Large rupture strain cotton ropes hybridized with affordable fiberglass chopped strand mat sheets for enhanced compressive behavior of reinforced concrete columns

Abstract

The hybrid confinement system combines various fiber types within a single matrix, allowing for the adjustment of volumetric ratios to optimize confinement performance. Synthetic FRPs are more expensive and have a higher carbon footprint due to significant CO₂ emissions during production. In response, this study presents an innovative hybrid confinement approach using two natural materials: cotton ropes and FSMS (CFS) to improve concrete strength and ductility. Specimens, standardized at 300 mm height and 150 mm diameter with longitudinal steel bars and stirrups, were divided into two groups based on CFS configurations. The stress-strain response of CFS-confined concrete displayed distinctive behavior: an initial parabolic phase leading to peak compressive stress (ultimate strength), followed by a linearly degrading phase. Across all subgroups, CFS confinement significantly enhanced ultimate strength and corresponding compressive strains, with Subgroup 2A achieving the highest improvements of 246 % in ultimate strength and 1477 % in strain. Moreover, the ductility gain was reported as high as 20 for CFS-confined concrete. A non-proportional enhancement in the compressive behavior was observed with the increase in confinement ratio. Predictive models were developed for the idealized two-branch response of CFS-confined concrete, encompassing expressions based on nonlinear regression for ultimate strength, corresponding strain, ultimate strain, and elastic modulus. Two existing models were modified to trach each branch of the response. Integrating these two adjusted models closely replicated the experimental compressive curves.

1. Introduction

Substantial damage to aged structures from was extensively reported [[1], [2], [3]], often ascribed to insufficient reinforcement detailing that not meeting modern design standards [4,5]. This underscores the urgency of reinforcing existing structures with outdated designs. Traditional methods mainly comprise steel [[6], [7], [8], [9]] or reinforced concrete (RC) wraps [10,11]. But, there has been a shift towards fiber-reinforced polymer (FRP) wraps for their advantages such as relatively cheaper costs, stronger resistance against corrosion, higher strengths at similar weights, and easier applications compared to conventional methods [12,13].

In the past decade, researchers have increasingly focused on using environmentally friendly materials. Synthetic FRPs, such as those made with aramid or carbon fibers, have proven effective in reinforcing existing structures [[14], [15], [16]]. But the latest rise of natural FRPs has piqued researchers' interest. Contrary to synthetic FRPs, their natural counterparts are produced with no synthetic chemicals, offering environmentally friendlier results for strengthening works [17]. Furthermore, a single layer of synthetic FRP can reach 150 USD for 1 m² [18]. The significant cost of synthetic FRPs poses a challenge for researchers, leading to a focus on exploring cheaper solutions for replacement, especially FRPs made from natural materials [19]. Even with their cheaper prices over synthetic FRPs, their natural counterparts have proven effective in various structural rehabilitation works. Till date, natural FRPs have successfully been employed to escalate the compressive response of concrete [[20], [21], [22], [23]], upgrading the shear resistance of concrete [19,24], and improving the flexural capacity of RC members [[25], [26], [27]].

Ropes made with natural fibers are found effective in various strengthening works, similar to natural FRPs. Hussain et al. [28] employed hemp and cotton confinements to improve the response of concrete specimens of square shape by varying the corner radius, indicating a correlation among strength enhancement and the size of corner radius. Rodsin et al. [29] conducted a comparison of the confinement effects on circular concrete specimens using cotton ropes, carbon, and glass FRPs. They found that samples strengthened with cotton exhibited greatest improvement in compressive response. Joyklad et al. [30] proposed cheap fiberglass sheets of chopped strand mats (FSMS) to improve the mechanical characteristics of concrete incorporating recycled bricks coarse aggregates. Their findings demonstrated improvements reaching 360 % in compressive strength and 560 % in ultimate strain. In a separate study, Joyklad et al. [17] noted a significant increase of up to 320 % in the compressive strength of recycled brick aggregate concrete with the application of FSMS confinement. Sen and Paul [31] reported up to 66 % and 48 % improvement in the compressive strength due to sisal and jute FRP confinement, respectively. Bai et al. [32] enhanced the dynamic compressive behavior of concrete by using unidirectional natural flax FRP and reported significant improvement against impact loads. Numerous other studies also demonstrated the efficacy of natural FRPs in developing the compressive response of concrete [22,28,33,34].

