Skip to content
Frontiers
Search

Original Research

Frontiers in Built Environment ·

Volume 12 - 2026 | https://doi.org/10.3389/fbuil.2026.1952751

Mechanical strength prediction of steel fiber-reinforced recycled aggregate concrete: model accuracy and key influencing parameters

  • Wafaa Abbas Hasan1
  • Alaa Jaleel Naji2
  • Ali Jaafar Dakhil2
  • Wael Hamd3
  • Firas Barraj3*corresponding author
  • Ali Jahami3
  1. 1Polytechnic College Al-Hawija, Northern Technical University, Kirkuk, Iraq
  2. 2Department of Roads and Transport Engineering, College of Engineering, University of Al-Qadisiyah, Al-Diwaniyah, Iraq
  3. 3Faculty of Engineering, University of Balamand, El-Koura, Lebanon
Article metrics0 viewsView details
PDFCiteMetrics

Abstract

Recycled coarse aggregate (RCA) can reduce natural-resource consumption and construction-waste disposal. However, adhered mortar, high porosity, and weak interfacial transition zones may impair the mechanical performance of recycled aggregate concrete. Steel fibers can partially offset these deficiencies by improving crack control and post-cracking resistance. This study evaluates the applicability of existing empirical equations for predicting the mechanical properties of steel fiber-reinforced recycled aggregate concrete (SFRAC). An experimental database was compiled from published studies covering the compressive, splitting tensile, and flexural strengths of SFRAC. The predictive performance of the selected equations was evaluated using the mean experimental-to-predicted (Exp./Pred.) strength ratio, standard deviation, coefficient of variation, mean absolute percentage error, root mean square error, parity plots, and prediction-error-band distributions. The effects of the RCA replacement level and fiber reinforcement index (RI) on prediction accuracy were also examined. The compressive-strength equations exhibited the highest overall predictive accuracy. The model proposed by Ezeldin et al. produced the lowest prediction error, whereas the model of Ou et al. exhibited the lowest scatter. For splitting tensile strength, the Thomas and Ramaswamy equation provided the most balanced predictions. The Swamy and Mangat equation demonstrated the best performance for flexural strength. Prediction accuracy generally declined for tensile-dominated properties and was strongly influenced by full RCA replacement and RI. The results indicate that equations developed for conventional steel fiber-reinforced concrete do not consistently account for the effects of RCA on strength development and fiber contribution. Accordingly, RCA-sensitive modifications incorporating aggregate replacement level and fiber reinforcement characteristics are required before these equations can be reliably applied to SFRAC mixtures.

Keywords

1 Introduction

Concrete is the most common building material in the world due to its versatility and durability, and low production costs. With the rising urbanization and infrastructure development, a huge demand of concrete has been observed, which has resulted in the increasing demand for natural aggregates (NAs) which they are used in 60%–75% volume of concrete. In parallel, the construction and demolition waste (CDW), which is an unavoidable by-product of the construction sector, is generated and disposal into landfills has led to severe environmental issues related to landfill waste management and natural resource depletion (Behera et al., 2014). Worldwide statistics on CDW are scarce, but it can be said that the total amount of CDW produced in Europe, USA and Japan is about 900 million tons per year (Soares et al., 2014). As such, recycling and reusing CDW (Circular Economy and Resource Conservation) for the production of concrete have become a focus of attention to reduce environmental impacts (Behnood et al., 2015; Alqarni et al., 2021).

One of the most promising recycling alternatives to use in the structural concrete is the recycled concrete aggregate (RCA) produced from the crushed CDW. The general composition of RCA is original natural aggregate with the cement mortar adhered around the aggregate, the volume of which is about 30%–35% of the aggregate. The resulted porosity and density of this adhered mortar are higher than natural aggregate which cause greater water absorption, reduced stiffness and inferior mechanical property of mortar. A number of studies have reported that performance of mechanical and durability of concrete will be affected negatively by increasing the content of RCA resulting in decreasing the compressive and tensile strength, elastic modulus, and durability against environmental hazards (Wang et al., 2021; Shi et al., 2016; Kou et al., 2011; Al-Rekabi et al., 2023; Al-Rekabi and Abo Daheer, 2024; Al-Jasimee and Abo Dhaheer, 2019; Tüfekçi and Çakır, 2017; Bai and Sun, 2010; Sayhood et al., 2019; Corinaldesi, 2011; Malešev et al., 2010; Zhou et al., 2010). More specifically, the substitution of natural aggregate for RCA has been found to have an impact on the compressive strength (24%–25% reduction) and tensile strength (15%–30% reduction) as well as elastic modulus of concrete, with maximum 25% reduction compared with conventional concrete (Tüfekçi and Çakır, 2017; Bai and Sun, 2010; Sayhood et al., 2019; Corinaldesi, 2011; Malešev et al., 2010; Zhou et al., 2010). The amount of reduction, however, is dependent on various factors like quality of concrete from which it comes, quantity of adhering mortar, type of method used in the process of aggregate and replacement ratio (Al-Rekabi et al., 2023; Al-Jasimee and Abo Dhaheer, 2019).

There are various suggestions that can improve the quality and performance of RCA and address these issues. The general approach of these methods is either to wash the adhered mortar off the surface of the recycled aggregate or to improve the properties of the existing mortar by a physical, chemical or mineral process treatment. These methods may be used to lower porosity and water absorption, but add more manufacturing processes which are somewhat expensive and cumbersome. Therefore, continuous studies have been directed towards either alternative methods that could improve the structural performances of recycled aggregate concrete (RAC) and still maintain their positive environmental impacts.

Incorporating fibers into RAC is one such alternative that has been widely proposed. The use of fibers as a reinforcing component in cement-based materials, giving rise to fiber-reinforced concrete (FRC), has been explored for over a century as an effective means of enhancing crack resistance and tensile behavior. FRC consists of conventional concrete with the addition of short, discontinuous fibers randomly distributed within the cementitious matrix (Al-Rekabi et al., 2023). The inclusion of fibers improves the control of crack initiation and propagation as well as the post-cracking behavior of concrete. Four main fiber types are used to enhance the structural performance of concrete: steel fiber-reinforced concrete (SFRC), glass fiber-reinforced concrete (GFRC), natural fiber-reinforced concrete (NFRC), and synthetic fiber-reinforced concrete (SNFRC) (Purushothaman et al., 2015; Paluri et al., 2020). The reinforcing efficiency of these fibers is governed by multiple parameters, including geometry, length, aspect ratio, surface characteristics, orientation, and Steel fiber volume fraction (Vf) (Prakash Chandar et al., 2017). Typical fibers have equivalent diameters of about 0.15–2 mm, lengths of 7–75 mm, and aspect ratios of approximately 20–100 (Ramesh et al., 2019). While increasing Vf can adversely affect workability due to fiber interaction and agglomeration, this effect can be effectively mitigated using high-range water-reducing admixtures that promote uniform fiber dispersion within the matrix (Al-Rekabi et al., 2023).

Among the commercially available fiber types, steel fibers are generally regarded as more advantageous than other fibers for concrete applications, owing to their reinforcing efficiency, cost-effectiveness, environmental resistance, and ease of manufacture (Sahoo et al., 2015; Senaratne et al., 2016). Steel fibers are produced in various geometries, including straight, hooked-end, crimped, stranded, and twisted forms, each influencing bond behavior and mechanical performance differently, as shown in Figure 1 (Xie and Ozbakkaloglu, 2015).

Types of steel fibers (Xie and Ozbakkaloglu, 2015).
Figure 1. Types of steel fibers (Xie and Ozbakkaloglu, 2015).

Steel fibers were initially introduced into concrete primarily to control plastic and drying shrinkage cracking. However, extensive research has since demonstrated that their benefits extend well beyond crack control. By bridging microcracks, delaying crack initiation, and restricting crack propagation, steel fibers substantially enhance the mechanical performance of concrete, improving compressive strength, splitting tensile strength, flexural strength, stiffness, ductility, fatigue resistance, impact resistance, and energy absorption (Sahoo et al., 2015; Yue et al., 2020; Bai et al., 2020; Kou et al., 2012). These benefits are even more pronounced in RAC, as the inherently weaker imperfect bonding area (IBA) of the adhered mortar is partially mitigated through fiber inclusion. A typical Vf in RAC ranges from 1% to 3% of the total concrete volume, depending on the target mechanical properties.

