Experimental design and analysis of toughness and modulus of rupture (MOR) of cement mortar reinforced with PET fibers

Abstract

This study examines the impact of polyethylene terephthalate (PET) fibers on major mechanical properties of cement mortar including toughness and modulus of rupture (MOR). For this purpose, various mixes were designed and PET fibers were incorporated into mortar mixes at two dosage levels (0.5% and 1% by volume), along with two other varying parameters i.e. water-to-binder (w/b) ratios, and superplasticizer (SP) ratio to adjust the workability of the cement mixtures. The key mechanical characteristics of hardened cement composite including strength, toughness, and MOR were evaluated and a comprehensive parametric study was implemented. Besides, correlation analyses of each pair of the mechanical properties were performed and the coefficients of determination were determined. The experimental outcomes indicated that the optimum fiber volumes for compressive toughness and flexural toughness were 0.5% and 1%, respectively. While lower w/b ratios such as w/b = 0.35 resulted in higher strength properties, improved toughness was noted in higher rations. RSM analysis implemented showed that the optimum MOR can be achieved at the lowest level of w/b and middle levels of SP and Fiber%. Correlation analyses results demonstrated a strong correlation between compressive strength-toughness and compressive strength-MOR with R² = 0.90 and R² = 0.96, respectively. However, lower correlations were observed for flexural strength-toughness and flexural toughness-MOR with similar R² = 0.75.

Introduction

Concrete and mortar are ubiquitous in civil engineering because of their high compressive strength, economy, and versatility; yet their heterogeneous, porous micro/meso-structure makes them quasi-brittle with limited tensile capacity. Heterogeneities promote micro-cracks and voids that increase vulnerability, degrade service life and structural performance under long-term operational conditions^1,2,3,4,5. It also enhances tensile load capacity, since in many projects the structure may be subjected to tensile stresses^6,7.

To address these challenges, numerous studies have been conducted to enhance the tensile strength, mechanical properties, and long-term durability of concrete. These efforts have primarily focused on incorporating additives (SCMs, VMAs, SPs, SAPs) and fibers to improve fresh rheology and hardened behavior^8,9,10.In fiber-reinforced composites (FRC), fibers (such as carbon, glass, basalt, polypropylene, natural, and polyester), due to their stitching-like effect, bridge cracks, have improved toughness, ductility, and resistance to environmental degradation^{11,12,13,14,15,16,17,18,19,20,21}.

The failure mechanism in FRC typically involves fiber pull-out or debonding, and its toughness, measured by the area under the load–deflection curve, is a critical parameter. In this regard, flexural testing is also employed as an indicator of the modulus of rupture (MOR or MR)^22,23,24.

On the other hand, in recent years, plastic waste has become a major environmental threat. However, the use of plastic fibers in concrete offers a sustainable solution to plastic waste accumulation^19,25,26. Beyond plastics, machining-industry by-products (e.g., steel swarf/turning chips) and electronic waste fiber (E‑waste ‑fiber) have also been utilized as discrete reinforcement in cementitious composites, delivering concurrent gains in mechanical performance and environmental impact reduction^27,28,29. Consequently, there is growing interest in using recycled materials to develop more sustainable cement-based composites. A promising approach involves using recycled polyethylene terephthalate (PET) fibers, which are primarily derived from plastic waste. Plastic fibers, especially PET, can significantly enhance the mechanical and chemical properties of cementitious materials, such as tensile strength, toughness, and ductility, with lower cost and energy consumption compared to steel and conventional fibers like PVA. This superior performance is largely attributed to the molecular structure of PET, composed of repeating units of ethylene glycol and terephthalic acid, which provides high mechanical stress resistance^{30,31,32,33,34,35,36}.

The effectiveness of these fibers strongly depends on their geometric characteristics, including length, diameter, aspect ratio, and surface roughness, parameters that play a decisive role in improving fiber-cement matrix bonding and structural performance^37,38,39. One of the key mechanisms of PET fiber function in the cement matrix is the “stitching effect,” whereby the fibers restrain micro-cracks, particularly during early-age shrinkage, preventing their propagation and spread^{12,26,40,41,42,43,44}.

In self-compacting concrete (SCC), the inclusion of PET fibers enhances mechanical behavior and opens new prospects for broader application of fiber-reinforced concretes in sustainable structures. This effect is particularly significant in tensile zones of concrete members, whereas compressive zones are only marginally influenced by fiber volume increase^26,45. The use of optimized PET fiber volume fractions ranging from 0.5% to 1.5% leads to substantial improvements in tensile strength, flexural toughness, and effective crack control, thereby enhancing concrete durability⁴⁶.

At the structural engineering level, PET fibers can serve as a viable substitute for steel fibers in discrete reinforcement applications^26,41. Additionally, Compared with concrete, mortar’s finer grading promotes more homogeneous fiber dispersion and stronger fiber–paste bonding, which is advantageous for thin overlays, plasters, and crack-resistant layers^47,48.

As a result, PET fiber-reinforced mortar (PETFRM) is considered a promising option for applications such as surface coatings, plasters, and masonry units that require thin, flexible, and crack-resistant layers⁴⁷. The finer particle size of mortar also reduces fiber entanglement, enhances crack-bridging performance, and improves the overall flexural behavior of the system^49,50.

Experimental studies have shown that the addition of PET fibers improves key mechanical properties, including compressive strength, flexural strength, and splitting tensile strength. For example, Abed et al. (2021) reported an 18% increase in tensile strength using short PET fibers (8 mm in length)⁴⁸, while Fraternali et al.⁵¹ noted significant improvements in impact resistance and energy absorption. Ahad et al.⁵² also identified two optimal mixtures for enhancing compressive strength: a combination of 2.5% recycled PET fibers and 10% natural zeolite (NZ) and a mix of 1.0% PET and 15% NZ as cement replacement, resulting in 6.45% and 1.0% increases in compressive strength, respectively. In magnesium silicate hydrate-based systems, polyester fibers like PET have shown a fracture toughness enhancement without compromising compressive strength due to strong fiber–matrix bonding in a microstructural scale³⁶.