Hussain et al. [22] highlighted that cotton confinement exhibit a large tensile strain, exceeding 0.15. In latest years, Large Rupture Strain (LaRS) confinement has gained attention. Mei et al. [35] enhanced the shear performance of RC columns using LaRS PET FRP and noticed significant improvements. Bai et al. [36] enhanced the seismic performance of RC circular columns using PET FRP. Bai et al. [37] also enhanced the lateral response of circular RC columns with high axial loads using PEN FRP, whereas the performance of square columns were also enhanced by Bai et al. [38]. In another work [39,40], analytical models were proposed for LaRS-confined concrete. Traditional FRP-strengthened RC often fail due to FRP tear. Nonetheless, RC columns reinforced with LaRS FRPs, which have a rupture strain exceeding 5 %, can mitigate this failure mode, thereby enhancing seismic performance [41,42]. Despite their effectiveness in providing confinement, FSMS typically rupture at lower strains, approximately between 1.5 % and 2.5 %. Additionally, cotton has a tensile capacity exceeding 130 MPa [30]. Therefore, combining cotton and fiberglass FSMS wraps could address the limitations of both methods. The hybridization of confinements integrates different fiber types within a single matrix, enabling the adjustment of volumetric ratios to achieve optimal confinement effects. This approach presents promising strengthening methods for improving the seismic response of RC structures. Bai et al. [43] introduced a hybrid system that combines carbon FRPs with PET or PEN FRPs to capitalize on the high tensile strains of PET and PEN confinement. It was found that concrete solely under CFRP confinement exhibited brittle response, whereas the combination of CFRP with each of PET or PEN confinement resulted in progressive failure modes. Acknowledging the brittleness of CFRP, Ribeiro et al. [44] suggested combining CFRP with E-glass or basalt FRPs. This hybridization approach led to progressive failure in the confined concrete. Varma et al. [45] hybridized jute and basalt FRPs and noted improvement in the compressive strength, energy absorption, and resistance to alkaline environments of concrete. Other researchers have also documented substantial improvements in compressive response by hybridization of CFRP and PET FRP [46,47]. Therefore, it is important to note that achieving increased ductility involved initially strengthening the concrete with FRPs that have low tensile strains, preceded by applying FRPs with high rupture strains. The compatibility among lateral deformation of core and strengthening FRPs is assumed. FRPs applied first, with lower tensile strains, are anticipated to rupture earlier, followed by the failure of outer FRPs facilitating the progressive failure of the outer FRP layers and thereby enhancing the compressive response of the strengthened concrete.

The current argument underscores the efficiency of hybridized strengthening, particularly in strengthening concrete to fulfill seismic requirements. This work introduces an innovative hybridized confinement method using two natural confinements: cotton ropes and FSMS (CFS). The proposed hybridization aims to improve the compressive response of concrete made with natural aggregates, offering a green solution. Additionally, the work proposes equations to predict the compressive strength and strain of CFS-confined concrete. The proposed equations are then incorporated into a design-oriented scheme to trace the compressive behavior of concrete under CFS strengthening.

2. Experimental framework

2.1. Specimen details and their classification

In this study, two groups were formed based on the configuration of CFS confinement. All specimens had a height of 300 mm and a diameter of 150 mm. Fig. 1 shows the typical dimensions of specimens. Four longitudinal steel bars of 12 mm diameter were used. Two stirrups of 6 mm diameter were also used at each end. The details of all samples are presented in Table 1. Each group was further divided into two subgroups, labeled Type I and Type II, based on their compressive strength characteristics. Group 1 specimens were reinforced with varying numbers of FSMS layers, while maintaining one layer of cotton ropes. In contrast, both cotton and FSMS layers were adjusted in Group 2, where the number of strengthening wraps ranged from 1 to 3. Moving forward, samples are designated as follows: the first letter indicates the cross-sectional shape (C for circular). The second letter denotes the type of unconfined concrete strength (I for low strength, II for high strength). Lastly, the last part specifies the quantity of external wrap layers. The first Arabic number represents the number of internal FRP wraps, with the first characters signifying the nature of internal FRP (G for FSMS). The following Arabic numbers and characters specify the number and nature of external FRP wraps (C for cotton), respectively.