The compressive strength of steel fiber-reinforced RAC (SFRAC) depends mainly on the strength of the matrix, the stiffness of the aggregates, and the composite density, with steel fibers contributing primarily by slowing crack propagation, enhancing confinement, and improving post-peak ductility (Ezeldin and Balaguru, 1992; Ou et al., 2012; Nataraja et al., 1999; Padmarajaiah, 1999; Gao et al., 1997; Thomas and Ramaswamy, 2007; Song and Hwang, 2004; Ghosh and Kumar, 1997; Swamy and Mangat, 1974; Yazıcı et al., 2007). As a result, the improvement in compressive strength is generally moderate and depends chiefly on Vf, aspect ratio, and fiber–matrix interaction (Yazıcı et al., 2007; Katzer and Domski, 2012; Nili and Afroughsabet, 2010; Someh and Saeki, 1994; Mansur et al., 1999). Splitting tensile strength is more sensitive than compressive strength to Vf, geometry, orientation, and fiber–matrix bond characteristics (Thomas, 2009; Iqbal et al., 2019; Camps et al., 2008; Li et al., 2017; Park et al., 2012; Oliveira et al., 2016; S¨oylev and ¨Ozturan, 2014). Flexural strength is the most sensitive mechanical property to fiber addition, as flexural failure is governed by crack initiation, crack propagation, and load transfer across cracked sections after cracking. Steel fibers enhance flexural performance by bridging cracks, increasing tensile stress transfer across cracked regions, and improving toughness, ductility, and residual load-bearing capacity, with the degree of improvement again governed by fiber fraction, aspect ratio, geometry, orientation, and bond properties (Park et al., 2012; Oliveira et al., 2016; S¨oylev and ¨Ozturan, 2014; Lia et al., 2014; Barnett et al., 2010; Atis¸ et al., 2009; Nanakorn and Horii, 1996; Uyguno˘glu, 2008; Topcu and Canbaz, 2007; Carneiro et al., 2014). Beyond these mechanical benefits, the economic feasibility of incorporating steel fibers into RAC has also been demonstrated: Senaratne et al. (2016) showed that the additional cost associated with including 0.6% steel fibers can be effectively offset by replacing approximately 30% of natural aggregates with recycled aggregates.

To predict the mechanical properties of steel fiber-reinforced concrete, several empirical models have been proposed in the literature. For compressive strength, widely used regression-based formulations include those of Ezeldin and Balaguru (1992), Ou et al. (2012), Nataraja et al. (1999), Padmarajaiah (1999), which relate compressive strength to a fiber reinforcement index (RI) based on experimental databases. Although these models have proven sufficiently accurate for conventional steel fiber-reinforced concrete, they have not been extensively validated for RAC, as they were primarily calibrated using natural aggregate concrete (NAC) data. Similarly, several empirical equations have been developed to predict splitting tensile strength, including those of Gao et al. (1997), Thomas and Ramaswamy (2007), Song and Hwang (2004), Ghosh and Kumar (1997), Yazıcı et al. (2007), and Padmarajaiah (1999), which generally express tensile strength as a function of matrix strength and RI. However, because these models were developed predominantly for conventional steel fiber-reinforced concrete, their reliability for SFRAC remains uncertain, given that recycled aggregates substantially alter crack propagation behavior and fiber–matrix interaction. Prediction equations for flexural strength, such as those proposed by Gao et al. (1997), Swamy and Mangat (1974), Yazıcı et al. (2007), and Padmarajaiah (1999), are similarly based on regression analyses or mechanics-based formulations correlating matrix strength with reinforcement parameters. While these equations have been validated for conventional steel fiber-reinforced concrete, their applicability to RAC has not yet been systematically examined, given that recycled aggregates influence both crack development and fiber effectiveness.

Overall, most existing prediction models have been developed and calibrated using NAC, and their applicability to steel fiber-reinforced recycled aggregate concrete (SFRAC) has yet to be fully established. To address this gap, the present study critically evaluates the predictive capability of existing empirical models for the compressive, flexural, and splitting tensile properties of SFRAC, based on a comprehensive database compiled from the literature. Each model is assessed using statistical performance indicators and parity-plot analysis to identify the most reliable prediction approach and to evaluate the influence of the RCA replacement ratio and RI on model accuracy.

2 Methodology

A structured literature search was conducted to identify experimental studies reporting the mechanical properties of steel fiber-reinforced recycled aggregate concrete (SFRAC). The search was performed using Scopus and Web of Science Core Collection, covering publications available from 2009 to 2021 (Afroughsabet et al., 2017; Ahmadi et al., 2017; Bhan and Kaur, 2018; Bhikshma and Manipal, 2011; Chaboki et al., 2019; Gao and Zhang, 2018; He et al., 2020; Heeralal et al., 2009; Kaplan et al., 2021; Sryh and Forth, 2015; Su, 2020; Xia et al., 2021). Combinations of the keywords “recycled aggregate concrete,” “recycled coarse aggregate,” “steel fiber reinforced concrete,” “steel fibre reinforced recycled aggregate concrete,” “compressive strength,” “splitting tensile strength,” and “flexural strength” were used with Boolean operators. Reference lists of the retrieved articles were also examined to identify additional relevant experimental studies that were not captured directly by the database searches.

Studies were included when they: (1) experimentally investigated concrete incorporating recycled coarse aggregate and steel fibers; (2) explicitly reported the RCA replacement ratio and steel-fiber content; (3) provided the fiber geometry or aspect ratio required to determine the reinforcement index (RI); (4) reported at least one of the investigated mechanical properties, namely, compressive, splitting tensile, or flexural strength; and (5) provided the material and reference-strength information required for application of the selected empirical equations. Studies were excluded when they were review articles, purely numerical or analytical investigations, did not contain steel fibers, did not clearly report the RCA replacement level, lacked the input parameters required by the prediction equations, or contained insufficient specimen-level data for reliable extraction. Where the same experimental dataset appeared in more than one publication, duplicate data were retained only once.

Following screening according to these criteria, the final database comprised 106 property-specific experimental records obtained from 16 published studies, including 39 compressive-strength, 36 splitting-tensile-strength, and 31 flexural-strength observations (Table 1). For each eligible mixture, the RCA replacement ratio, steel-fiber volume fraction (V *f*), fiber aspect ratio, reinforcement index (RI), corresponding reference-concrete strength required by the applicable prediction equation, and experimentally measured mechanical strength were extracted. The complete specimen-level datasets and corresponding model predictions are provided in Supplementary Tables A–C to enable verification of the calculations and statistical analyses.

TABLE 1. Summary statistics of the compiled experimental database.

Database characteristicf’cftfrOverall database
No. experimental records393631106
No. contributing studies16141116 unique studies
RCA (%)25–10025–10025–10025–100
(Vf) (%)0.30–2.000.30–2.000.50–2.000.30–2.00
Exp. strength range (MPa)17.60–74.821.93–7.633.60–12.89—
No. prediction models evaluated45413 model–property combinations

The research overall framework is depicted in Figure 2. It is summarized by the workflow that includes literature review, construction of the databases, choice of empirical prediction models, statistical analysis, graphic evaluation, parametric analysis, comparison of models and ranking.

Overall research methodology adopted for evaluating the prediction accuracy of empirical models for the mechanical properties of SFRAC.
Figure 2. Overall research methodology adopted for evaluating the prediction accuracy of empirical models for the mechanical properties of SFRAC.

Prediction models selected in present study are the most used empirical equations from the literature to predict the mechanical properties of steel fiber-reinforced concrete. To determine compressive strength, a total of 4 models were taken into consideration (Ezeldin and Balaguru, 1992; Ou et al., 2012; Nataraja et al., 1999; Padmarajaiah, 1999), to determine splitting tensile strength a total of 5 models (Padmarajaiah, 1999; Gao et al., 1997; Thomas and Ramaswamy, 2007; Song and Hwang, 2004; Ghosh and Kumar, 1997) were considered and for flexural strength 4 models (Padmarajaiah, 1999; Gao et al., 1997; Swamy and Mangat, 1974; Yazıcı et al., 2007) were considered. The set of reported data for each specimen (material parameters and reinforcement parameters) of the compiled database were used in each equation, respectively. The strengths from the experimental values were then compared to the predicted ones for quantification of prediction accuracy. All the investigated empirical equations are summarized in Table 2 along with their given mathematical expression, the required input parameters and the reference. These equations formed the basis for all subsequent statistical, graphical, and parametric analyses.

TABLE 2. Standardized codes and suggested equations for predicting the compressive, splitting tensile, and flexural strength.

Compressive strength
ReferencesEquations
Ezeldin and Balaguru (1992)f c f = f c u ′ + 3.51RI
Ou et al. (2012)f S F R C = f c u ′ + 2.35RI
Nataraja et al. (1999)f S F R C = f c u ′ + 2.1604RI
Padmarajaiah (1999)f c f = f c u ′ + 2.274RI
Splitting tensile strength
Gao et al. (1997)f s t = 0.94 f t 1 − v f + 3.02 v f l f / d f
Swamy and Mangat (1974)f s p c F = 0.63 f c u ′ 0.5 + 0.288 f c u ′ 0.5 R I + 0.052 R I
Song and Hwang (2004)f t f = 0.63 f c u ′ + 3.01 v f − 0.02 v f 2
Ghosh and Kumar (1997)f s t = 2.2121 + 0.0077 l / d + 1.4233 v f
Padmarajaiah (1999)f c f = f c u ′ 0.5 / 3 + 1.918RI
Flexural strength
Gao et al. (1997)f r = 0.92 f w 1 − v f + 4.19 v f l f / d f
Swamy and Mangat (1974)f r = 0.97 f r 1 − v f + 3.14 v f l / d
Yazıcı et al. (2007)f r = 0.8261 + 0.0638 l / d + 3.0000 v f
Padmarajaiah (1999)f r = f r + 4.419 R I

Where f s t : Splitting tensile strength, f r : F l e x u r a l s t r e n g t h , v f: Volume fraction, l f / d f : aspect ratio, f w : flexural strength of high-strength, f c u ′: Cubic compressive strength, f t f: Splitting tensile strength.

