6817 {(z)}^{- 4} + 0.7603 {(z)}^{- 5} - 0.3062 {(z)}^{- 6} + 0.7983 {(z)}^{- 7} + 0.6638 {(z)}^{- 8} + 0.6566 {(z)}^{- 9} - 0.7647 {(z)}^{- 10} - 0.4527 {(z)}^{- 11}, \end{matrix}$ \begin{array}{c}B1(z)=-0.1737-1.12{(z)}^{-1}-0.4362{(z)}^{-2}+0.1083{(z)}^{-3}+0.6817{(z)}^{-4}+0.7603{(z)}^{-5}-0.3062{(z)}^{-6}+0.7983{(z)}^{-7}+0.6638{(z)}^{-8}+0.6566{(z)}^{-9}-0.7647{(z)}^{-10}-0.4527{(z)}^{-11},\end{array} (17) $\begin{matrix} B 2 (z) = - 0.3241 - 0.07702 {(z)}^{- 1} - 0.06975 {(z)}^{- 2} + 0.1208 {(z)}^{- 3} + 0.08553 {(z)}^{- 4} - 0.1087 {(z)}^{- 5} - 0.09673 {(z)}^{- 6} - 0.3436 {(z)}^{- 7} - 0.3817 {(z)}^{- 8} - 0.05339 {(z)}^{- 9} - 0.1342 {(z)}^{- 10} + 0.24 {(z)}^{- 11}, \end{matrix}$ \begin{array}{c}B2(z)=-0.3241-0.07702{(z)}^{-1}-0.06975{(z)}^{-2}+0.1208{(z)}^{-3}+0.08553{(z)}^{-4}-0.1087{(z)}^{-5}-0.09673{(z)}^{-6}-0.3436{(z)}^{-7}-0.3817{(z)}^{-8}-0.05339{(z)}^{-9}-0.1342{(z)}^{-10}+0.24{(z)}^{-11},\end{array} (18) $\begin{matrix} B 3 (z) = - 0.4455 + 0.3379 {(z)}^{- 1} + 0.2047 {(z)}^{- 2} + 0.001156 {(z)}^{- 3} - 0.2143 {(z)}^{- 4} - 1.078 {(z)}^{- 5} - 0.4938 {(z)}^{- 6} - 1.002 {(z)}^{- 7} - 0.3353 {(z)}^{- 8} + 0.2794 {(z)}^{- 9} - 0.1648 {(z)}^{- 10} + 0.8127 {(z)}^{- 11}, \end{matrix}$ \begin{array}{c}B3(z)=-0.4455+0.3379{(z)}^{-1}+0.2047{(z)}^{-2}+0.001156{(z)}^{-3}-0.2143{(z)}^{-4}-1.078{(z)}^{-5}-0.4938{(z)}^{-6}-1.002{(z)}^{-7}-0.3353{(z)}^{-8}+0.2794{(z)}^{-9}-0.1648{(z)}^{-10}+0.8127{(z)}^{-11},\end{array} (19) $\begin{matrix} B 4 (z) = - 0.6233 - 0.3855 {(z)}^{- 1} - 0.4236 {(z)}^{- 2} - 0.09665 {(z)}^{- 3} + 0.4073 {(z)}^{- 4} + 0.3819 {(z)}^{- 5} + 0.6809 {(z)}^{- 6} + 0.2792 {(z)}^{- 7} + 0.06653 {(z)}^{- 8} - 0.05163 {(z)}^{- 9} - 0.1817 {(z)}^{- 10} + 0.1881 {(z)}^{- 11}, \end{matrix}$ \begin{array}{c}B4(z)=-0.6233-0.3855{(z)}^{-1}-0.4236{(z)}^{-2}-0.09665{(z)}^{-3}+0.4073{(z)}^{-4}+0.3819{(z)}^{-5}+0.6809{(z)}^{-6}+0.2792{(z)}^{-7}+0.06653{(z)}^{-8}-0.05163{(z)}^{-9}-0.1817{(z)}^{-10}+0.1881{(z)}^{-11},\end{array} (20) $\begin{matrix} B 5 (z) = 3.569 + 3.922 {(z)}^{- 1} + 3.563 {(z)}^{- 2} - 0.7074 {(z)}^{- 3} - 3.582 {(z)}^{- 4} - 2.927 {(z)}^{- 5} + 10.1 {(z)}^{- 6} + 8.705 {(z)}^{- 7} + 1.162 {(z)}^{- 8} - 3.643 {(z)}^{- 9} - 10.6 {(z)}^{- 10} + 7.642 {(z)}^{- 11}, \end{matrix}$ \begin{array}{c}B5(z)=3.569+3.922{(z)}^{-1}+3.563{(z)}^{-2}-0.7074{(z)}^{-3}-3.582{(z)}^{-4}-2.927{(z)}^{-5}+10.1{(z)}^{-6}+8.705{(z)}^{-7}+1.162{(z)}^{-8}-3.643{(z)}^{-9}-10.6{(z)}^{-10}+7.642{(z)}^{-11},\end{array} (21) $\begin{matrix} B 6 (z) = - 0.3812 - 0.591 {(z)}^{- 1} - 0.2519 {(z)}^{- 2} - 0.3994 {(z)}^{- 3} - 0.5502 {(z)}^{- 4} + 0.6725 {(z)}^{- 5} + 1.395 {(z)}^{- 6} + 1.404 {(z)}^{- 7} + 0.3607 {(z)}^{- 8} - 0.9919 {(z)}^{- 9} - 0.2615 {(z)}^{- 10} - 0.1063 {(z)}^{- 11} . \end{matrix}$ \begin{array}{c}B6(z)=-0.3812-0.591{(z)}^{-1}-0.2519{(z)}^{-2}-0.3994{(z)}^{-3}-0.5502{(z)}^{-4}+0.6725{(z)}^{-5}+1.395{(z)}^{-6}+1.404{(z)}^{-7}+0.3607{(z)}^{-8}-0.9919{(z)}^{-9}-0.2615{(z)}^{-10}-0.1063{(z)}^{-11}.\end{array}