Fig. 1.

(a)Typical specimen details and (b) typical steel cage of specimens.

Table 1.

Summary of specimens used in this study.

Group	Subgroup	Specimen Name	Type of Unconfined Strength	Quantity
				FSMS	Cotton
1	1A	C-I-CON	I	None	None
		C-I-1G1C	I	1	1
		C-I-2G1C	I	2	1
		C-I-3G1C	I	3	1
	1B	C-II-CON	II	None	None
		C-II-1G1C	II	1	1
		C-II-2G1C	II	2	1
		C-II-3G1C	II	3	1
2	2A	C-I-CON	I	None	None
		C-I-1G1C	I	1	1
		C-I-2G2C	I	2	2
		C-I-3G3C	I	3	3
	2B	C-II-CON	II	None	None
		C-II-1G1C	II	1	1
		C-I-2G2C	II	2	2
		C-II-3G3C	II	3	3

Note: Type I represents 15 MPa, and Type II corresponds to 25 MPa.

2.2. Material properties

ASTM D3039/D3039M − 17 [48] guidelines are followed to establish the mechanical characteristics of FSMS and cotton ropes. The calculated properties are detailed in Table 2. In this study, the cotton ropes were obtained from Nanacenter Supply, Bangkok, Thailand. The FSMS and resin were purchased from Rugsvanic Company Ltd., Bangkok, Thailand. Importantly, cotton exhibited a rupture strain of 13.40 %, that is 437 % higher than the strain of FSMS. The size and diameter of FSMS were 0.52 mm and for cotton 2.45 mm, respectively, with the tensile capacity of FSMS being 39.50 % greater than that of cotton. The tensile and flexural strength of polyester resin were 50 MPa and 75 MPa, respectively. Moreover, the elongation and cutting time were 2.5 % and 6–10 min, respectively. The size of coarse aggregate did not exceed 19 mm. Locally available river sand was utilized. The final mix proportions are shown in Table 3. The target compressive strength for Type I and II concrete was 25 MPa and 40 MPa, respectively. In this study, the stirrups were provided only at the ends of vertical bars to avoid crushing of the concrete. Whereas; in the middle portion the stirrups were not provided. The stirrup spacing is shown in Fig. 1(a). A typical steel cage is shown in Fig. 1(b) The longitudinal reinforcement ratio was 2.56 %. FSMS and cotton ropes are shown in Fig. 2(a) and (b), respectively.

Table 2.

Properties of confining wraps and resin.

Type	Thickness (mm)	Tensile Capacity (MPa)	Flexural Capacity (MPa)	Tensile Rupture Strain (%)	Curing Time (hours)	Elastic modulus (MPa)
FCMS	0.52	180.00	N/A	2.50	N/A	7200
Cotton	2.45	129.30	N/A	13.40	N/A	964
Polyester Resin	N/A	50.00	75.00	2.50	6–10	–

Table 3.

Mix ratios of concrete in kg to produce 1 cubic meter of concrete.

Ingredient	I	II
Cement	242	444
Fine Aggregates	726	605
Coarse Aggregates	1210	1008
W/C ratio	0.45	0.40

Fig. 2.

Confining type: (a) FSMS and (b) cotton.

2.3. Strengthening method

The hybridized CFS-strengthening (Fig. 3(a)) involved several steps. Initially, the face of each specimen was cleansed, followed by the application of an polyester resin layer utilizing a roller. Subsequently, confinement with low tensile strain, specifically FSMS, was enclosed around the samples. Cotton ropes were wrapped after the FSMS wraps, as observed from Fig. 3(b). A 150 mm overlap was kept avoiding the premature slippage of confinement, visible in Fig. 3. For later layers, polyester resin was brushed over the existing FCMS or cotton ropes. Fig. 4 illustrates the various steps involved in the strengthening method. After application, the reinforced samples were left for curing for one week prior to testing. Notably, cotton confinement was applied over the FSMS confinement using a straightforward hand process.

Fig. 3.