The predictive capability of each empirical equation was evaluated using a range of complementary statistical metricsBias was quantified by the (Exp./Pred.) strength ratio while prediction consistency was evaluated by the population standard deviation (SD) and the coefficient of variation (COV). The mean absolute percentage error (MAPE) and root mean square error (RMSE) were determined to represent the magnitude of the prediction errors. Together these indicators are sufficient to form a solid evaluation of the precision and accuracy of every prediction-model. Below are the details for each statistical metric: Where E i: experimental strength for observation i (MPa), P i: predicted strength for observation i (MPa), R i: experimental-to-predicted strength ratio for observation i, R ¯: mean experimental-to-predicted strength ratio, and n: number of valid experimental–prediction pairs for the model considered.

Exp . / Pred . = E i P i (1)

R ¯ = 1 n ∑ i = 1 n E i P i (2)

SD = 1 n ∑ i = 1 n R i − R ¯ 2 (3)

COV = S D R ¯ × 100 % (4)

MAPE = 100 n ∑ i = 1 n E i − P i E i (5)

RMSE = 1 n ∑ i = 1 n E i − P i 2 (6)

Parity plots displaying the differences between the proposed strengths and the experimental ones were made for all the studied models for completion of the statistical evaluation. To visually assess prediction bias and data spread, an agreement line 1:1% and ±10%, ±20%, and ±30% error bands were used. Thereafter, the percentages of the predictions inside each of the error bands were compared and used in determining the practical reliability of the equations investigated.

A parametric analysis was performed to assess the effects of recycled aggregate replacement ratio and RI on the accuracy and reliability of the prediction models. The experimental database was classified according to RCA replacement and RI levels, and the ratio between predicted and measured strength values was analyzed using the average response of each subgroup for each empirical equation. This approach enables a more comprehensive evaluation of the applicability of existing prediction models for various material combinations and highlights the specific conditions that may lead to increased prediction bias.

The statistical indicators were all applied together with the graphical assessment for comparing the various prediction models, and the most appropriate equation was selected for each mechanical property. Both prediction accuracy and prediction consistency were taken into account in the ranking of the consequence to offer practical recommendations for the prediction of mechanical properties of SFRAC.

3 Results and discussion

3.1 Statistical assessment of prediction accuracy

The models chosen were tested in terms of their predictive performance using average Exp./Pred. strength ratio, standard deviation, coefficient of variation, mean absolute percentage error and root mean square error (Table 3). Using average Exp./Pred. ratios, model bias was assessed, with the ratios close to 1.0 indicating unbiased prediction, ratios >1.0 indicating underestimation (conservative), and ratios <1.0 indicating overestimation (non-conservative). COV, MAPE and RMSE were instead developed to measure the dispersion and magnitude of the prediction errors.

TABLE 3. Statistical performance evaluation of the investigated empirical models for predicting the compressive, splitting tensile, and flexural strengths of steel-fiber-reinforced recycled aggregate concrete.

PropertyModelAvgSDCOVMAPERMSE
f’cEzeldin and Balaguru (1992)1.050.098.747.344.14
Ou et al. (2012)0.960.033.098.434.57
Padmarajaiah (1999)1.080.098.768.524.60
Nataraja et al. (1999)1.080.098.778.654.65
frYazıcı et al. (2007)1.230.4435.9725.702.19
Gao et al. (1997)0.850.1619.1924.601.65
Swamy and Mangat (1974)0.890.1517.1118.571.31
Padmarajaiah (1999)0.790.1519.1832.852.00
ftSong and Hwang (2004)1.220.3024.8920.441.49
Thomas and Ramaswamy (2007)0.870.2023.2327.811.34
Gao et al. (1997)0.980.2828.1828.461.44
Ghosh and Kumar (1997)0.840.2023.8531.631.65
Padmarajaiah (1999)1.390.3726.7431.011.81

For compressive strength, the investigated models produced relatively close MAPE values, ranging from 7.34% to 8.65%, indicating generally satisfactory prediction accuracy. The Ezeldin and Balaguru (1992) equation achieved the lowest MAPE and RMSE, at 7.34% and 4.14 MPa, respectively, and therefore provided the smallest overall prediction-error magnitude. By contrast, the Ou et al. (2012) equation exhibited the lowest SD and COV, at 0.03% and 3.09%, respectively, indicating the most consistent distribution of the Exp./Pred. ratios, although its mean ratio of 0.96 revealed a slight average overestimation of approximately 4%. This apparent difference does not represent a contradiction among the indicators: MAPE measures the average relative error, RMSE gives greater weight to large absolute deviations, and COV measures the relative scatter of the prediction ratios. Thus, the Ezeldin and Balaguru (1992) model was superior in terms of overall error magnitude, whereas the Ou et al. (2012) model produced more uniform predictions. The Padmarajaiah (1999) and Nataraja et al. (1999) equations showed nearly identical performance, with mean Exp./Pred. ratios of 1.08 and COV values of approximately 8.8%, indicating moderate and slightly conservative prediction scatter.

It can be explained that the compressive strength models has performed relatively well since compression is mostly determined by the strength of the matrix, stiffness of aggregates and the overall density of the composite. Steel fibers can slow the rate of crack propagation, but in general their impact on compressive behavior is not as significant as their effect on tensile and flexural behavior. Thus, it is reasonable to assume the use of RI based empirical expressions to give reasonable estimates provided that the base compressive strength is properly represented.

A significant prediction error occurred for splitting tensile strength. The MAPE values ranged from 20.44% to 31.63%-about 2.8 to 4.3 times higher than the best compressive-strength MAPE. This verifies that existing empirical equations can not predict tensile strength as easily. The Song and Hwang model (Song and Hwang, 2004) gave the lowest MAPE of 20.44% which is 26.5% lower than Thomas and Ramaswamy model (Thomas and Ramaswamy, 2007) while 28.2% less than Gao model (Gao et al., 1997) and 35.4% lesser than Ghosh model (Ghosh and Kumar, 1997) and 34.1% less than Padmarajaiah model (Gao et al., 1997). However, its average Exp./Pred. ratio was 1.22 meaning that it was underestimated by ∼22% – conservative. However, even though it had a relatively small absolute percentage error, it was not the most well-balanced model.

The model of Thomas and Ramaswamy (Thomas and Ramaswamy, 2007) gave the lowest RMSE value of 1.34 MPa, moderate COV value of 23.23% and the average Exp./Pred. ratio of 0.87, which was indicative of the average overestimation of around 13%. The model which had the average Exp./Pred. ratio nearest to the value 1, was the Gao et al. (1997) model with Exp./Pred. ratio 0.98 and only 2% global bias. Despite this apparent advantage, the model was locally scattered, with relative high COV of 28.18% and MAPE of 28.46% which indicated that the model was unbiased globally. The Padmarajaiah (Gao et al., 1997) model was found to be the least reliable model for splitting tensile strength with the highest RMSE of 1.81 MPa and the largest bias as indicated by highest Exp./Pred. ratio of 1.39.

For flexural strength, the Swamy and Mangat (Swamy and Mangat, 1974) model achieved the best overall performance, with the lowest COV, MAPE, and RMSE values of 17.11%, 18.57%, and 1.31 MPa, respectively. Its improved performance may be attributed to its mechanics-based formulation, which represents flexural resistance through the combined contributions of the concrete matrix and fibers, including fiber–matrix bond, fiber aspect ratio, and crack-control mechanisms. The original theory is based on a dual criterion involving crack control and composite mechanics, with flexural fracture represented through bond slip, progressive fiber debonding, and stress transfer across the developing crack. This physical basis appears to provide greater transferability to SFRAC than equations relying predominantly on regression coefficients, although the weaker and more heterogeneous RCA matrix still introduces prediction uncertainty. The Gao et al. (1997) model ranked second, with MAPE and RMSE values of 24.60% and 1.65 MPa, respectively, while the Yazıcı et al. (2007) and Padmarajaiah (1999) equations exhibited greater bias or scatter.

The Gao et al. (1997) model performed second best with flexural strength, where the values of MAPE and RMSE were 24.60% and 1.65 MPa, respectively. On average, its Exp./Pred. ratio is 0.85, resulting in an average OVE of 15%. The Yazıcı et al. (2007) equation had the highest COV value, which is 35.97% more than double value of the COV obtained in the Swamy and Mangat (1974) equation, showing poor stability in prediction. Its mean Exp./Pred. ratio is 1.23 indicating conservative behavior, but the scatter is large and hence it is not very attractive for design-oriented prediction use. The highest average Exp./Pred. ratio being 0.79 and MAPE of 32.85% was obtained for the Padmarajaiah (1999) model which showed approximately 21% overestimation of flexural strength.