The predicted values from the ARX model, considering the developed expressions, are plotted in Figure 18. According to Figure 18, proposed models in Eqs (15)–(21) accurately estimate CS. These results show that the developed mathematical expressions can accurately describe experimental results.

In the same manner, by using Eq. (12), the MISO ARX model for STS value can be constituted via the following A(z) and B(z) expressions: (22) $\begin{matrix} A (z) = 1 + 0.5158 {(z)}^{- 1} - 0.2423 {(z)}^{- 2} + 0.1324 {(z)}^{- 3} - 0.08137 {(z)}^{- 4} + 0.9622 {(z)}^{- 5} - 0.433 {(z)}^{- 6} + 0.08627 {(z)}^{- 7} - 0.3187 {(z)}^{- 8} + 0.394 {(z)}^{- 9}, \end{matrix}$ \begin{array}{c}A(z)=1+0.5158{(z)}^{-1}-0.2423{(z)}^{-2}+0.1324{(z)}^{-3}-0.08137{(z)}^{-4}+0.9622{(z)}^{-5}-0.433{(z)}^{-6}+0.08627{(z)}^{-7}-0.3187{(z)}^{-8}+0.394{(z)}^{-9},\end{array} (23) $\begin{matrix} B 1 (z) = 0.01225 + 0.003711 {(z)}^{- 1} - 0.008909 {(z)}^{- 2} + 0.0024 {(z)}^{- 3} + 0.01283 {(z)}^{- 4} - 0.04885 {(z)}^{- 5} + 0.01478 {(z)}^{- 6} - 0.01269 {(z)}^{- 7} - 0.006995 {(z)}^{- 8} + 0.01459 {(z)}^{- 9}, \end{matrix}$ \begin{array}{c}B1(z)=0.01225+0.003711{(z)}^{-1}-0.008909{(z)}^{-2}+0.0024{(z)}^{-3}+0.01283{(z)}^{-4}-0.04885{(z)}^{-5}+0.01478{(z)}^{-6}-0.01269{(z)}^{-7}-0.006995{(z)}^{-8}+0.01459{(z)}^{-9},\end{array} (24) $\begin{matrix} B 2 (z) = 0.002325 + 0.002846 {(z)}^{- 1} - 0.005121 {(z)}^{- 2} + 0.002612 {(z)}^{- 3} + 0.003464 {(z)}^{- 4} - 0.0184 {(z)}^{- 5} + 0.009525 {(z)}^{- 6} - 0.01111 {(z)}^{- 7} - 0.003818 {(z)}^{- 8} + 0.003837 {(z)}^{- 9}, \end{matrix}$ \begin{array}{c}B2(z)=0.002325+0.002846{(z)}^{-1}-0.005121{(z)}^{-2}+0.002612{(z)}^{-3}+0.003464{(z)}^{-4}-0.0184{(z)}^{-5}+0.009525{(z)}^{-6}-0.01111{(z)}^{-7}-0.003818{(z)}^{-8}+0.003837{(z)}^{-9},\end{array} (25) $\begin{matrix} B 3 (z) = 0.003262 + 0.0004632 {(z)}^{- 1} - 0.0009615 {(z)}^{- 2} - 0.0009833 {(z)}^{- 3} + 0.007717 {(z)}^{- 4} - 0.0227 {(z)}^{- 5} + 0.01753 {(z)}^{- 6} - 0.03281 {(z)}^{- 7} - 0.01449 {(z)}^{- 8} + 0.01036 {(z)}^{- 9}, \end{matrix}$ \begin{array}{c}B3(z)=0.003262+0.0004632{(z)}^{-1}-0.0009615{(z)}^{-2}-0.0009833{(z)}^{-3}+0.007717{(z)}^{-4}-0.0227{(z)}^{-5}+0.01753{(z)}^{-6}-0.03281{(z)}^{-7}-0.01449{(z)}^{-8}+0.01036{(z)}^{-9},\end{array} (26) $\begin{matrix} B 4 (z) = 0.00354 + 0.005489 {(z)}^{- 1} - 0.01384 {(z)}^{- 2} + 0.004508 {(z)}^{- 3} - 8.45 e - 5 {(z)}^{- 4} - 0.02077 {(z)}^{- 5} + 0.01154 {(z)}^{- 6} - 0.004781 {(z)}^{- 7} - 0.004626 {(z)}^{- 8} + 0.01075 {(z)}^{- 9}, \end{matrix}$ \begin{array}{c}B4(z)=0.00354+0.005489{(z)}^{-1}-0.01384{(z)}^{-2}+0.004508{(z)}^{-3}-8.45e-5{(z)}^{-4}-0.02077{(z)}^{-5}+0.01154{(z)}^{-6}-0.004781{(z)}^{-7}-0.004626{(z)}^{-8}+0.01075{(z)}^{-9},\end{array} (27) $\begin{matrix} B 5 (z) = - 0.0719 + 0.02148 {(z)}^{- 1} + 0.01469 {(z)}^{- 2} + 0.002914 {(z)}^{- 3} - 0.02947 {(z)}^{- 4} + 0.1153 {(z)}^{- 5} - 0.165 {(z)}^{- 6} + 0.3611 {(z)}^{- 7} + 0.1782 {(z)}^{- 8} - 0.14 {(z)}^{- 9}, \end{matrix}$ \begin{array}{c}B5(z)=-0.0719+0.02148{(z)}^{-1}+0.01469{(z)}^{-2}+0.002914{(z)}^{-3}-0.02947{(z)}^{-4}+0.1153{(z)}^{-5}-0.165{(z)}^{-6}+0.3611{(z)}^{-7}+0.1782{(z)}^{-8}-0.14{(z)}^{-9},\end{array} (28) $\begin{matrix} B 6 (z) = 0.001661 + 0.003002 {(z)}^{- 1} - 0.003399 {(z)}^{- 2} + 0.003562 {(z)}^{- 3} - 0.01228 {(z)}^{- 4} - 0.004435 {(z)}^{- 5} + 0.01351 {(z)}^{- 6} - 0.008859 {(z)}^{- 7} + 0.003987 {(z)}^{- 8} - 0.01572 {(z)}^{- 9} . \end{matrix}$ \begin{array}{c}B6(z)=0.001661+0.003002{(z)}^{-1}-0.003399{(z)}^{-2}+0.003562{(z)}^{-3}-0.01228{(z)}^{-4}-0.004435{(z)}^{-5}+0.01351{(z)}^{-6}-0.008859{(z)}^{-7}+0.003987{(z)}^{-8}-0.01572{(z)}^{-9}.\end{array}

Using the developed expressions, the predicted values from the ARX model are plotted in Figure 19. According to Figure 19, proposed models in Eqs. (22)–(28) accurately estimate STS. These results show that developed expressions can accurately describe experimental results.