In a study by Elmir et al.⁵³, the effects of various mix design parameters on workability, mechanical properties, water absorption, and carbonation resistance of mortar modified with styrene–butadiene rubber (SBR) and PET fibers were examined. Using Taguchi and TOPSIS methods, the optimal mix, consisting of 525 kg/m³ of cement, a 0.55 water-to-cement ratio, 3.5% SBR, and 4.5% PET, was identified for superior fresh and hardened performance.

Other researches show that PET fibers recycled from plastic bottles can be effectively utilized in binary cement concrete mixtures⁵⁴. Specifically, Kim et al.³ investigated the impact of increasing micro-fiber content in hybrid systems and found that improvements in flexural toughness, deflection capacity, and equivalent flexural strength depended on the type of macro fibers used.

In another study an increase in compressive strength was observed by 10.67% compared to the control mix in the mix containing 0.4% recycled PET and 10% metakaolin (MK). Specimens with 0.4% fiber and 10% MK demonstrated 84.6% and 80% enhancements in tensile and flexural strength, respectively⁵⁵. These improvements were attributed to the fineness of MK and its role in pore filling.

Additionally, Hou et al.⁵⁶ assessed the combined effects of recycled powder (HRP) from composite concrete and brick waste along with recycled PET fibers (RPETF) in mortar. They found that 2% RPETF increased compressive and flexural strength by 14.25% and 22.50%, respectively, compared to fiber-free mortar.

Despite these mechanical enhancements, excessive PET fiber content can reduce concrete workability, mainly due to fiber entanglement in the cement matrix^57,58,59. To maintain a balance between workability and mechanical benefits, fiber dosage should be optimized, geometry might be modified, or plasticizers can be used. Many studies recommend an optimal PET fiber volume fraction of 0.1% to 1% for best mechanical and practical performance⁶⁰.

For instance, in a study on recycled aggregate concrete (RAC), the combined use of steel and PET fibers, although it reduced workability, yielded substantial improvements in most mechanical properties; however, PET had no positive effect on compressive strength⁶¹. In another study, Yarah et al.⁶² evaluated the effects of PET fiber volume fractions (0.5%, 1%, and 1.5%) on the mechanical behavior of concrete. Although changes in compressive and tensile strength were relatively limited (< 10% and ~ 5%), energy absorption capacity increased significantly.

Furthermore, Parhi et al.⁶³ aimed to optimize the mix design of PET fiber-reinforced concrete (PFRC) by testing volume fractions of 0.3%, 0.4%, and 0.5%. Results showed significant increases in flexural strength at all fiber dosages; notably, 0.5% PET improved flexural strength by about 17% compared to plain concrete. However, increasing PET content slightly reduced compressive strength, mainly due to decreased internal bonding. From a durability standpoint, studies have shown that PET fibers enhance concrete resistance to dynamic loads, freeze–thaw cycles, and chemical attacks, making PETFRM concrete suitable for harsh environments⁶⁴. Although PET generally exhibits stable performance, research is ongoing on fiber surface modifications, such as plasma coatings and chemical treatments, to improve fiber–matrix compatibility and durability^51,65,66. Tang et al.⁵⁰, reported that adding 0.1% PET fibers (6 mm long) increased early-age compressive strength without significantly affecting dry density or water absorption, ultimately enhancing the durability.

Overall, although some studies report limited or negative effects of PET on compressive strength, the primary objective of using these fibers lies in improving the quasi-brittle properties of concrete by enhancing toughness, energy absorption, impact resistance, and crack control⁴¹. Hence, the growing trend in research indicates PET’s high potential for improving the mechanical performance and durability of cementitious materials.

The above literature on PET fibers in cementitious systems has predominantly centered on concrete, frequently deploying PET as a secondary fiber in hybrid blends and at higher volume fractions that impair rheology; most works emphasize compressive/tensile strength or provide screening-type rankings rather than interaction-aware models. In contrast, this study targets cement mortar, whose finer gradation promotes more homogeneous PET dispersion, and it isolates the PET-only effect at field-realistic dosages (0.5–1.0% vol.). We prioritize toughness (flexural and compressive) and modulus of rupture (MOR), properties most sensitive to fiber-bridging, and we directly compare our outcomes to prior PET reports. Methodologically, we jointly model the roles of w/b, SP, and PET% via a validated second-order response surface methodology (RSM) using a central composite design (CCD), quantifying main effects, curvature, and interaction terms (notably PET% × w/b and PET% × SP) while enforcing flowability/workability limits appropriate to flowable repair-mortar applications. Experimentally, flexural toughness peaks near 1.0% PET, compressive toughness near 0.5% PET, and optimal MOR occurs at low w/b with intermediate SP and PET%; complementary correlation (R²) analyses clarify where strength and toughness co-evolve versus decouple. What has been missing in the literature, a multivariate, optimization-driven understanding of toughness + MOR in PET fiber–reinforced mortar (PETFRM), is provided here as interaction-driven design maps that balance energy absorption, MOR, and castability. In short, by explicitly expressing MOR and flexural toughness as functions of w/b, SP, and PET% through a validated second-order RSM, we reveal workability-constrained mix windows that single-factor or screening studies could not expose.

Materials and method

Materials

In this study, Portland cement served as the primary binder for preparing PET fiber-reinforced mortar (PETFRM) specimens. The chemical composition of the cement used is detailed in Table 1. To enhance the environmental sustainability and reduce overall cement consumption, 10 wt.% of the Portland cement was partially replaced with lime powder. Beyond its ecological benefit, lime powder also acts as a micro-filler, improving mix consistency by occupying voids between cement particles and aggregates.

Table 1 Chemical composition of the cement.

A polycarboxylate-based superplasticizer (SP), compliant with ASTM C494 standards⁶⁷, was utilized in this study due to its compatibility with various pozzolanic admixtures.

The fine aggregates used in this study had a specific gravity of 2.65, an absorption capacity of 0.40%, and a dry rodded unit weight (DRUW) of 1.70 g/cm³. The particle size distribution of the sand, along with the ASTM C33⁶⁸-specified upper and lower grading limits, is illustrated in Fig. 1.

Fig. 1

Particle size distribution of the sand.