The larger errors obtained for splitting tensile and flexural strength arise from the greater sensitivity of tensile-dominated responses to local fracture mechanisms. Unlike compressive strength, which is governed mainly by the average matrix strength, aggregate stiffness, and composite density, tensile failure depends on the location of crack initiation, the number and orientation of fibers intersecting the critical crack, fiber–matrix bond strength, progressive debonding, and fiber pull-out resistance. These mechanisms exhibit substantial specimen-to-specimen variability even at an identical RI. In SFRAC, the uncertainty is further amplified by the heterogeneous distribution of adhered mortar, variable RCA quality, increased porosity, and the coexistence of old and new interfacial transition zones. Consequently, simplified equations based mainly on matrix strength and RI cannot fully represent the local interactions controlling crack development and post-cracking stress transfer, explaining the substantially higher prediction errors for splitting tensile and flexural strengths.

3.2 Parity-plot assessment and error-band evaluation

The output strengths are plotted on parity plots in Figures 3–5 to compare with the predicted strengths. The lines of perfect agreement (1:1) and the error bands of ±10%, ±20% and ±30% illustrate the dispersion of the prediction. These are especially valuable figures as they not only display the mean bias that the model commits on average, but also the distribution of model predictions.

Comparison of the experimental and predicted compressive strengths using the equations proposed by **(a)** Ezeldin and Balaguru (1992), **(b)** Ou et al. (2012), **(c)** Padmarajaiah (1999), and **(d)** Nataraja et al. (1999).
Figure 3. Comparison of the experimental and predicted compressive strengths using the equations proposed by (a) Ezeldin and Balaguru (1992), (b) Ou et al. (2012), (c) Padmarajaiah (1999), and (d) Nataraja et al. (1999).
Comparison of the experimental and predicted splitting tensile strengths using the equations proposed by **(a)** Song and Hwang (2004), **(b)** Thomas and Ramaswamy (2007), **(c)** Gao et al. (1997), **(d)** Ghosh and Kumar (1997), and **(e)** Padmarajaiah (1999).
Figure 4. Comparison of the experimental and predicted splitting tensile strengths using the equations proposed by (a) Song and Hwang (2004), (b) Thomas and Ramaswamy (2007), (c) Gao et al. (1997), (d) Ghosh and Kumar (1997), and (e) Padmarajaiah (1999).
Comparison of the experimental and predicted flexural strengths using the equations proposed by **(a)** Yazıcı et al. (2007), **(b)** Gao et al. (1997), **(c)** Swamy and Mangat (1974), and **(d)** Padmarajaiah (1999).
Figure 5. Comparison of the experimental and predicted flexural strengths using the equations proposed by (a) Yazıcı et al. (2007), (b) Gao et al. (1997), (c) Swamy and Mangat (1974), and (d) Padmarajaiah (1999).

As far as compressive strength is concerned, the good prediction power of the evaluated equations contrasted to the tensile and flexural ones can be verified for the case using Figure 3. The distribution point around the 1:1 line was the smallest for the Ou model (Ou et al., 2012). It failed to provide a prediction within the ±10% error band in only 4.7% of the cases and not a single prediction was out of the ±20% error band. This means that 95.4% of the Ou predictions were within ±10%, and 100% were within ±20%. The very low COV of 3.09%, is an excellent concentration of points. Most however, were slightly above the 1:1 level which also indicated that the Ou prediction was mildly overestimated, as exhibited by the average Exp./Pred. Ratio of 0.96.

The Ezeldin and Balaguru (1992) equation also demonstrated good agreement with the experimental data, with only 34.9% of the predictions falling outside the ±10% error band and 7.0% outside the ±20% error band, indicating that 93.0% of the predictions were within ±20% of the experimental values. Although its predictions were slightly more dispersed than those of the Ou et al. (2012) model, the Ezeldin and Balaguru (1992) equation retained excellent overall agreement with the experimental database. In comparison, the Padmarajaiah (1999) and Nataraja et al. (1999) models exhibited larger prediction scatter, with 37.2% and 41.9% of the predictions falling outside the ±10% error band, respectively, and 9.3% of the predictions outside the ±20% error band. Consequently, approximately 90.7% of their predictions remained within the ±20% error band, indicating acceptable but comparatively lower prediction reliability than the Ezeldin and Balaguru (1992) and Ou et al. (2012) models.

A much greater scatter can be seen for splitting tensile strength in Figure 4. The Song and Hwang (Song and Hwang, 2004) model had 70% of predictions outside the ±10% band, 52.5% outside ±20%, and 32.5% outside ±30%. Even with its lowest MAPE of all the tensile models, it was still able to achieve only a 47.5% accuracy within a 20% error band. The Thomas and Ramaswamy (Thomas and Ramaswamy, 2007) model was better in terms of the larger error bands, 42.5% and 20% of points falling outside an error of ±20% and ±30% respectively. As a result, 57.5% of its predictions were within ±20% and 80% within ±30%, which is the reason why it rated to be the best among the four models even though it was not the lowest MAPE.

As in other models, the Gao et al. (1997) model had 77.5% outside ±10% with average Exp./Pred. ratio near unity which was not enough to guarantee local accuracy. The Ghosh and Kumar (1997) model had 82.5% of the prediction points outside ±10% but outside ±20% and ±30% the ratio was only 45% and 20% respectively. This means that its errors were many though not necessarily big. The tensile prediction distribution was worst with 90% of the points outside the limits of ±10%, 77.5% of the points outside the limits of ±20% and 60% outside the limits of ±30% for the Gao et al. (1997) model. As such, it was able to correctly predict only 22.5% of its guesses within a 20% range of the tensile strength database.

Figure 5 indicates that the Swamy and Mangat (Swamy and Mangat, 1974) equation provided the best distribution of the flexural-strength predictions. Although 64.5% of the predictions fell outside the ±10% error band, only 22.6% and 9.7% exceeded the ±20% and ±30% error bands, respectively. Accordingly, 77.4% of the predictions were contained within ±20% and 90.3% within ±30% of the experimental values. This error-band distribution confirms the comparatively strong flexural prediction performance identified in Table 3. The Gao et al. (1997) model also performed reasonably well, with 67.7%, 38.7%, and 16.1% of the predictions falling outside the ±10%, ±20%, and ±30% error bands, respectively, indicating that 61.3% of its predictions remained within the ±20% error band.

The second-best performance was obtained with the Yazici model with 71% of predictions being outside of the ±10%, 61.3% of predictions outside of ±20% and 51.6% of predictions outside of ±30%. Thus, almost half of its worthy was above the band ±30%, acknowledging its high COV: 36%. The Padmarajaiah (Padmarajaiah, 1999) model produced the lowest accuracy near the 1:1 line with 83.8% of the forecasts lying outside the ±10% limits, 58.1% outside the ±20% limits and 32.3% outside the ±30% limits. This verifies that it had a large MAPE (32.9%) that was linked to a good amount of dispersion and also systematic bias.

3.3 Effect of RCA replacement level on prediction accuracy

The effect of RCA replacement level on the Exp./Pred. Mean values of compressive strength and splitting tensile strength is presented in Figure 6. The system was segmented to RCA replacement <50% and total RCA replacement. This comparison helps since many empirical equations were not calibrated using many full-RCAs and may need to be adjusted when using only fully all-natural aggregate.

Mean Exp./Pred. With different RCA replacement levels for: **(a)** compressive strength **(b)** Splitting tensile strength.
Figure 6. Mean Exp./Pred. With different RCA replacement levels for: (a) compressive strength (b) Splitting tensile strength.

In terms of compressive strength, the influence of the RCA replacement level was relatively small, but significant. Exp./Pred. Ratio of the mean value for the Ezeldin and Balaguru (1992) model rose from 1.02 for the case RCA replacement< 50% to 1.07 for the case RCA replacement = 100%, which is 4.8% increase of conservatism. To investigate the overestimation with full RCA, the ratio for Ou et al. (2012) model decreased slightly from 0.97 to 0.95, whereas the ratio for the other models remained almost unchanged. Padmarajaiah (1999) had raised this ratio from 1.04 to 1.09 (5.4% rise). The same went for the Nataraja model whose selection grew by 5.5 per cent, from 1.04 to 1.09.

It is found from these results that most of the compressive-strength models turned more conservative as the percentage of RCA replacement was raised to 100 per cent except the Ou model which was slightly non-conservative. This indicates that the effect of full RCA replacement on the strength may not be completely reproduced by the experimental input strength to the equations and the corrections for the RI may be insufficient. The marked change in the levels of conservatism for Ezeldin and Balaguru (1992), Padmarajaiah (1999) and Nataraja et al. (1999) can also suggest that these equations do not capture the positive influence of steel fibers in full-RCA mixtures to the same level they provide for the binder mixture.