In the same manner, by using Eq. (12), the MISO ARX model for FS value can be constituted via the following A(z) and B(z) expressions: (29) $\begin{matrix} A (z) = 1 - 0.4203 {(z)}^{- 1} + 0.001436 {(z)}^{- 2} + 0.2292 {(z)}^{- 3} - 0.09532 {(z)}^{- 4} + 0.7151 {(z)}^{- 5} + 0.588 {(z)}^{- 6}, \end{matrix}$ \begin{array}{c}A(z)=1-0.4203{(z)}^{-1}+0.001436{(z)}^{-2}+0.2292{(z)}^{-3}-0.09532{(z)}^{-4}+0.7151{(z)}^{-5}+0.588{(z)}^{-6},\end{array} (30) $\begin{matrix} B 1 (z) = 0.08769 - 0.1563 {(z)}^{- 1} - 0.0517 {(z)}^{- 2} - 0.03147 {(z)}^{- 3} + 0.04067 {(z)}^{- 4} + 0.08095 {(z)}^{- 5} + 0.0533 {(z)}^{- 6}, \end{matrix}$ \begin{array}{c}B1(z)=0.08769-0.1563{(z)}^{-1}-0.0517{(z)}^{-2}-0.03147{(z)}^{-3}+0.04067{(z)}^{-4}+0.08095{(z)}^{-5}+0.0533{(z)}^{-6},\end{array} (31) $\begin{matrix} B 2 (z) = - 0.008314 - 0.01154 {(z)}^{- 1} - 0.005799 {(z)}^{- 2} + 0.0007587 {(z)}^{- 3} + 0.0131 {(z)}^{- 4} + 0.01246 {(z)}^{- 5} - 0.0007973 {(z)}^{- 6}, \end{matrix}$ \begin{array}{c}B2(z)=-0.008314-0.01154{(z)}^{-1}-0.005799{(z)}^{-2}+0.0007587{(z)}^{-3}+0.0131{(z)}^{-4}+0.01246{(z)}^{-5}-0.0007973{(z)}^{-6},\end{array} (32) $\begin{matrix} B 3 (z) = 0.0003771 - 0.02831 {(z)}^{- 1} - 0.01359 {(z)}^{- 2} - 0.005877 {(z)}^{- 3} + 0.01813 {(z)}^{- 4} + 0.02254 {(z)}^{- 5} - 0.0029 {(z)}^{- 6}, \end{matrix}$ \begin{array}{c}B3(z)=0.0003771-0.02831{(z)}^{-1}-0.01359{(z)}^{-2}-0.005877{(z)}^{-3}+0.01813{(z)}^{-4}+0.02254{(z)}^{-5}-0.0029{(z)}^{-6},\end{array} (33) $\begin{matrix} B 4 (z) = - 0.007613 - 0.01662 {(z)}^{- 1} - 0.01156 {(z)}^{- 2} - 0.005758 {(z)}^{- 3} - 0.002022 {(z)}^{- 4} - 0.003493 {(z)}^{- 5} - 0.003791 {(z)}^{- 6}, \end{matrix}$ \begin{array}{c}B4(z)=-0.007613-0.01662{(z)}^{-1}-0.01156{(z)}^{-2}-0.005758{(z)}^{-3}-0.002022{(z)}^{-4}-0.003493{(z)}^{-5}-0.003791{(z)}^{-6},\end{array} (34) $\begin{matrix} B 5 (z) = - 0.1348 + 0.3123 {(z)}^{- 1} + 0.1303 {(z)}^{- 2} + 0.05659 {(z)}^{- 3} - 0.08763 {(z)}^{- 4} - 0.1892 {(z)}^{- 5} - 0.05127 {(z)}^{- 6}, \end{matrix}$ \begin{array}{c}B5(z)=-0.1348+0.3123{(z)}^{-1}+0.1303{(z)}^{-2}+0.05659{(z)}^{-3}-0.08763{(z)}^{-4}-0.1892{(z)}^{-5}-0.05127{(z)}^{-6},\end{array} (35) $\begin{matrix} B 6 (z) = 0.06115 - 0.002228 {(z)}^{- 1} + 0.04805 {(z)}^{- 2} - 0.003102 {(z)}^{- 3} - 0.04251 {(z)}^{- 4} - 0.0804 {(z)}^{- 5} + 0.004543 {(z)}^{- 6} . \end{matrix}$ \begin{array}{c}B6(z)=0.06115-0.002228{(z)}^{-1}+0.04805{(z)}^{-2}-0.003102{(z)}^{-3}-0.04251{(z)}^{-4}-0.0804{(z)}^{-5}+0.004543{(z)}^{-6}.\end{array}

Using the developed expressions, the predicted values from the ARX model are plotted in Figure 20. According to Figure 20, proposed models in Eqs. (29)–(35) provide accurate estimates of FS. These results show that developed expressions can accurately describe experimental results.