PET fibers are commonly incorporated into cementitious composites to mitigate crack initiation and propagation, while enhancing impact resistance and overall durability. Some other characteristics of PET fibers that makes it a desirable additive for cement mixtures reinforcement include High temperature stability, superior absorptivity and tensile strength, crack and fatigue resistance, good elastic resilience, and water stability^26,60,69,70. In this study, Commercial PET fibers (cut length 6 mm) were used as reinforcement. The nominal diameter and density are listed in Table 2, and a representative image of the fibers is shown in Fig. 2, as provided by the manufacturer. To document fiber form and surface texture, the as-received fibers were examined by SEM (Hitachi S-4800, 5.0 kV, working distance 5.0 mm) at low and high magnifications (Fig. 3a-b). At × 100, the fibers appear as straight, circular filaments that readily pack in parallel bundles, indicating a propensity to cluster if workability is limited. At × 2000, the surface is smooth/low-roughness with faint longitudinal drawing marks and no intentional embossing or coating; no surface pitting or micro-porosity was observed. This morphology implies that the PET–matrix bond is governed primarily by frictional/mechanical interlock within the ITZ, so dispersion quality (controlled by w/b and SP) is critical to maximize pull-out work and energy absorption. No surface treatment of fibers was applied in this study.

Table 2 Properties of PET fibers.

Fig. 2

Image of polyester (PET) fibers used it this study.

Fig. 3

SEM micrographs of the as-received PET fibers used in this study: (a) × 100 overview showing parallel alignment and a tendency to form bundles clusters (scale bar 500 μm); (b) × 2000 single filament surface showing a smooth texture with faint longitudinal striations and no coating/embossing (scale bar 20 μm). Imaging conditions: Hitachi S-4800, 5.0 kV, working distance 5.0 mm.

Mix proportions and designs of PETFRM

In this study, a few trial mixes were tested to determine an optimal binder content for the PETFRM, with 700 kg/m³ identified as the most suitable binder amount. Additionally, following previous studies^15,16,17, and to enhance the mix consistency, 10 wt.% lime powder was incorporated as a partial replacement of the cement. It was also decided from the trial tests that 2 different fiber percentages. i.e. 0.5% and 1% to be tested in this study. Besides, in order to maintain a desirable workability, SP ratio range of 16–22 and w/b ratio of 0.35–0.45 were determined as optimum and three levels of each parameter, i.e. SP ratio = 16, 19, 22, and w/b = 0.35, 0.40, 0.45 were respectively selected for the mixture design. Based on preliminary trial tests, two fiber dosage levels 0.5% and 1% were selected for further investigation in this study. To ensure adequate workability of the mixtures, a SP ratio range of 16 to 22 and a water-to-binder (w/b) ratio range of 0.35 to 0.45 were identified as desirable. Accordingly, three discrete levels were chosen for each parameter: SP dosages of 16, 19, and 22, and w/b ratios of 0.35, 0.40, and 0.45 were utilized in the mixture design. The mix design proportions for the PETFRM are shown in Table 3, while the mixture weights are provided in Table 4.

Table 3 Experimental design of the PETFRCM mixtures.

Table 4 Mix proportions of PETFRM mixtures.

Specimens’ preparation

After determining the mix proportions for the PETFRM samples, the sand as fine aggregates, was conditioned to a saturated surface dry (SSD) state prior to use, and tap water was employed in the preparation of the mortar mixtures. Then for the mixing procedure, the fine aggregates, cementitious materials, and fibers were initially dry-mixed for one minute. Following this, the mixing water, which had been pre-blended with the superplasticizer (SP), was gradually added while mixing continued for an additional minute. The mixture was then allowed to rest for 30 s before resuming mixing for another minute. Rheological tests were performed immediately after the mixing process. The fresh mortar was subsequently cast into molds for compressive and flexural tests, i.e. 50 × 50 × 50 mm cubes and 25 × 25 × 285 mm prismatic beams, respectively. After light compaction through gentle tapping and covering with plastic sheets, the specimens were placed in a curing room set at 20 °C with 95% relative humidity. Samples were demolded following 28 days of curing period and were prepared for mechanical testing.

Test procedures

The tests were conducted in accordance with standardized procedures. Upon completion of the mixing process, rheological tests were performed. Then, Cubic specimens were tested under compression to and beam samples were examined under flexural loading in order to assess the compressive strength and toughness under compression, as well as MOR and flexural toughness, respectively.

The testing procedures for both fresh and hardened mortar specimens are summarized in the following sections.

Test on fresh mortar

To assess the rheological properties of the PETFCM, mini slump tests was conducted in accordance with ASTM C1611, the spread diameter from the mini slump test was measured along two perpendicular axes, with the average value recorded as the mini slump flow diameter.

Test on hardened mortar

• Compressive Strength (CS): Performed on 50 × 50 × 50 mm cubic specimens in accordance with ASTM C109.

• Flexural Strength (MOR): Assessed using 25 × 25 × 285 mm beam specimens following ASTM C78.

According to the ASTM C78 Standard,

• 1. Should the fracture initiate in the tension surface within the middle third of the sample’s span length, MOR is calculated by Eq. (1).

  $$R = \frac{PL}{{bd^{2} }}$$

  (1)

  where:

  R = modulus of rupture, MPa,

  P = maximum applied load recorded by the testing apparatus, N,

  L = span length, mm,

  b = average width of sample, mm,

  d = average depth of sample, mm.

• 2. If the fracture takes place outside of the middle third of the sample’s span length by not more than 5% of the span length, MOR should be calculated through Eq. (2).

  $$R = \frac{{3P{\text{a}}}}{{bd^{2} }}$$

  (2)

  where:

  a = average distance between line of fracture and the nearest support measured on the tension surface of the beam, mm.

• 3. If the fracture starts outside of the middle third of the sample’s span length by more than 5 % of the span length, test results are not reliable.

  In this study, for all the flexural strength tests, the fractures initiated in the tension surface within the middle third of the span length, hence the modulus of rupture was calculated according to Equation (1).