The effect of RCA replacement was far more significant when splitting tensile strength was considered. The rate of the Song and Hwang (2004) dropped by 22.1% from 1.44 to 1.12 as the RCA replacement value increased from 50% to 100%. The model of Thomas and Ramaswamy (2007) reduced from 1.01 to 0.81, which is close to the line of unbiased prediction to overestimation by 18.7%. The Gao et al. (1997) model went down from 1.22 to 0.88, which is a 27.8% drop, and moving toward non-conservative overestimation from conservative underestimation. Overestimation of Ghosh model was 7.1% when the model value was 0.93, but has increased to 20.2% with a model value of 0.8. At full RCA, even the Padmarajaiah (1999) model was still conservative, albeit at a reduced rate of 1.29.

This shows that complete RCA replacement is a significant factor in altering the prediction bias of models of tensile strength. There seems to be a trend towards overestimation for Thomas and Ramaswamy (2007), Gao et al. (1997) and Ghosh and Kumar (1997) at RCA replacement = 100% which suggests that for these models, the steel could be overestimated when the matrix made of the recycled aggregate becomes weaker. Physically this makes sense, as the interfacial transition zone (ITZ) and the bond between the aggregate and the mortar are major factors in influencing tensile failure. Old mortar still attached to the concrete contributes to porosity and a poor bond between the aggregate and the matrix of RCA, which may compromise the effectiveness of fiber bridging and aggregate to matrix stress transfer. Hence, equations based on normal (NWC) or containing a small amount of RCA might not be conservative for use in full-RCA mixtures.

3.4 Effect of reinforcement index (RI) on prediction accuracy

In Figure 7, the impacts of RI on model bias are considered. RI represents the combined effects of Vf and aspect ratio and it is mostly used for characterizing the steel fiber reinforcing efficiency. The database was divided into RI < 0.4, RI = 0.4–0.8, and RI = 0.8–1.2. The results were then subdivided in terms of compressive and splitting tensile strength into RCA replacement <50% and RCA replacement = 100% and flexural strength into RCA replacement = 100%.

Mean Exp./Pred. With different RI for: **(a)** compressive strength with RCA<50% **(b)** compressive strength with RCA = 100% **(c)** splitting tensile strength with RCA<50% **(d)** splitting tensile strength with RCA = 100% **(e)** flexural strength with RCA = 100%.
Figure 7. Mean Exp./Pred. With different RI for: (a) compressive strength with RCA<50% (b) compressive strength with RCA = 100% (c) splitting tensile strength with RCA<50% (d) splitting tensile strength with RCA = 100% (e) flexural strength with RCA = 100%.

In the case of compressive strength with RCA replacement< 50%, the mean Exp./Pred. Ratios were close to unity (Exp. = Pred.) throughout the RI ranges, showing that there was a limited influence of RI on the compressive prediction bias. These two models – Ezeldin and Balaguru (1992) and Ou et al. (2012) – were almost unbiased and somewhat underestimated and overestimated respectively. The Padmarajaiah (1999) and the model by Nataraja et al. (1999) exhibited slightly conservative response to higher RI values. Similar changed trends were seen for RCA replacement = 100%, although the models were a bit more conservative in this case, specifically at higher RI. This suggests that fibers do not play a major part in compression, after that of the quality of the matrix and the properties of the aggregates.

The effects of RI were higher for splitting tensile strength with RCA replacement< 50%. The Song and Hwang (2004) model increased from 1.05 at RI < 0.4 to 1.29 at RI = 0.4–0.8 and 1.87 at RI = 0.8–1.2. This indicated that the model was growing more conservative with higher RI, with the average breaking down by 4.7%–87.3%. The Padmarajaiah (1999) exhibited the similar trend from 1.49 to 1.56 and then to 1.80. Both models underestimate the gains in tensile strength with increase in fiber reinforcement, in mixes that contains less than 50% RCA.

The Thomas and Ramaswamy (2007) model grew from 0.86 to 0.94, and then to 1.2 as RI was elevated, ranging from overestimation in the low RI space to conservative underestimation in the high RI space. The Gao et al. (1997) model also was conservative at all RI levels, with an increase from 1.203 to 1.347 at the highest RI. The Ghosh and Kumar (1997) model changed from 0.73 to 0.8 to 1.23 which is clearly a change from being non-conservatively overestimated to being conservatively under estimated as RI increased. The results indicate that the fiber scaling with RI is not correctly performed using some of the equations, when RCA replacement is less than or equal to 50%.

The trends were different for splitting tensile strength at a RCA replacement of 100%. The model of Song and Hwang (Song and Hwang, 2004) was very close to unity at low RI (Exp./Pred. = 1.07), and rose to 1.18 at RI = 0.4–0.8, and declined slightly to 1.14 at RI = 0.8–1.2. According to the Thomas and Ramaswamy model the value was reduced from 0.88 to 0.86 to 0.72, thus indicating that rise in RI led to overestimation from 12.5% to 27.7%. Similarly, the Gao et al. (1997) model was reduced to 0.98, then to 0.94 and finally to 0.75 at high RI showing increased overestimation. The Ghosh and Kumar (1997) model had always non-conservative values in between 0.77 and 0.83. Using the Padmarajaiah (1999), the model was decreased from 1.48 to 1.35 and then to 1.05, which shows that model is being reduced in its excessive conservatism in higher RI.

The results indicate that the influence of RI on the splitting tensile strength is dependent on the percentage of RCA. For RA<50%, an increase in RI was commonly causing models to become more conservative, suggesting that the contribution of the fiber will be underestimated. Several models behaved in a less conservative or non-conservative manner when the RI increased with RCA replacement = 100%, which indicates that these models overestimated the effective fiber effect in a less strong recycled aggregate matrix. This indicates that, for the same RI value, different strength enhancement was obtained for both the N.A.C and R.A.C.

The RI effect had been most evident for flexural strength with RCA REPLACEMENT = 100%. The Yazıcı et al. (2007) model decreased from 1.39 at RI < 0.4 to 1.15 at RI = 0.4–0.8 and 1.16 at RI = 0.8–1.2. As such it was conservative, but it was less conservative, about 15%–16%, than it was at 39.0%. The model of Gao was decreased from 0.95 to 0.87 and 0.72 which showed the overestimation rising by 5.4%–28.1% while increasing RI. Similarly Swamy and Mangat (1974) model reduced to 0.94, 0.92 and 0.77, respectively, i.e., overestimation increased from 5.6% to 22.8%. The development of the Padmarajaiah (1999) model showed it moving from 1.01 to 0.81 and finally to 0.67 which eventually ended up being a heavy bias (about 33.4%) towards overestimation at high RI.

Most of the models overestimate the effect of high RI in full-RCA concrete based on the flexural results. In the case of flexural strength, this observation is particularly important because of the strong contribution of fiber bridging, which acts as a mechanical crack-transfer mechanism after cracking. The weaker ITZ in full-RCA mixtures and the greater matrix heterogeneity may reduce the efficiency of fiber anchorage, pull-out resistance, and crack-bridging action. Consequently, the improvement in flexural strength with increasing RI is not necessarily linear. This explains why some equations become increasingly non-conservative as RI increases.

3.5 Overall ranking of prediction models

Rank sum technique was employed to select the most appropriate equation for each mechanical property based on the results given in Table 4. The average Exp./Pred. Ratio closest to 1, least COV, least MAPE and least RMSE were used as ranking criteria. The equation of lowest rank out of all the equations was deemed to be the best overall model.

TABLE 4. Comparative ranking of the evaluated prediction models for compressive, splitting tensile, and flexural strength based on multiple statistical performance indicators.

​ModelAvg. rankCOV rankMAPE rankRMSE rankTotal
f’cEzeldin and Balaguru (1992)22116
Ou et al. (2012)11226
Padmarajaiah (1999)333312
Nataraja et al. (1999)444416
frSwamy and Mangat (1974)21115
Gao et al. (1997)12227
Padmarajaiah (1999)334313
Yazıcı et al. (2007)443415
ftGao et al. (1997)143210
Thomas and Ramaswamy (2007)22217
Ghosh and Kumar (1997)335415
Song and Hwang (2004)41139
Padmarajaiah (1999)554519

In the compressive strength, the total scores of Ezeldin and Balaguru (1992) and Ou models were the same with 6. Ezeldin and Balaguru (1992) model appeared to be most accurate in MAPE and RMSE and least accurate in bias and COV, whereas Ou et al. (2012) model appeared to be most accurate in bias and COV and least accurate in MAPE and RMSE. So, it is suggested that the model developed by Ezeldin and Balaguru (1992) would be more appropriate for situations in which the absolute accuracy is the parameter of interest, while the model developed by Ou would be more suitable for situations in which the prediction value and scatter are both interests. This model was followed by Padmarajaiah (1999) model with 12 total score and Nataraja et al. (1999) model with 16 total score and they come in third and fourth places respectively. The difference between Ezeldin and Balaguru (1992), Ou et al. (2012) and Nataraja et al. (1999) was significantly different, where the maximum difference was the sum of the scores obtained by Nataraja et al.’s model, 166.7% better than the best-performing models.