5

SEM analysis

Aggregates replaced with 20% WFC yielded good results in many respects, so SEM analysis was performed on this sample. Significant conclusions are observable in the figures with SEM images magnified 500 times. The column on the left shows the replacement of fireclay by FA, and the column on the right shows the replacement by cement. Both images show well-formed mortar matrix formation. Figure 21a shows that a long crack has formed. In Figure 21b, it is seen that fireclay provides a better bond. Figure 21c and d shows some calcium silicate hydrate (C–S–H) in a compact structure with the effect of hydration [47]. C–S–H is slightly more visible in Figure 21d when replacing cement with fireclay. This result also confirms the results related to strength. In other words, the decrease in cement results in some agglomeration and weakening of strength. As shown in Figure 21c, it is noteworthy that the fireclay layers overlap and there are gaps between them. An excess of this can lead to decreased hydration and decreased strength. The interface transition zone (ITZ) is defined as the weak zone of normal concrete [48]. Cracking and weakening may occur in the ITZ as shown in Figure 21d. In cementitious concrete, ettringite occurs due to the high content of the mineral calcium sulfoaluminate [49,50]. Figure 21e shows the beginning of ettringite. It is known that ettringite formation positively affects the CS of concrete [51]. When the CS results of this study are examined, it is seen that replacing fireclay with FA gives better results than replacing it with cement. From this, it can be said that the formation of ettringite is beneficial. In Figure 21f, a decrease in ettringite formation is observed. This difference also has an effect on the strength results of the study.

6

Conclusions

In this investigational study, the influence of different percentages of WFC as a replacement of FA and cement was examined. For that purpose, WFC was replaced with FA and cement. These replacement percentages were 10, 20, 30, 40, and 50%. In the hardened condition, the CS, STS, and FS of the considered investigation instances were observed. In addition, SEM was conducted to compare the implications for strength obtained from the investigative inquiry. Based on this study, the following results can be drawn from this research:

As FA was replaced by the use of WFC, there was an improvement in the CS values up to a certain proportion of the amount of WFC. Using an admixture of WFC at 10, 20, and 30% of FA weight, the improvement in CS was observed as 6, 15, and 3.2%, respectively. On the other hand, after 30% replacement of small aggregates, it was detected that the CS of the concrete admixture reduced by 4.2 and 10% on average compared to the reference example (22 MPa).
As cement was replaced with the use of WFC, there was a decrease in the CS values. It was discovered that the CS of concrete admixture was reduced by 12.2, 25, 34, 46, and 68% compared to the reference value of 22 MPa.
While the FA was replaced by the use of WFC, there was an improvement in the STS values up to a certain proportion of the quantity of the waste WFC. When the aggregate was exchanged with WFC at levels of 10, 20, and 30%, it was discovered that the STSs of the concrete admixture were enhanced by 7.1, 9, and 4.3%, respectively. Conversely, after a 30% replacement of aggregate, it was discovered that the STSs of concrete admixture reduced by 6.5 and 12%.
As cement was replaced with the use of WFC, there was a decrease in the STS values. It was revealed that the STSs of concrete admixture were reduced by 8.2, 22, 33, 48, and 63% (2.1 MPa).
Aggregates for 10, 20, 30, 40, and 50% were swapped with WFC. It was observed that the FSs of the concrete admixture were enhanced by 11.5, 25.6, 18, 12.8, and 7.7%. On the other hand, for cement, the finite sizes (FSs) of concrete admixture were observed to be at very low levels.
The equations derived from empirical data for the CS, STS, and FS, which were established based on the experimental findings and the results of literature, are highly accurate, and the predicted values can be easily calculated for the concrete with WFC.
The proposed ARX model can also be used for more precise prediction of the engineering properties (CS, STS, and FS), taking multiple inputs into account.
This investigation is recommended to estimate whether a certain percentage of WFC, including FA and cement, might enhance the performance of the recycled concrete. With this study, the specified optimum percentage uses are expected to guide future research.
For future research, the use of concrete including WFC in columns and beams may be investigated for structural weight, crack size, bending behavior, rigidity, the fundamental period of structures, and earthquake performance.

Improvement and predictive modeling of the mechanical performance of waste fire clay blended concrete

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