Application of response surface methodology (RSM)

Response Surface Methodology (RSM) is a widely accepted statistical approach that provides a systematic and economic framework for evaluating the effects of multiple interacting variables on a specific response. In this study, RSM was applied to optimize the modulus of rupture (MOR) of cement mortar reinforced with polyethylene terephthalate (PET) fibers. A Central Composite Design (CCD) was selected for experimental planning due to its ability to efficiently capture both curvature and interaction effects through second-order polynomial modeling. The selected input factors, water-to-binder ratio (w/b), superplasticizer dosage (SP), and fiber volume fraction (F%) were systematically varied, and their influence on MOR was assessed. RSM not only supports accurate prediction with a limited number of experiments but also facilitates multi-objective decision-making and identification of optimal mix proportions. Its proven effectiveness in cement-based systems makes it a valuable tool for engineering design and optimization. The general form of the second-order (quadratic) regression model used in RSM to estimate the response variable (Y) based on multiple input factors (xi) is expressed in Eq. (3).

$$Y= {\beta }_{0} + \sum \left({\beta }_{i}{X}_{i}\right)+ \sum \left({\beta }_{ii}{X}_{i}^{2}\right)+\sum \sum \left({\beta }_{ij}{X}_{i}{X}_{j}\right)+\varepsilon$$

(3)

where Y is the predicted response (e.g., MOR), ${x}_{i}$ and ${x}_{j}$ are the coded independent variables, ${\beta }_{0}$ is the intercept term, ${\beta }_{i}$ , ${\beta }_{ii}$ and ${\beta }_{ij}$ are the linear, quadratic, and interaction coefficients respectively, and $\varepsilon$ is the random error. This model structure allows the estimation of both individual and combined effects of the input factors, making it highly suitable for analyzing complex engineering systems. Its flexibility enables accurate prediction and optimization, particularly when nonlinearity and variable interactions play a significant role in determining the system response^61,63,71,72.

Results and discussion

Test results of fresh mixes

The results (see Fig. 4) reveal a clear rheological trend in which the incorporation of PET fibers into mortar mixtures substantially impairs their workability. Approximately 50% of the mix designs exhibited insufficient flowability. Notably, Fig. 5 presents the mini-slump flow diameter for all mixes, computed as the average of two perpendicular measurements. PET addition reduced flowability relative to the PET-free control (D0: 350 mm). For 0.5% PET (D1-D3), the average flow increased with w/b and SP, from 105 mm (D1) to 118 mm (D2) and 138 mm (D3), indicating improved spread at higher water/admixture levels. At 1.0% PET (D4-D6), flow stabilized near 100 mm across the w/b-SP range, reflecting the dominant influence of fiber dosage on fresh behavior and the onset of fiber-induced internal friction/cluster formation. Overall, the results confirm that while w/b and SP modulate rheology, PET dosage governs the flow regime under the tested conditions. This reduction in workability has also been reported in several studies^59,60,73. The impaired flowability is mainly attributed to the high aspect ratio, rigidity, and hydrophobic nature of PET fibers, which promote fiber clustering and internal friction, thereby resisting deformation under load^37,58.

Fig. 4

Workability of Mixtures containing PET fibers.

Fig. 5

Mini-slump flow diameter (mm) by mix (mean of two perpendicular spreads).

Compressive strength and toughness

For each design, two samples were tested under compression and the average values were obtained. Table 5 summarizes the average test results of compressive strengths and toughness values from compression tests.

Table 5 Summary of compressive strength and toughness values derived from compression tests for different mixtures.

It is observed from the results presented in Table 5 that D1 and D2 proved to be the optimum designs for toughness and compressive strength, respectively. It is also worth noticing that D4 and D1 represent the first and second highest values for the compressive strength, while those of the toughness are D1 and D4, respectively.

The experimental results reveal a trend in the mechanical performance of the PET fiber-reinforced cement mortars. In the 0.5% PET fiber group (D1-D3), a noticeable reduction in compressive strengths was observed with an increase in the water-to-binder (w/b) ratio. For example, Mix D1 (w/b = 0.35) achieved an average compressive strength of 45.02 MPa, while Mix D3 (w/b = 0.45) exhibited only 26.7 MPa. This decline aligns with the anticipated behavior of cementitious materials, where higher water content results in increased porosity, thereby leading to a decrease in strength properties⁵¹. An excessive water-to-cement ratio adversely affects the structural integrity of the cementitious matrix by increasing porosity, and hence weakening the overall mechanical properties of the material.

Compared to the specimens containing 0.5% PET fibers, the 1% fiber-reinforced mortar series (D4–D6) exhibited a more pronounced decline in compressive strength with increasing water-to-cement ratios. This trend suggests that the combined effects of elevated water content, leading to greater porosity and higher fiber volume, which may impair the matrix-fiber interfacial bonding, exacerbate the negative impact of excessive water. While an increased volume of PET fibers can enhance crack resistance and load-bearing capacity, overly high dosages may result in fiber balling and entanglement, compromising the uniformity and mechanical integrity of the mix. Therefore, a meticulous optimization of fiber content along with other influencing design parameters is essential to achieve a balanced enhancement in performance without sacrificing the composite material’s homogeneity. The experimental findings corroborate several key aspects observed in recent literature. For example, the reduction in mechanical strength with higher water-to-binder ratios is well-documented^{15,46,60,74,75,76}.

For a better illustration of the results with respect to design variables and an easier comparison, the load displacement curves along with the area under the curve (toughness) are plotted and displayed for different Fiber % and w/b ratios in Figures. 6 and 7. It is observed form the plots that w/b plays a major role in the compressive strength of the mortar samples at both fiber percentages of 0.5 and 1. It is also observed that while the mixes with w/b = 0.40 and 0.45 show a very similar behavior at F% = 0.5, a clear increase in strength and toughness at those w/b values are noticed at F% = 1.

Fig. 6

Load–displacement and toughness behavior of the samples under compression for different w/b rations in samples with (a) 0.5% PET fiber and (b) 1% PET fiber.

Fig. 7

Load–displacement and toughness behavior of the samples under compression containing different PET fiber % at different w/b ratios (a) w/b = 0.35, (b) w/b = 0.40 and (c) w/b = 0.45.

In our PETFRM mixes, PET addition generally reduced compressive strength; at w/b = 0.35, the loss was negligible (D4 = 47.17 MPa, − 0.9% vs. D0 = 47.6 MPa), while D1 = 45.02 MPa (− 5.4%). Raising w/b to 0.45 caused severe drops (D3/D6 ≈ − 44% to − 46%), confirming w/b as the dominant factor. Studies on hybrid fiber-reinforced MOC composites often report concurrent strength retention/improvement at optimal hybrid dosages due to denser matrices/ITZ and synergistic bridging, consistent with our finding that matrix quality governs peak load, while fiber dosage mainly shapes post-peak response^59,73,77.