Graphic of the intended hybridized strengthening: (a) front and (b) cross-sectional position.

Fig. 4.

The strengthening method.

2.4. Test setup

To ensure even load distribution, the ends of the specimens were ground. The loads were applied utilizing a UTM capable of 1000 kN capability. Steel clamps were employed at each end to prevent localized concrete crushing, as illustrated in Fig. 5. Additionally, two displacement transducers with a 25 mm capability were utilized to observe axial compression throughout testing process. The loading rate was kept at 5 kN/s.

Fig. 5.

Typical test setup.

3. Experimental results

3.1. Failure patterns of samples

Fig. 6 illustrates the failures observed specimens. The failure typically occurred at mid-height, characterized by the failure of FCMS and cotton perpendicular to longitudinal direction. Control specimens displayed typical unconfined concrete failure modes, involving crushing and splitting. Specimens reinforced in subgroups 1A and 2A produced loud failures, possibly ascribed to the one cotton layer. Nevertheless, as the quantity of cotton ropes grew in subgroups 1B and 2B, the failures transitioned towards ductile, ascribed to the high tensile strain of cotton confinement. Concrete strengthened with hybridized confinement with different tensile capacities exhibited progressive failure patterns, avoiding sudden failures. Subsequently, hybrid confined concrete displayed pseudo-ductile behavior in its strain-strain response, illustrated by a strain-hardening phase. As compressive loads grew, audible fracturing sounds were detected from the inner FSMS, although no external damage was visible. Specimens did not fail instantly after FSMS failure due to continued lateral confining pressure from the cotton ropes. Subsequent failure was marked by splitting sounds from the polyester adhesive, culminating in outer cotton rope fracture. Previous research by Ispir et al. [46] suggested that combining low and high tensile strain wraps altered failure modes to become ductile, with inner wraps rupturing before outer cotton wraps, as evidenced by their fracture sounds. Samples in subgroups 1A and 1B did not demonstrate the fracture of transverse steel reinforcement. However, the buckling of the longitudinal bars was evident and expected under high compressive loads. The transverse reinforcement in Subgroup 2B was fractured, suggesting that these specimens endured the maximum compressive loads.

Fig. 6.

Failure modes of specimens.

3.2. Curves for compressive response

The curves exhibiting compressive response of specimens are shown in Fig. 7. The average response of two representative specimens against each type is shown in Fig. 7. The response of CFS-confined concrete mainly consisted of two parts: (1) the initial part was characteristically parabolic until the peak compressive stress (compressive strength), and (2) the second branch was characteristically a linearly degrading line. The proposed CFS strengthening enriched the compressive strength and ultimate strain of concrete in all subgroups. After passing the compressive strength, the slope of unconfined concrete specimens degraded suddenly. However, a rather gradual descent was associated with the degrading slope of CFS-confinement specimens. The comparison of the response of specimens with different CFS layers, unconfined compressive strength, and the number of cotton layers is presented in subsequent sections. Rousakis [49] performed a hybrid confinement using fiber-reinforced polymer sheets made with glass fibers and by polypropylene fiber ropes and found a similar compressive stress vs. strain behavior, as reported in this study. It is noteworthy that the strength of unconfined concrete dropped suddenly after reaching the compressive strength. On the contrary, the strengthened specimens demonstrated a gradual decrease in their compressive strength. This can be attributed to the synergistic mechanism involved in the use of hybrid confinement. The inner confinement fails first due to its lower rupture strain, thereby transferring the confinement demand to the outer LRS cotton ropes. This in turn, imparts additional ductility to the concrete.

Fig. 7.

Compressive response of CFS-confined concrete in subgroup.