The maximum total scores exhibit the Swamy and Mangat (Swamy and Mangat, 1974) model with a flexural strength score of 5 followed by Gao et al. (1997) model with a score of 7. The Swamy and Mangat (Swamy and Mangat, 1974) model scored 28.6% better than the model proposed as by Gao et al. (1997) in terms of rank sum score and had lower values of MAPE, RMSE and COV. Padmarajaiah (Padmarajaiah, 1999) was in the third position and Yazıcı et al. (2007) were in the fourth position with score 13 and 15 respectively. Yazıcı et al. (2007) had lowest MAPE, but due to very high COV and RMSE it was moved to the last leagues.

It was found that the Thomas and Ramaswamy (Thomas and Ramaswamy, 2007) model was first in the class for splitting tensile strength with a total score of 7. Although the Song and Hwang (Song and Hwang, 2004) model had the lowest MAPE and COV, it was ranked second due to the highest bias compared with the Thomas and Ramaswamy (Thomas and Ramaswamy, 2007) model and Gao et al. (1997) model. The third ranking model was the model by Gao et al. (1997) with a score of 10, mostly because of its excellent average Exp./Pred. Ratio but relatively higher COV and MAPE. In this regard, Ghosh (Ghosh and Kumar, 1997) had scored 15 and Padmarajaiah (Padmarajaiah, 1999) scored 19 and was last. It is noted that, the score of the Padmarajaiah was 171.4% higher than the best model and, this showed that the ability of the limited score to predict the splitting tensile strength was questionable.

4 Study limitations

Although the present study provides a comprehensive assessment of existing empirical equations for predicting the compressive, splitting tensile, and flexural strengths of SFRAC, several limitations should be acknowledged. First, the compiled database contains clustered observations originating from the same studies or experimental programs, which may introduce dependence among data points and may cause some research programs to have a greater influence on the overall statistical assessment. In addition, the numbers of observations within the investigated subgroups are unequal, particularly across different replacement ratios, fiber contents, and mechanical properties, which limits the direct comparability of model performance between subgroups. Second, the database combines results obtained using different specimen geometries, curing conditions, testing standards, loading procedures, and material characterization methods, introducing experimental heterogeneity that could not be fully standardized. Third, the original applicability domains of several empirical equations were not always explicitly reported, and some models were therefore evaluated beyond the material or parameter ranges for which they were initially developed. Moreover, not all equations could generate valid predictions for every observation because of missing input variables, unavailable reference-concrete properties, or restrictions inherent to the mathematical formulation, resulting in different sample sizes among the model evaluations. Another limitation is that the assessment was based mainly on point-estimate performance indicators, while prediction intervals and other measures of model uncertainty were not available for most of the published equations and therefore could not be systematically evaluated. The study was also restricted to empirical prediction models derived from published experimental data and to steel-fiber-reinforced aggregate concrete, while data-driven approaches, other fiber systems, durability-related properties, long-term performance, and structural-scale behavior were beyond its scope. These limitations should be considered when interpreting the comparative rankings of the equations and highlight the need for future studies based on more balanced and standardized datasets, clearly defined model applicability domains, and explicit quantification of prediction uncertainty.

5 Conclusion

This study has critically reviewed the available empirical models to predict the compressive, splitting tensile and flexural strengths in case of SFRAC. Literature-experimental results were analyzed through statistical indicators, parity plots, distributions of error-bands and a rank-sum procedure. The influence of RCA replacement level and RI was also investigated to see if the equations, mainly developed based on conventional steel fiber-reinforced concrete (SFRC) can be used to adequately account for the combined effects of RCA and steel fibers. The main findings are as follows.

  • Compressive strength was predicted more accurately than the tensile-dominated properties. The investigated compressive-strength equations produced MAPE values between 7.34% and 8.65%, indicating that reinforcement-index-based models can reasonably represent the compressive response of SFRAC when the underlying matrix strength is appropriately defined.
  • Ezeldin and Balaguru (1992) and Ou et al. (2012) provided the strongest overall compressive-strength predictions. The Ezeldin and Balaguru (1992) model achieved the lowest MAPE and RMSE, at 7.34% and 4.14 MPa, respectively, whereas the Ou et al. (2012) model exhibited the lowest scatter, with a COV of 3.09%, and placed 95.4% of its predictions within the ±10% error band. Their identical rank-sum scores indicate that model selection should depend on whether minimum absolute error or maximum prediction consistency is prioritized.
  • Splitting tensile strength exhibited the greatest model uncertainty. The evaluated equations produced MAPE values of 20.44%–31.63%, reflecting the difficulty of representing tensile behavior through simplified relationships based mainly on matrix strength and RI. The Thomas and Ramaswamy (Thomas and Ramaswamy, 2007) equation achieved the most balanced overall ranking because of its comparatively low RMSE and moderate bias, whereas Song and Hwang (Song and Hwang, 2004) provided the lowest MAPE but remained conservative, with a mean Exp./Pred. Ratio of 1.22.
  • The Swamy and Mangat (Swamy and Mangat, 1974) equation was the most reliable model for flexural strength. It achieved the lowest COV, MAPE, and RMSE, at 17.11%, 18.57%, and 1.31 MPa, respectively. It also placed 77.4% and 90.3% of the predictions within the ±20% and ±30% error bands, confirming that its mechanics-based treatment of crack control and fiber contribution better captures the flexural response of SFRAC than the other investigated formulations.
  • RCA replacement level substantially affected prediction bias, particularly for splitting tensile strength. Increasing the RCA replacement to 100% produced relatively modest changes in compressive-strength predictions but caused several tensile-strength models to shift from conservative or nearly unbiased predictions toward non-conservative overestimation. This behavior indicates that the deterioration of the aggregate–mortar interfaces and the increased heterogeneity associated with full RCA replacement are not adequately represented by equations calibrated using natural-aggregate concrete.
  • The influence of RI depended on both the mechanical property and RCA replacement level. Its effect on compressive-strength prediction was limited, whereas pronounced and inconsistent changes were observed for splitting tensile and flexural strengths. At high RCA replacement levels, several models increasingly overestimated the effective fiber contribution as the RI increased, demonstrating that identical reinforcement-index values do not necessarily produce equivalent strength enhancements in natural- and recycled-aggregate matrices.

Overall, there was no single empirical equation that could be universally applied to all three mechanical properties. The reliability of the models investigated also decreased in an incremental fashion as the response was increasingly affected by crack initiation, the fiber orientation, fiber pull-out, and fiber–matrix interaction. Future work should thus try to establish prediction equations specially tuned to SFRAC, based on larger and more balanced databases in which the quality of the RCA, the replacement ratio, the strength of the parent-concrete, the adhered-mortar content, the fiber geometry, the fiber orientation, the bond characteristics between fibers and mortar and the matrix-fiber interaction are explicitly taken into account. The use of independent, experimental validation, uncertainty quantification and physically interpretable, data-driven approaches should also be implemented. Bias and scatter were higher for full-RCA mixtures and higher reinforcement-index ranges, suggesting specific focus for these.

Generative AI statement

The author(s) declared that generative AI was not used in the creation of this manuscript.

Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Supplementary material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fbuil.2026.1952751/full#supplementary-material

Supplementary material Supplementary material at the source

Nomenclature

f’ **c** Compressive strength MPa f **t** Splitting tensile strength MPa f **r** Flexural strength (modulus of rupture) MPa V **f** Steel fiber volume fraction % l **f** Fiber length mm d **f** Fiber diameter mm l **f** /d **f** Fiber aspect ratio RI Reinforcement index ((Vf \times lf/df)) Exp./Pred. Experimental-to-predicted strength ratio SD Standard deviation COV Coefficient of variation % MAPE Mean absolute percentage error % RMSE Root mean square error MPa RCA Recycled coarse aggregate RAC Recycled aggregate concrete SFRAC Steel fiber-reinforced recycled aggregate concrete SFRC Steel fiber-reinforced concrete NAC Natural aggregate concrete ITZ Interfacial transition zone IBA Imperfect bonding area CDW Construction and demolition waste

Footnotes

Edited by: Assed N. Haddad, Federal University of Rio de Janeiro, Brazil

Reviewed by: Hassan Ghanem, Beirut Arab University, Lebanon

R. A. Hamid, University of Al-Qadisiyah, Iraq

Statements

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The reviewer HG declared a past co-authorship with two of the authors FB and AJ to the handling editor during the time of review.

Funding

The author(s) declared that financial support was not received for this work and/or its publication.

Data availability

The original contributions presented in the study are included in the article/Supplementary Material, further inquiries can be directed to the corresponding author.

Author contributions

WfH: Validation, Conceptualization, Writing – review and editing, Software, Writing – original draft. AN: Project administration, Methodology, Visualization, Software, Writing – review and editing, Writing – original draft. AD: Writing – original draft, Conceptualization, Visualization, Validation, Formal Analysis. WeH: Project administration, Investigation, Supervision, Writing – review and editing. FB: Writing – review and editing, Supervision, Resources, Data curation, Investigation. AJ: Writing – original draft, Methodology, Validation, Conceptualization.