MOR and flexural toughness

Two prismatic specimens were tested for each design under flexural loading and the average values were calculated. Presented in Table 6 are the average values of MOR and the flexural toughness obtained for each design.

Table 6 Summary of MOR and the flexural toughness obtained for each design values derived from flexural tests for different mixture compositions.

The results exhibit that design 1 (D1: F = 0.5%, w/b = 0.35) and design 4 (D4: F = 1%, w/b = 0.35) show the same greatest average MOR values equal to 7.67 MPa, where the second rank belongs to D2 with the value of 7.44 MPa. However, comparing the flexural toughness of various designs indicate that D1 and D2 show the same highest values equal to 0.12 kN.mm with D4 being the second highest flexural toughness with the value of 0.11 kN.mm.

The entire load–displacement performance of all deigns along with the flexural toughness areas are illustrated in Figures. 8 and 9. It is vividly observed in Fig. 8(a) that the peak of the curves increases by decreasing the w/b ratio. However, this pattern is more notable in mixes containing 0.5% of fibers. It can be attributed to the fact that due to lower w/b ratios and lower fiber entanglement, a denser microstructure with less porosity is achieved that can result in a stronger fiber-matrix boning, thereby leading to a higher MOR in mixtures with lower fiber percentage. However, in samples with higher fiber volume i.e. 1%, the bridge effect of fibers can partially compensate for the MOR reduction due to higher porosity.

Fig. 8

Load–displacement and toughness behavior of the samples under flexural loading for different w/b rations in samples with (a) 0.5% PET fiber and (b) 1% PET fiber.

Fig. 9

Load–displacement and toughness behavior of the samples under flexural loading containing different PET fiber % at different w/b ratios.

By comparing the flexural behavior curves at different fiber percentage and constant w/b, there can be seen a notable shift in the load–displacement curves towards the left the plot as the fiber percentage increases. It indicates that the deformation of the samples containing 1% fibers under a certain flexural load is less than that of samples with 0.5% fibers. Hence, the toughness and ductility of the mixtures incorporating 1% of fibers are improved relative to those of 0.5% fibers. However, the effect of fibers on the peak load of the curve for every w/b ratio may not be as significant.

MOR peaked at w/b = 0.35 for both F = 0.5% and F = 1.0% (7.67 MPa, ≈ + 11.5% vs. D0 = 6.88 MPa); at w/b = 0.40 and F = 0.5%, D2 = 7.44 MPa (+ 8.1%). These modest but consistent gains align with reports that matrix densification/ITZ quality controls near-peak bending capacity, whereas hybrid MOC systems can sustain higher peaks when hybrid fibers and reactive additives (e.g., MK, GGBFS) jointly refine the matrix^59,73,77.

Relative to D0 = 0.07 N·m, flexural energy absorption increased by ≈ + 71–74% at F = 0.5% (D1/D2 = 0.12 N·m) and ≈ + 57% at F = 1.0% (D4 = 0.11 N·m), confirming a substantially more ductile, energy-absorbing response. This trend, larger post-peak gains than peak-load gains, is consistent with the broader fiber-reinforced literature and with hybrid MOC studies that attribute enhanced toughness/ductility to crack-bridging, pull-out, and crack-path deflection; differences in magnitude reflect matrix chemistry (MOC vs. Portland mortar), fiber system (hybrid vs. PET-only), and scale^59,73.

Our flexural energy absorption rose substantially≈ + 71–74% (F = 0.5%) and ≈ + 57% (F = 1.0%) vs. the control-reflecting a more ductile, post-peak response. The companion study likewise shows fracture-toughness (R-curve) enhancement and higher K with PET (notably at 0.5%), and reports load-bearing capacity improvements of ≈ + 10–30% for 0.5–1.5% PET, both attributable to fiber bridging/pull-out and crack-path deflection⁶³. As the fiber percentage increased, we observed commensurate gains in flexural strength and post-peak energy absorption, which depend critically on interfacial bonding for efficient load transfer between fibers and the cement matrix, an outcome also documented in related studies^4,62,63.

In term of post-peak and ductility about mixes that showed in Figs. 6–9, the control mix drops steeply after the peak load, showing a brittle response. With PET fibers, the descending branch becomes gentler and the curves carry more load at larger deflections. In practice, that means cracks keep opening but fibers bridge and slow crack growth, so the beam doesn’t “snap”, it dissipates more energy. At F = 0.5%, you get the best balance: a high peak plus a noticeably extended tail. At F = 1.0%, the tail is even longer (more ductile, more post-peak work), though the peak can be more sensitive to dispersion/workability. Another way to see it on the plots: at the same mid-span deflection beyond the peak, fiber-reinforced mixes hold a higher residual load than the control, confirming a more ductile, energy-absorbing behavior consistent with the toughness results and our SEM observations of crack-bridging and pull-out.

Microstructural interpretation (SEM)

Representative SEMs of the control mortar (D0) and a PET-reinforced mix are shown in Fig. 10(a,b). In D0, the fractured surface shows a relatively dense paste with fine capillary porosity and a more direct crack path, consistent with higher peak strength for a given w/b but limited post-peak energy absorption. In contrast, the PET-reinforced specimen exhibits multiple PET filaments with local bundles/clusters; a thin interfacial gap/porous ITZ and entrapped voids are occasionally visible adjacent to clusters. Given the fibers’ smooth surface (also seen at higher magnification), bonding is primarily frictional/mechanical, so dispersion quality strongly governs load transfer. These features rationalize our mechanical trends: at moderate F% (0.5%) and low w/b, well-dispersed fibers deflect cracks and bridge them, increasing the area under the load–deflection curve (toughness) with minimal penalty to MOR/CS; at higher F% (1%), clustering-induced voids/weak ITZ reduce peak load and MOR, yet pull-out and bridging still enhance post-peak ductility.

Fig. 10

SEM of (a) control mortar (D0) showing a dense matrix and relatively straight fracture path; (b) PET-reinforced mortar showing parallel PET filaments with occasional bundles and nearby voids/porous ITZ, plus evidence of crack deflection/bridging that underpins the observed toughness gains. (Instrument: Hitachi S-4800, 5.0 kV; scale bars as shown.)