3.3. Compressive strength, corresponding peak strain, and ultimate strain

The strain at the compressive strength is defined as the peak strain in this work. The compressive strength and peak compressive strains are presented in Table 4. A substantial improvement in both the compressive strength and peak strains represents the efficacy of the proposed CFS-confined concrete. Notably, the efficiency of CFS confinement was maximum in Subgroup 2A, demonstrating an increase of 246 % and 1477 % in the compressive strength and the peak strain, respectively. The second-best improvement in the compressive strength and the peak strain was observed in Subgroup 2B. This indicates that specimens strengthened with more than one cotton rope layer underwent greater compressive loads than specimens strengthened with a single cotton rope layer. It is apparent that the quantity of CFS wraps, the unconfined compressive strength, and the number of large tensile strain strengthening, i.e., the cotton ropes, significantly influenced the gain in the compressive strength and ductility of concrete. These indicators are summarized in subsequent sections. The improvement in ductility, also shown in Tables 4 and is described as the ratio between the strain in confined concrete when its stress reduces to 20 % of the maximum value and the strain in unconfined concrete [50], as exhibited in Fig. 8. The ductility gain ranged from 6.74 to 20.06, highlighting that the concrete demonstrated a ductile behavior.

Table 4.

Summary of strength and strain indicators.

Subgroup	Specimen Name	$f_{cc}$ (MPa)	Increase in $f_{cc}$ (%)	${ϵ}_{cc}$	Increase in ${ϵ}_{cc}$ (%)	${ϵ}_{cu}$	Ductility Gain
1A	C-I-CON	25.97		0.0035	–	0.0035	–
	C-I-1G1C	45.26	74	0.0167	378	0.0388	11.10
	C-I-2G1C	59.87	131	0.0293	737	0.0439	12.53
	C-I-3G1C	72.54	179	0.0338	865	0.0528	15.07
1B	C-II-CON	38.54		0.0039	–	0.0039	–
	C-II-1G1C	54.32	41	0.0182	368	0.0263	6.75
	C-II-2G1C	79.26	106	0.0226	478	0.0321	8.23
	C-II-3G1C	89.74	133	0.0329	744	0.0436	11.18
2A	C-I-CON	25.97	–	0.0035	–	0.0035	–
	C-I-1G1C	45.26	74	0.0167	378	0.0388	11.10
	C-I-2G2C	80.00	208	0.0387	1006	0.0571	16.31
	C-I-3G3C	89.77	246	0.0552	1477	0.0700	20.06
2B	C-II-CON	38.54	–	0.0039	–	0.0039	–
	C-II-1G1C	54.32	41	0.0182	368	0.0263	6.75
	C-II-2G2C	97.68	153	0.0406	941	0.0565	14.50
	C-II-3G3C	110.54	187	0.0457	1072	0.0675	17.32

Note:$f_{cc}$and${ϵ}_{cc}$refer to compressive strength and peak strain, respectively.

Fig. 8.

Definition of ductility gain by CFS-confined concrete [50].

3.4. Effect of unconfined compressive strength

The efficiency of the proposed CFS confinement was found to be significantly affected by the unconfined compressive strength. That is, the efficiency was reduced as the unconfined compressive strength increased from 25.97 MPa to 38.54 MPa. This observation was prevalent in both the groups. Moreover, increase in the compressive strength and the peak strain were observed to decrease as the unconfined compressive strength increased. Several existing works have also reported similar observations [[51], [52], [53], [54]]. Ozbakkaloglu and Akin [55] reported that the hoop strains of FRP reduced at fracture as the strength of the unconfined concrete increased. A similar trend was also reported by Vincent and Ozbakkaloglu [56]. This was ascribed to the change in the pattern of concrete cracking “from heterogenic microcracks to localized macrocracks”. The formation of microcracks is crucial in determining the lateral deformation capacity of the concrete under axial loads. The passive confinement, similar to the proposed CFS confinement, is activated mainly as concrete expands laterally. Thus, for a reduced dilation, the efficiency of the passive confinement is expected to decrease. An analogous effect of unconfined compressive strength on ductility gain was observed, as shown in Fig. 9.

Fig. 9.

Impact of the unconfined compressive strength on the efficacy of CFS confinement.