References

  1. Afroughsabet V., Biolzi L., Ozbakkaloglu T. (2017). Influence of double hooked-end steel fibers and slag on mechanical and durability properties of high performance recycled aggregate concrete. Compos. Struct. 181, 273 – 284. doi:10.1016/j.compstruct.2017.08.086
  2. Ahmadi M., Farzin S., Hassani A., Motamedi M. (2017). Mechanical properties of the concrete containing recycled fibers and aggregates. Constr. Build. Mater. 144, 392 – 398. doi:10.1016/j.conbuildmat.2017.03.215
  3. Al-Jasimee D. H., Abo Dhaheer M. S. (2019). Shear behaviour of reinforced self-compacting concrete beams made with treated recycled aggregate. Al-Qadisiyah J. Eng. Sci. 12 (3), 193 – 198. doi:10.30772/qjes.v12i3.617
  4. Al-Rekabi A. H., Abo Daheer M. S. (2024). Performance of sustainable fiber reinforced concrete with recycled aggregates: a critical review. AIP Conf. Proc. 3079, 060014. doi:10.1063/5.0202348
  5. Al-Rekabi A. H., Al-Marmadi S. H., Abo Dhaheer M. S., Al-Ramahee M. (2023). Experimental investigation on sustainable fiber reinforced self-compacting concrete made with treated recycled aggregate. AIP Conf. Proc. 2775, 020032. doi:10.1063/5.0140655
  6. Alqarni A. S., Abbas H., Al-Shwikh K. M., Al-Salloum Y. A. (2021). Treatment of recycled concrete aggregate to enhance concrete performance. Constr. Build. Mater 307, 12496. doi:10.1016/j.conbuildmat.2021.124960
  7. Atis¸ C. D., Karahan O. (2009). Properties of steel fiber reinforced fly ash concrete. Constr. Build. Mater 23 (1), 392 – 399. doi:10.1016/j.conbuildmat.2007.11.002
  8. Bai W. H., Sun B. X. (2010). Experimental study on flexural behavior of recycled coarse aggregate concrete beam. Appl. Mech. Mater. 29-32, 543 – 548. doi:10.4028/www.scientific.net/amm.29-32.543
  9. Bai G., Zhu C., Liu C., Liu B. (2020). An evaluation of the recycled aggregate characteristics and the recycled aggregate concrete mechanical properties. Constr. Build. Mater. 240, 117978. doi:10.1016/j.conbuildmat.2019.117978
  10. Barnett S. J., Jean-Francois L., Parry T., Millard S. G., Soutsos M. N. (2010). Assessment of fibre orientation in ultra high performance fibre reinforced concrete and its effect on flexural strength. Mater Struct. 43 (7), 1009 – 1023. doi:10.1617/s11527-009-9562-3
  11. Behera M., Bhattacharyya S. K., Minocha A. K., Deoliya R., Maiti S. (2014). Recycled aggregate from C&D waste and its use in concrete - a breakthrough towards sustainability in construction sector: a review. Constr. Build. Mater 68, 501 – 516. doi:10.1016/j.conbuildmat.2014.07.003
  12. Behnood A., Olek J., Glinicki M. A. (2015). Predicting modulus elasticity of recycled aggregate concrete using M5′ odel tree algorithm. Constr. Build. Mater 94, 137 – 147. doi:10.1016/j.conbuildmat.2015.06.055
  13. Bhan C., Kaur M. (2018). Strength characteristics of recycled concrete aggregate with addition of steel fibres. Int. J.Adv. Res. Dev. 3 (11), 10 – 15.
  14. Bhikshma V., Manipal K. (2011). Study on mechanical properties of recycled aggregate concrete containing steel fibers. Asian J. Civ. Eng. 3 (2), 157 – 163. Available online at:.
  15. Camps G., Turatsinze A., Sellier A., Escadeillas G., Bourbon X. (2008). Steel-fiber reinforcement and hydration coupled effects on concrete tensile behavior. Eng. Fract. Mech. 75, 5207 – 5216. doi:10.1016/j.engfracmech.2008.08.008
  16. Carneiro J. A., Lima P. R. L., Leite M. B., Toledo Filho R. D. (2014). Compressive stress-strain behavior of steel fiber reinforced-recycled aggregate concrete. Cem. Concr. Compos. 46, 65 – 72. doi:10.1016/j.cemconcomp.2013.11.006
  17. Chaboki H. R., Ghalehnovi M., Karimipour A., de Brito J., Khatibinia M. (2019). Shear behaviour of concrete beams with recycled aggregate and steel fibres. Constr. Build. Mater. 204, 809 – 827. doi:10.1016/j.conbuildmat.2019.01.130
  18. Corinaldesi, V. (2011). Structural concrete prepared with coarse recycled concrete aggregate: from investigation to design. Adv. Civ. Eng. Hindawi 283984, 6. doi:10.1155/2011/283984
  19. Ezeldin A. S., Balaguru P. N. (1992). Normal- and high-strength fiber-reinforced concrete under compression. J. Mater. Civ. Eng. 4 (4), 415 – 429. doi:10.1061/(ASCE)0899-1561(1992)4:4(415)
  20. Gao D., Zhang L. (2018). Flexural performance and evaluation method of steel fiber reinforced recycled coarse aggregate concrete. Constr. Build. Mater. 159, 126 – 136. doi:10.1016/j.conbuildmat.2017.10.073
  21. Gao J., Sun W., Morino K. (1997). Mechanical properties of steel fiber-reinforced, high-strength, lightweight concrete. Cem. Concr. Compos. 19 (4), 307 – 313. doi:10.1016/S0958-9465(97)00023-1
  22. Ghosh S., Kumar A. (1997). Effect of silica fume and steel fibers on some properties of high-strength concrete. Constr. Build. Mater. 11 (7–8), 373 – 382. doi:10.1016/S0950-0618(97)00058-5
  23. He W., Kong X., Fu Y., Zhou C., Zheng Z. (2020). Experimental investigation on the mechanical properties and microstructure of hybrid fiber reinforced recycled aggregate concrete. Constr. Build. Mater. 261, 120488. doi:10.1016/j.conbuildmat.2020.120488
  24. Heeralal M., Kumar R., Rao Y. V. (2009). Flexural fatigue characteristics of steel fiber reinforced recycled aggregate concrete (SFRRAC). Facta Univ. - Ser. Archit. Civ. Eng. 7 (1), 19 – 33. doi:10.2298/fuace0901019h
  25. Iqbal S., Ali I., Room S., Khan S. A., Ali A. (2019). Enhanced mechanical properties of fiber reinforced concrete using closed steel fibers. Mater Struct. 52 (3), 56. doi:10.1617/s11527-019-1357-6
  26. Kaplan G., Bayraktar O. Y., Gholampour A., Gencel O., Koksal F., Ozbakkaloglu T. (2021). Mechanical and durability properties of steel fiber-reinforced concrete containing coarse recycled concrete aggregate. Struct. Concr. 22 (5), 2791 – 2812. doi:10.1002/suco.202100028
  27. Katzer J., Domski J. (2012). Quality and mechanical properties of engineered steel fibres used as reinforcement for concrete. Constr. Build. Mater 34, 243 – 248. doi:10.1016/j.conbuildmat.2012.02.058
  28. Kou S., Poon C., Etxeberria M. (2011). Influence of recycled aggregates on long term mechanical properties and pore size distribution of concrete. Cem. Concr. Compos 33 (2), 286 – 291. doi:10.1016/j.cemconcomp.2010.10.003
  29. Kou S., Poon C., Wan H. (2012). Properties of concrete prepared with low-grade recycled aggregates C and D waste. Constr. Build. Mater. 36, 881 – 889. doi:10.1016/j.conbuildmat.2012.06.060
  30. Li B., Xu L. H., Chi Y., Huang B., Li C. N. (2017). Experimental investigation on the stress-strain behavior of steel fiber reinforced concrete subjected to uniaxial cyclic compression. Constr. Build. Mater 140, 109 – 118. doi:10.1016/j.conbuildmat.2017.02.094
  31. Liao L., Cavalaro S., Fuente de la A., Aguado A. (2014). Complementary use of inductive test and bending test for the characterization of SFRC. Appl. Mech. Mater. 580-583, 2213 – 2219. doi:10.4028/www.scientific.net/AMM.580-583.2213
  32. Malešev M., Radonjanin V., Marinković S. (2010). Recycled concrete as aggregate for structural concrete production. Sustainability 2 (5), 1204 – 1225. doi:10.3390/su2051204
  33. Mansur M. A., Chin M. S., Wee T. H. (1999). Stress-strain relationship of high-strength fiber concrete in compression. J. Mater Civ. Eng. 11 (1), 21 – 29. doi:10.1061/(ASCE)0899-1561(1999)11:1(21)
  34. Nanakorn P., Horii H. (1996). A fracture-mechanics-based design method for SFRC tunnel linings. Tunn. Undergr. Space Technol. 11 (1), 39 – 43. doi:10.1016/0886-7798(96)00050-8
  35. Nataraja M., Dhang N., Gupta A. (1999). Stress-strain curves for steel-fiber reinforced concrete under compression. Cem. Concr. Compos 21 (5–6), 383 – 390. doi:10.1016/S0958-9465(99)00021-9
  36. Nili M., Afroughsabet V. (2010). Combined effect of silica fume and steel fibers on the impact resistance and mechanical properties of concrete. Int. J. Impact Eng. 37 (8), 879 – 886. doi:10.1016/j.ijimpeng.2010.03.004
  37. Oliveira de L. ´A., Araújo D. D., Toledo R. D., Fairbairn E. D. R. (2016). Andrade de MAS tension stiffening of steel-fiber-reinforced concrete. Acta Sci. Technol. 38 (4), 455 – 463. doi:10.4025/actascitechnol.v38i4.28077
  38. Ou Y. C., Tsai M. S., Liu K. Y., Chang K. C. (2012). Compressive behavior of steel-fiber-reinforced concrete with a high reinforcing index. J. Mater Civ. Eng. 24 (2), 207 – 215. doi:10.1061/(ASCE)MT.1943-5533.0000372
  39. Padmarajaiah S. K. (1999). Influence of Fibers on the Behavior of High Strength Concrete in fully/partially Prestressed Beams: An Experimental and Analytical Study. India: Indian Institute of Science, Ban galore. Ph.D. thesis.
  40. Paluri Y., Mogili S., Mudavath H., Noolu V. (2020). Effect of fibres on the strength and toughness characteristics of recycled aggregate concrete. Mater. Today Proc. 38, 2537 – 2540. doi:10.1016/j.matpr.2020.07.555
  41. Park S. H., Kim D. J., Ryu G. S., Koh K. T. (2012). Tensile behavior of ultra high performance hybrid fiber reinforced concrete. Cem. Concr. Compos 34 (2), 172 – 184. doi:10.1016/j.cemconcomp.2011.09.009
  42. Prakash Chandar S., Gunasekaran K., Sai Sandeep N., Manikandaprabhu S. (2017). An experimental investigation on strength properties of steel fibres along with recycled aggregate in cement concrete. Rasayan J. Chem. 10 (2), 528 – 533. doi:10.7324/RJC.2017.1021636
  43. Purushothaman R., Ram Kumar B., Amudhavalli N. K. (2015). Treatment of recycled concrete aggregate to enhance concrete properties – a review. J. Chem. Pharm. Sci. (JCPS), Special Issue.
  44. Ramesh R. B., Mirza O., Kang W. H. (2019). Mechanical properties of steel fiber reinforced recycled aggregate concrete. Struct. Concr. 20 (2), 745 – 755. doi:10.1002/suco.201800156
  45. Sahoo D. R., Maran K., Kumar A. (2015). Effect of steel and synthetic fibers on shear strength of RC beams without shear stirrups. Constr. and Building Materials 83, 150 – 158. doi:10.1016/j.conbuildmat.2015.03.010
  46. Sayhood E., Resheq A., Raoof F. (2019). Behavior of recycled aggregate fibrous reinforced beams under flexural and shear loading. Eng. Technol. J. 37 (3C), 338 – 344. doi:10.30684/etj.37.3c.6
  47. Senaratne S., Gerace D., Mirza O., Tam V. W. Y., Kang W.-H. (2016). The costs and benefits of combining recycled aggregate with steel fibres as a sustainable structural material. J. Clean. Prod. 112, 2318 – 2327. doi:10.1016/j.jclepro.2015.10.041
  48. Shi C., Li Y., Zhang J., Li W., Chong L., Xie Z. (2016). Performance enhancement of recycled concrete aggregate – a review. J. Clean. Prod. 112, 466 – 472. doi:10.1016/j.jclepro.2015.08.057
  49. Soares D., De Brito J., Ferreira J., Pacheco J. (2014). Use of coarse recycled aggregates from precast concrete rejects: mechanical and durability performance. Constr. Build. Mater 71, 263 – 272. doi:10.1016/j.conbuildmat.2014.08.034
  50. Someh A. K., Saeki N. (1994). Prediction for the stress-strain curve of steel fiber reinforced concrete. Trans. Jpn. Concr. Inst. 18, 1149 – 1154.
  51. Song P. S., Hwang S. (2004). Mechanical properties of high-strength steel fiber-reinforced concrete. Constr. Build. Mater 18 (9), 669 – 673. doi:10.1016/j.conbuildmat.2004.04.027
  52. Sryh L., Forth J. (2015). Experimental investigation on the effect of steel fibres on the mechanical properties of recycled aggregate concrete. Proc. Int. Conf. FIBRE Concr. 2015-Janua, Sept. 444 – 453. doi:10.13140/RG.2.1.4665.4967
  53. Su Q. (2020). Strengths of recycled concrete added with steel fiber. Arch. Civ. Eng. 66 (3), 693 – 703. doi:10.24425/ace.2020.134421
  54. Swamy R. N., Mangat P. S. (1974). A theory for the flexural strength of steel fiber reinforced concrete. Cem. Concr. Res. 4 (2), 313 – 325. doi:10.1016/0008-8846(74)90142-2
  55. S¨oylev T. A., ¨Ozturan T. (2014). Durability, physical and mechanical properties of fiber reinforced concretes at low-volume fraction. Constr. Build. Mater 73, 67 – 75. doi:10.1016/j.conbuildmat.2014.09.058
  56. Thomas A. (2009). Sprayed Concrete Lined Tunnels. London and New York: Taylor & Francis.
  57. Thomas J., Ramaswamy A. (2007). Mechanical properties of steel fiber-reinforced concrete. J. Mater Civ. Eng. 19 (5), 385 – 392. doi:10.1061/(ASCE)0899-1561(2007)19:5(385)
  58. Topcu I. B., Canbaz M. (2007). Effect of different fibers on the mechanical properties of concrete containing fly ash. Constr. Build. Mater 21 (7), 1486 – 1491. doi:10.1016/j.conbuildmat.2006.06.026
  59. Tüfekçi M. M., Çakır Ö. (2017). An investigation on mechanical and physical properties of recycled coarse aggregate (RCA) concrete with GGBFS. Int. J. Civ. Eng. 15 (4), 549 – 563. doi:10.1007/s40999-017-0167-x
  60. Uyguno˘glu T. (2008). Investigation of microstructure and flexural behavior of steel-fiber reinforced concrete. Mater Struct. 41 (8), 1441 – 1449. doi:10.1617/s11527-007-9341-y
  61. Wang B., Yan L., Fu Q., Kasal B. (2021). A comprehensive review on recycled aggregate and recycled aggregate concrete. Resour. Conserv. Recycl 171 (May), 105565. doi:10.1016/j.resconrec.2021.105565
  62. Xia D. T., Xie S. J., Fu M., Zhu F. (2021). Effects of maximum particle size of coarse aggregates and steel fiber contents on the mechanical properties and impact resistance of recycled aggregate concrete. Adv. Struct. Eng. 24 (13), 3085 – 3098. doi:10.1177/13694332211017998
  63. Xie T., Ozbakkaloglu T. (2015). Behavior of steel fiber-reinforced high-strength concrete-filled FRP tube columns under axial compression. Eng. Struct. 90, 158 – 171. doi:10.1016/j.engstruct.2015.02.020
  64. Yazıcı S., Inan G., Tabak V. (2007). Effect of aspect ratio and volume fraction of steel fiber on the mechanical properties of SFRC. Constr. Build. Mater 21 (6), 1250 – 1253. doi:10.1016/j.conbuildmat.2006.05.025
  65. Yue Y., Zhou Y., Xing F., Gong G., Hu B., Guo M. (2020). An industrial applicable method to improve the properties of recycled aggregate concrete by incorporating nano-silica and micro-CaCO3. J. Clean. Prod. 259, 120920. doi:10.1016/j.jclepro.2020.120920
  66. Zhou J. H., He H. J., Meng Xh Y. Y. (2010). Basic mechanical properties of recycled concrete experimental study. J. Shenyang Jianzhu Univ. 26 (3), 8 – 464.