Response Surface Analysis of MOR

Informed by preliminary trials and prior studies, the selection of experimental variables and their respective ranges was designed to capture the most influential parameters affecting the flexural performance of PET fiber-reinforced mortar. As detailed in Table 7, three independent input factors were considered for the response surface design: the water-to-binder ratio (w/b), varied between 0.35 and 0.45; superplasticizer dosage (SP), ranging from 16 to 22 kg/m³; and the fiber volume fraction (F%), set between 0.0% and 1.0%. These levels were chosen to reflect practical design limits and to enable the identification of both linear and nonlinear effects through a systematic modeling approach.

Table 7 Variables and their range of variation.

Using a Central Composite Design (CCD), an experimental matrix was developed to explore the individual and interactive effects of the selected variables. The modulus of rupture (MOR), obtained from flexural strength testing, was adopted as the response variable for model construction. A second-order polynomial regression equation was fitted to the data. During model refinement, interaction terms that did not contribute significantly namely, w/b × SP, w/b × F%, and SP × F%, were eliminated to improve model simplicity and reliability. The final regression model, formulated in uncoded units (Eq. (4)), captures the quantitative relationships between input variables and the MOR response.

$$\begin{aligned} MOR = & - 10.38 - 63.03(X_{1} ) + 3.513(X_{2} ) \\ & + 2.261(X_{3} ) + 62.00(X_{1} )^{2} \\ & - 0.09472(X_{2} ) - 2.300(X_{3} )^{2} \\ \end{aligned}$$

(4)

where:

$${X}_{1}=W/b$$

$${x}_{2}=SP$$

$${X}_{3}=F\%$$

The final regression model, derived from the experimental data specific to this study, accurately reflects both the linear and nonlinear effects of the influencing variables and demonstrates strong potential for guiding the optimization of flexural strength in PET fiber-reinforced mortars.

The response surface contour plots generated in this study offer valuable visual insights into the interaction effects among water-to-binder ratio (w/b), superplasticizer dosage (SP), and fiber content (F%) on the modulus of rupture (MOR) of PET fiber-reinforced cement mortar.

Figure 11(a) illustrates the interaction between superplasticizer dosage (SP) and water-to-binder ratio (w/b) on the modulus of rupture (MOR), with fiber content maintained at 0.5%. The results indicate that maximum MOR values (> 8 MPa) occur at lower w/b ratios (0.35–0.38) combined with moderate to high SP levels (19–21 kg/m³). In contrast, higher w/b ratios consistently reduce MOR, especially when SP dosage is insufficient, underscoring the importance of jointly optimizing these parameters to improve flexural performance.

Fig. 11

Response surface and contour plots of variables and their interaction; (a) Interaction Effect of Water-to-Binder Ratio and Superplasticizer on MOR; (b) Interaction Effect of Water-to-Binder Ratio and Fiber content on MOR; (c) Interaction Effect of Superplasticizer and Fiber content on MOR.

Figure 11(b) presents the combined effect of w/b and PET fiber volume fraction (F%) on MOR at a fixed SP dosage of 19 kg/m³. An increase in fiber content up to approximately 0.5% enhances MOR, beyond which performance gradually declines. The optimal range corresponds to w/b ratios between 0.35 and 0.38 and F% around 0.4–0.6%, indicating that excessive water or fiber dosage may impair matrix integrity and fiber-matrix interaction.

Figure 11(c) shows the interaction between SP and F% at a constant w/b ratio of 0.40. A distinct elliptical contour pattern is observed, with MOR peaking at SP ≈ 19 kg/m³ and F% ≈ 0.5%. Further increases in either parameter result in reduced MOR, likely due to segregation effects or reduced homogeneity. These trends confirm that both SP and F% exhibit nonlinear behaviors, and their concurrent optimization is essential to achieve maximum flexural strength in PET fiber-reinforced mortars.

The response surface contour plots offered valuable insights into how the combined effects of water-to-binder ratio (w/b), superplasticizer dosage (SP), and fiber content (F%) influence the modulus of rupture (MOR) in PET fiber-reinforced mortar. Among all variable combinations, lower w/b ratios consistently yielded superior MOR, underscoring the negative influence of excess water on matrix strength and fiber bonding. Additionally, an SP dosage of approximately 18–19 kg/m³ and a fiber volume fraction near 0.5% were identified as optimal levels that maximize MOR. Deviations from these ranges, particularly higher values of SP or F%, resulted in diminished performance, likely due to matrix instability, segregation, or poor fiber dispersion. These findings clearly indicate that maximum flexural strength is achieved through the synergistic tuning of all three parameters, rather than adjusting each variable in isolation, thereby reinforcing the importance of integrated multi-variable optimization in mortar mix design.

The RSM-based optimization was performed to identify the most favorable combination of design parameters for maximizing the modulus of rupture (MOR) in PET fiber-reinforced mortar. As illustrated in Fig. 12, the optimization plot shows how each variable independently affects the predicted MOR within its tested range.

Fig. 12

Optimization plot showing the predicted maximum MOR.

The analysis reveals that w/b ratio exhibits a strictly decreasing trend, where any increase in water content results in a steady reduction in MOR. This behavior confirms the well-established detrimental effect of excess water on matrix density and fiber-matrix bonding. In contrast, both superplasticizer dosage (SP) and fiber volume fraction (F%) demonstrate nonlinear (curvilinear) behavior, with MOR increasing up to an optimal point and then declining beyond that. This is indicative of a balance between improved workability and dispersion at moderate levels versus matrix segregation or fiber clustering at higher dosages.

The optimization model predicts a maximum MOR of 8.29 MPa under the following optimal conditions: w/b = 0.35 (lowest tested level), SP = 18.55, F% = 0.495.

These values are highlighted by red lines on each subplot in Fig. 12. The desirability score of 1.000 indicates a perfect optimization outcome, reflecting a high level of agreement between the target objective and the fitted model. Notably, the linear effect of w/b differs fundamentally from the parabolic behavior of SP and F%, reinforcing the importance of treating each variable according to its specific influence pattern. These findings confirm that a coordinated, multi-parameter adjustment rather than isolated tuning, is essential for achieving optimal flexural strength in cementitious composites reinforced with PET fibers.