3.5. Effect of confinement ratio

Knowing the influence of unconfined compressive strength on passive confinement, several works have implemented the confinement ratio to quantify how external passive confinement affects concrete's mechanical properties [[57], [58], [59]]. This concept is supported by the findings discussed earlier. The confinement ratio is stated as the proportion of the passive pressure applied by external confinement (f_l) to the unstrengthened compressive strength (f_co) [60]. Literature suggests that the greatest possible hoop strain under external confinement is smaller than its failure capacity [[61], [62], [63]]. In this initial work on hybrid CFS strengthening, lacking experimental data to confirm this phenomenon specifically for CFS, fracture is assumed to occur at the ultimate tensile strain capability of the intended hybridized CFS strengthening. Consequently, the net external pressure was determined by summing the pressures from individual confinement types using Eq. (1) [64].

$$\begin{array}{c}{f}_l=\frac{2f_{CG}t}{D}\end{array}$$ (1)

where $f_{CG}$ is the maximum tensile capacity of FSMS or cotton in MPa, $t$ is thickness of FCMS and cotton rope, and $D$ represents the diameter of the specimen. It is seen in Fig. 10(a) that both the compressive strength and the peak strain increased with the increase in confinement ratio. Moreover, this increase was not linearly related to the confinement ratio (Fig. 10(b)). This observation is important when establishing expressions to estimate the compressive strength and the peak strain of CFS-confined concrete. Similarly, the ductility gain is reported in Fig. 10(c), stating an increase with the increment in confinement ratio.

Fig. 10.

Impact of the confinement ratio on (a) compressive strength, (b) the peak strain, and (c) ultimate strain.

3.6. Effect of the number of large strain ropes

Specimens in Group 1 and Group 2 were differentiated based on the number of cotton ropes. Especially, Group 1 specimens were strengthened with a single cotton rope layer, whereas variable cotton ropes were used in Group 2. The compressive stress vs. strain responses are shown in Fig. 11 for specimens with unconfined strength I and II. The effect of the cotton ropes is evident both in terms of the compressive strength and the peak strain. In addition, the ultimate strain was also evident. Noting that the proposed CFS confined is passive, it is only activated under notable lateral dilations. Therefore, the elastic moduli of specimens with varying cotton ropes did not differ from those with a single cotton layer. Another remark is linked to the slope of post-peak degradation section that did not differ significantly.

Fig. 11.

Effect of the quantity of cotton rope layers for specimens with unconfined compressive strength.

4. Analytical modeling

In this part, expressions are developed for the compressive strength, the peak strain, and ultimate strain of concrete under CFS confinement. Previous sections have recognized that the improvement in compressive response can be expressed as functions of the confinement ratio and unconfined concrete strength. The idea is to utilize these parameters in forecasting the compressive stress vs. strain response of CFS-confined concrete till failure. It is important to note that the proposed CFS confinement is novel. There are numerous hybridization techniques available in the literature but the combination of FSMS and cotton ropes is proposed for the first time. Given that the intrinsic behavior of cotton and FSMS is unique, the confinement mechanism, despite being passive, should not be predicted by using the available models for hybrid confinement in the literature. Therefore, authors tried several expressions in the literature and found that the expression proposed by Popovics [65] closely resembled the ascending branch of the compressive curve of CFS-confined concrete. The expression is given in Eq. (2) and Eq. (3) as:

$$\begin{array}{c}{f}_c=f_{cc}\left[\frac{k\left(\frac{{ϵ}_c}{{ϵ}_{cc}}\right)}{k-1+{\left(\frac{{ϵ}_c}{{ϵ}_{cc}}\right)}^{0.8k}}\right]for{ϵ}_c\le {ϵ}_{cc}\end{array}$$ (2)

where

$$\begin{array}{c}k=\frac{E_c}{E_c-\frac{f_{cc}}{{ϵ}_{cc}}}\end{array}$$ (3)

where the curvature and the slope of the initial ascending branch is controlled by $k$ and $E_c$ is the elastic modulus of concrete. The term $\left(\frac{{ϵ}_c}{{ϵ}_{cc}}\right)$ in the denominator of Eq. (2) was raised to $k$ in the original formulation of Popovics [65]. However, a power of 0.8 times $k$ is suggested in this study for CFS-confined concrete. The descending branch was predicted by the formulation of Fafitis and Shah [66] as:

$$\begin{array}{c}{f}_c=f_{cc}.\exp \left[k_1{\left({ϵ}_c-{ϵ}_{cc}\right)}^{k_2}\right]for{ϵ}_c>{ϵ}_{cc}\end{array}$$ (4)

where

$$\begin{array}{c}{k}_1=\frac{\ln 0.75}{{\left({ϵ}_{cu}-{ϵ}_{cc}\right)}^{k_2}};k_2=0.58+16{\left(\frac{f_l}{f_{co}}\right)}^{1.4}\end{array}$$ (5)

It is noted that in the original formulation of Fafitis and Shah [66], the natural logarithm of 0.5 was used in Eq. (5). However, the natural logarithm of 0.75 was found appropriate for CFS-confined concrete. In this formulation, the necessary parameters required are $f_{cc}$, ${ϵ}_{cc}$, ${ϵ}_{cu}$, and $E_c$. In the following sections, nonlinear regression analysis is conducted on experimental data to propose expressions for these parameters.