Citation

Hasan, W. A., et al. (2026). Mechanical strength prediction of steel fiber-reinforced recycled aggregate concrete: model accuracy and key influencing parameters. Frontiers in Built Environment, Volume 12. https://doi.org/
Received
Accepted
Published
Volume
12 - 2026

Copyright

Copyright © 2026 Hasan, Naji, Dakhil, Hamd, Barraj and Jahami.

License: https://creativecommons.org/licenses/by/4.0/

*Correspondence: Firas Barraj

Article metrics

Views
0
Downloads
0
Citations
0
Shares
0

Related articles

Original ResearchEnhancing the residual strength of clay bricks exposed to elevated temperatures using metal oxides, carbon black, and sodium hydroxide activationHebah Mohammad Al-Jabali, Walid Fouad Edris, Amr Abdelkhalik, Abd Al-Kader A. Al Sayed, Shady KhairySystematic ReviewToward a sensory-gradient framework for neuroinclusive secondary-school design: an integrative review and contextualization for a tropical Nigerian settingOmoniyi Ogheneruemu Olagunju, Ayomide Teslim OgundeleReviewSteel mill scale in concrete and mortar: a critical review of the evidence base and a proposed framework for future quantitative synthesisG. Loganathan, M. Senthil Pandian, S. Deepa Nivethika