These findings confirm that a coordinated, multi-parameter adjustment rather than isolated tuning, is essential for achieving optimal flexural strength in cementitious composites reinforced with PET fibers. Moreover, the predicted optimal MOR closely aligns with the experimental results obtained in this study, thereby validating the accuracy of the RSM model and demonstrating its practical effectiveness as a tool for mix design optimization in fiber-reinforced cementitious systems.

Analysis of variance and regression coefficients

ANOVA was used to summarize variance attribution of the fitted quadratic model (Table 8). The model explains an adjusted sum of squares (Adj SS) of 5.12283 over 6 DF: Linear terms (w/b, SP, F) account for 1.94344 (with w/b = 1.35341 dominating), and Quadratic terms for 0.90624 (notably SP² = 0.72676, F² = 0.39664). With 7 runs and 7 fitted parameters (intercept + 6 terms), the design is saturated (residual DF = 0); therefore F-values, p-values, and lack-of-fit are not estimable. Interactions were screened and removed during model refinement based on Adj SS and parsimony.

Table 8 ANOVA summary for the quadratic MOR model (uncoded units).

The final uncoded regression for MOR (MPa) is:

$$MOR=-10.38 -63.03\left(W/b\right)+3.513\left(SP\right)+2.261\left(F\%\right)+62.00\left(W/b\right)^2-0.09472\left(SP\right)-2.300\left(F\%\right)^2$$

(5)

With w/b (–), SP in kg·m⁻³, and F in %. Coefficient signs match mechanics: w/b is strongly detrimental (negative linear, positive curvature), SP and F show concave optima (negative quadratic). VIFs are all < 2 (Table 9), indicating no multicollinearity.

Table 9 Regression coefficients, signs, and multicollinearity diagnostics (VIF) for the MOR model.

Comparison between predicted and experimental MOR values

Figure 13 presents a predicted-versus-measured parity plot for MOR across D0-D6. The solid line denotes the 1:1 identity, while the dashed lines illustrate small bias envelopes (+ 2% and − 4%) around the identity. All fiber-containing mixes (D1-D6) cluster tightly about the 1:1 line, with relative errors ≤ 0.17%, confirming that the quadratic model accurately captures the response over the PET-reinforced domain. The control mix (D0) exhibits the largest deviation (− 7.5% under-prediction), which is consistent with the model being chiefly calibrated to the fiber-reinforced region. The overall agreement is high (parity R² ≈ 0.99), supporting the adequacy of the fitted surface for optimization within the tested factor ranges.

Fig. 13

Predicted vs. measured MOR for D0–D6. Solid line = 1:1; dashed =  + 2%/ − 4% envelopes. Points cluster near identity (R² ≈ 0.99); D1–D6 show ≤ 0.17% error, while the control D0 has the largest deviation (− 7.5%).

Parametric study and correlation analyses

Parametric study

In order to evaluate the influence of each variable on the strength, toughness, and MOR of the fiber reinforced cement mortar, a comprehensive parametric study was implemented as presented in this section. It should be mentioned that the results of all replicates are presented in the parametric study. Further, the correlation analyses of the afore-mentioned mechanical properties were performed which are presented in the following.

Figure 14 displays the variations of toughness under compression in terms of three design variables, i.e. Fiber%, w/b, and SP, while Fig. 15 represents the effect of those variables on the compressive strength. Figures 16 and 17 show the changes in the MOR and flexural toughness based on various levels of each mixture deign parameter.

Fig. 14

Influence of design variables on toughness under compression for (a) various F% and w/b, and (b) various F% and SP.

Fig. 15

Influence of design variables on compressive strength for (a) various F% and w/b, and (b) various F% and SP.

Fig. 16

Effect of design variables on MOR for (a) various F% and w/b, and (b) various F% and SP.

Fig. 17

Effect of design variables on flexural toughness for (a) various F% and w/b, and (b) various F% and SP.

The parametric study demonstrated that the mechanical performance of PET fiber-reinforced mortar is highly dependent on the fiber content and w/b ratio, while the SP dosage effect is negligible. Increasing PET fiber content from 0.5% to 1.0% generally enhanced toughness under both compression and flexure, but this trend was not consistent across all the mix designs. Optimal toughness was achieved at 0.5% fiber content combined with lower w/b ratios (especially 0.35) and moderate SP dosage (19), suggesting that an improved matrix compactness and workability promote better fiber dispersion and bonding.

Conversely, higher fiber volumes in the mixes with higher w/b ratios or insufficient SP dosage led to reductions in both compressive strength and toughness, likely due to poor fiber distribution and increased porosity. Regarding MOR, improvements were primarily associated with reduced w/b ratios rather than fiber content alone, indicating that matrix density, and hence fiber-matrix bonding play a critical role in flexural strength enhancement.

Overall, the results indicate that PET fibers can improve mortar performance, but only when mix design parameters are carefully optimized to ensure homogeneity, adequate workability, and a strong matrix-fiber interaction.

Correlation analyses

Correlation analyses of strength and toughness properties were carried out to find out how well the various properties are correlated. The average test results were used in correlation analyses and the control sample with 0% fiber was not included. It is worth mention that since the compressive strength of the cement mortar is the major mechanical characteristic for structural performance of the composite, the correlations of toughness and MOR properties with the compressive strength were mainly evaluated. Figure 18 shows the correlations and trend line equations of toughness under compression vs. compressive strength (a), MOR vs. compressive strength (b), flexural toughness vs. compressive toughness (c), and MOR vs. flexural toughness (d). As indicated in the plots, there is strong correlation between compressive strength-compressive toughness as well as compressive strength-MOR with coefficient of determinations equal to R² = 0.90 and R² = 0.96, respectively. However, a relatively lower correlations is observed for each pair of flexural toughness-compressive toughness and flexural toughness-MOR with very close coefficients of determinations equal to R² = 0.748 and R² = 0.746, respectively.

Fig. 18

Correlation analysis results between different pairs of strength, toughness, and MOR.

To summarize, the correlation analyses demonstrated notable relationships between strength and toughness parameters in PET fiber-reinforced cement mortar. Compressive strength showed a strong linear correlation with compressive toughness (R² = 0.90), indicating that improvements in compressive strength are closely linked to enhanced energy absorption under compressive loading. An even stronger relationship was observed between compressive strength and the modulus of rupture (MOR), with R² reaching 0.96. This suggests that increased compressive strength significantly contributes to flexural performance, possibly due to better matrix consolidation and fiber-matrix interaction at higher strength levels.