4.1. Proposed expression for $f_{cc}$

In Section 3, it was noted that the gain in compressive strength was related to the unconfined compressive strength $f_{co}$ and the confinement ratio $f_l/f_{co}$. Nonlinear regression analysis was conducted on experimental $f_{cc}/f_{co}$ values (see Fig. 10(a)). The following equation closely predicted the experimental $f_{cc}/f_{co}$ values.

$$\begin{array}{c}\frac{f_{cc}}{f_{co}}=-265.284+269.603{\left(\frac{f_l}{f_{co}}\right)}^{0.005}\end{array}$$ (6)

Importantly, Eq. (6) provided an $R^2$ value of 0.90. The efficiency of the proposed Eq. (6) is graphically shown in Fig. 12(a).

Fig. 12.

The experimental vs. predicted (a) compressive strength, (b) the peak strain, (c) ultimate strain, and (d) elastic modulus of CFS-confined concrete.

4.2. Compressive strain ${ϵ}_{cc}$ at $f_{cc}$

The idealization of the compressive response comprises the initial parabolic branch till the compressive strength $f_{cc}$ is achieved. Therefore, the peak strain at $f_{cc}$ must be used in the model by Popovics [65]. Based on nonlinear regression analysis, the following equation is proposed.

$$\begin{array}{c}\frac{{ϵ}_{cc}}{{ϵ}_{co}}=-7.20+28.26{\left(\frac{f_l}{f_{co}}\right)}^{0.447}\end{array}$$ (7)

Importantly, Eq. (7) provided an $R^2$ value of 0.89. The efficiency of the proposed Eq. (7) is graphically shown in Fig. 12(b).

4.3. Ultimate strain ${ϵ}_{cu}$

It was noted in Eq. (4) and Eq. (5) that the value of the ultimate strain ${ϵ}_{cu}$ is required to trace the descending branch of the compressive response. The ultimate strain in this study was defined as the strain corresponding to the 20 % drop in the compressive strength in the post-peak branch. The experimental ${ϵ}_{cu}$ values are summarized in Table 4. Equation (8) is proposed based on nonlinear regression analysis to predict ${ϵ}_{cu}$ values of CFS-confined concrete.

$$\begin{array}{c}\frac{{ϵ}_{cu}}{{ϵ}_{co}}=-1580.424+1605.520{\left(\frac{f_l}{f_{co}}\right)}^{0.006}\end{array}$$ (8)

The $R^2$ value of Eq. (8) was 0.98 and its performance is graphically shown in Fig. 12(c).

4.4. Elastic modulus $E_c$

The elastic modulus of the concrete was found to vary with the unconfined compressive strength $f_{co}$. That is, the confinement did not influence the elastic modulus. This was observed in Section 3. The elastic modulus of strength Type I and Type II was around 7 GPa and 10 GPa, respectively. Thus, Eq. (9) is proposed to forecast the elastic modulus of CFS-confined concrete.

$$\begin{array}{c}{E}_c=435.52{\left(f_{co}\right)}^{0.86}\end{array}$$ (9)

It must be noted that Eq. (9) yielded an $R^2$ value of 0.90, whose efficiency is graphically demonstrated in Fig. 12(d).