In contrast, the correlation between compressive and flexural toughness was moderate (R² = 0.748), with a relatively low slope, implying that although a positive relationship exists, the rate of increase in flexural toughness with respect to compressive toughness is limited. This may be attributed to the different mechanisms of energy dissipation in compressive and flexural loading conditions. Similarly, the relationship between flexural toughness and MOR was also moderate (R² = 0.746), suggesting that while increased MOR contributes to enhanced flexural energy absorption, other influencing factors such as fiber dispersion, alignment, and interfacial bonding are also significant.

Overall, the results highlight that compressive strength is a strong predictor of both compressive toughness and MOR, whereas the development of flexural toughness appears to depend on a more complex interplay of mechanical and microstructural parameters.

Conclusions

The following concluding remarks were found in this study:

• Compressive strength vs. toughness in mixes with PET addition generally reduced compressive strength; however, at low w/b = 0.35 the loss was negligible. Among fibered mixes, D4 (w/b = 0.35, SP = 19, F = 1.0%) achieved 47.17 MPa (− 0.9% vs. control D0 = 47.6 MPa), and D1 (F = 0.5%) reached 45.02 MPa (− 5.4%). Raising w/b to 0.45 caused severe drops (D3/D6 =  − 44 to − 46%), confirming w/b as the dominant factor. In contrast, compressive toughness improved at low w/b with PET: D1 = 77.60 kN·mm (+ 7.5% vs. D0) and D4 = 76.39 kN·mm (+ 5.8%), while higher w/b reduced toughness (D3 − 23.4%, D6 − 15.4%, D5 − 15.2%). Actionable settings: for balancing strength retention and energy absorption, target w/b = 0.35, SP = 19 kg/m³, F = 0.5–1.0%, use 0.5% when peak strength/MOR is prioritized and 1.0% when post-peak toughness/ductility is the main objective. (For context: MOR peaked at 7.67 MPa at w/b = 0.35 (D1/D4); the RSM optimum predicts 8.29 MPa at w/b = 0.35, SP = 18.55, F = 0.495%.)

• MOR and flexural toughness. The highest MOR was obtained at low w/b = 0.35 in both D1 (F = 0.5%, SP = 16) and D4 (F = 1.0%, SP = 19), each reaching 7.67 MPa (+ 11.5% vs. control D0 = 6.88 MPa); D2 (w/b = 0.40, F = 0.5%) achieved 7.44 MPa (+ 8.1%), whereas higher w/b = 0.45 mixes showed reductions (D3/D5/D6: − 15.6% to − 16.6%). Flexural toughness peaked in D1/D2 = 0.12 N·m (+ 71.4% vs. D0 = 0.07 N·m), with D4 = 0.11 N·m (+ 57.1%); higher w/b reduced toughness (D3: + 28.6%, D5: + 42.9%, D6: + 14.3% relative to D0). Actionable settings: to maximize MOR while maintaining high toughness, target w/b ≈ 0.35 with SP ≈ 18–19 kg/m³ and F ≈ 0.5%; if post-peak ductility is prioritized, F ≈ 1.0% is effective provided flow/dispersion are controlled (consistent with the observed SEM trends).

• The compressive strengths generally experienced reductions due to fiber addition, however D4 mixture containing 1% fibers demonstrated the highest strength among fibrous samples. The highest compressive toughness values occurred in D1 and D4 mixtures with 0.5% and 1% fibers, respectively.

• The equally highest values of MOR were obtained in D1 and D4, but those of flexural toughness turned out to be in D1 and D2, with D4 being the second highest value in the mix design.

• It was concluded that the w/b ratio increase resulted in a decrease in all mechanical properties, though the reductions in strength properties were more pronounced than toughness properties. However, a higher w/b ratio improved the workability of the mix.

• It was found from correlation analyses that there was a strong relationship between compressive strength vs. compressive toughness as well as compressive strength vs. MOR, with R² = 0.90 and R² = 0.96, respectively. However, the correlations between compressive toughness—flexural toughness and MOR- flexural toughness were not as high, respectively equal to R² = 0.748 and R² = 0.746.

• It was concluded that the F% and w/b parameters were more influential than SP ratio. Besides, it was concluded that a trade-off between F% and w/b is crucial. An increase in the water-to-binder ratio generally resulted in a reduction of the mechanical properties. The incorporation of 0.5% PET fibers yields higher strength values compared to 1% PET fibers, where workability issues become more pronounced.

• While PET fibers improve post-cracking behavior and enhance ductility in cementitious composites, the fiber dosage must be carefully optimized to prevent negative impacts on workability and overall mechanical performance.

• RSM results indicated that the maximum MOR that can be achieved in this study occurs at lower level, middle level, and middle level of w/b, SP, and F%, respectively.

• An optimal PET fiber content, approximately 0.5% by volume, offers a balanced approach by enhancing ductility while maintaining acceptable workability and minimizing adverse effects on mechanical strength.

• In term of Practical significance (real-world use). Taken together, our results position PET-fiber-reinforced mortar as a practical, energy-absorbing overlay/repair material where post-cracking toughness and crack control are decisive (e.g., thin overlays, plasters, small precast elements, and impact/abrasion-exposed repairs). Guided by the RSM map and fresh-state measurements, a field-realistic mix window of w/b = 0.35–0.38, SP = 18–21 kg/m³, and PET = 0.4–0.6 vol.% achieves a workable mini-slump = 115–140 mm while sustaining high MOR (~ 8 MPa) and enhanced toughness, balancing placement/castability with mechanical performance. Where maximum energy absorption is prioritized (e.g., impact-sensitive patches), PET = 1.0 vol.% can be used with the expectation of lower flow (~ 100 mm) and MOR plateauing; in such cases, apply dispersion-oriented practices (accurate SP within the stated bounds, staged fiber addition, short high-shear mixing bursts, and light table vibration) to limit clustering/voids. Excess PET or SP should be avoided due to segregation risks that undermine flexural response. Beyond performance, PET fibers provide a corrosion-free, low-density, recycled reinforcement that helps divert plastic waste, aligning structural repair practice with circular-economy goals."