4.5. The predicted vs. experimental response

Table 5 presents the comparison of experimental and predicted key points and their corresponding mean absolute errors (MAE). It is noted that MAE values for $\frac{f_{cc}}{f_{co}}$, $\frac{{ϵ}_{cc}}{{ϵ}_{co}}$, $\frac{{ϵ}_{cu}}{{ϵ}_{co}}$, and $E_c$ were 0.14, 0.65, 0.84, and 0.13 that shows an excellent predictive capability of the proposed expressions. Fig. 13, Fig. 14 present comparisons of the predicted and experimental curves of CFS-confined concrete. It is noted that the intended methodology developed close predictions of experimental findings. The compressive strength and the peak strain well matched in most of the cases. The elastic modulus also resembled closely experimental results. The initial parabolic branch was also closely followed by the proposed methodology. Finally, the post-peak strength degradation was also predicted reasonably well. It is noted that the post-peak branch was only shown till the ultimate strain, i.e., the point where a 20 % reduction in the peak strength was achieved.

Table 5.

Comparison of experimental and predicted values and their mean absolute error.

ID	$\frac{f_{cc}}{f_{co}}$ (Exp)	$\frac{f_{cc}}{f_{co}}$ (Pred)	$\frac{{ϵ}_{cc}}{{ϵ}_{co}}$ (Exp)	$\frac{{ϵ}_{cc}}{{ϵ}_{co}}$ (Pred)	$\frac{{ϵ}_{cu}}{{ϵ}_{co}}$ (Exp)	$\frac{{ϵ}_{cu}}{{ϵ}_{co}}$ (Pred)	$E_{c,\mathit{exp}}$ (GPa)	$E_{c,pred}$ (GPa)
C-I-1G1C	1.74	1.78	4.77	5.76	11.10	9.97	7.09	7.17
C-I-2G1C	2.31	2.47	8.37	8.08	12.53	11.90	7.17	7.17
C-I-3G1C	2.79	2.70	9.66	9.27	15.07	13.50	7.45	7.39
C-II-1G1C	1.41	1.67	4.67	4.50	6.75	6.20	7.09	7.11
C-II-2G1C	2.06	1.94	5.79	5.61	8.23	8.13	7.05	7.09
C-II-3G1C	2.33	2.17	8.44	6.61	11.18	9.73	7.21	7.17
C-I-1G1C	1.74	1.76	4.77	5.76	11.10	9.97	9.78	9.80
C-I-2G2C	3.08	3.13	11.06	11.83	16.31	16.59	9.97	9.98
C-I-3G3C	3.46	3.67	15.77	15.61	20.06	20.48	10.29	10.07
C-II-1G1C	1.41	1.67	4.67	4.50	6.75	6.20	9.78	10.07
C-II-2G2C	2.53	2.60	10.41	8.75	14.50	12.82	9.93	10.07
C-II-3G3C	2.87	3.14	11.72	11.92	17.32	16.70	10.72	10.07
MAE	0.14		0.65		0.84		0.13

Fig. 13.

The predicted vs. experimental compressive responses.

Fig. 14.

The predicted vs. experimental compressive responses.

5. Conclusions

This study organized two groups based on CFS confinement configurations, with all specimens standardized at 300 mm height and 150 mm diameter. Specimens featured four 12 mm diameter longitudinal steel bars and two 6 mm diameter stirrups at each end. Each group was subdivided into Type I and Type II based on compressive strength characteristics. Group 1 utilized varying FSMS layers alongside a constant layer of cotton ropes, while Group 2 adjusted both cotton and FSMS layers across specimens, ranging from 1 to 3 layers. The subsequent key conclusions were drawn from experimental and analytical results.

• 1.Failure typically occurred at mid-height due to failure of FCMS and cotton ropes in the hoop direction. Control specimens showed standard unconfined concrete failures with crushing and splitting. Subgroups 1A and 2A exhibited louder failures, likely due to single cotton rope use, while ductility improved in 1B and 2B with more cotton ropes, benefiting from their high rupture strain. Hybrid FRP-wrapped concrete displayed progressive failure, avoiding sudden failures and demonstrating pseudo-ductile behavior with a strain-softening phase.
• 2.The response of CFS-confined concrete exhibited two distinct branches: initially, a parabolic shape leading to peak compressive stress (compressive strength), followed by a linearly degrading phase. The proposed CFS confinement improved both the compressive strength and ductility across all subgroups. Unlike unconfined concrete specimens that experienced a sudden slope descent post-peak stress, CFS-confined specimens showed a more gradual decline in their slope.
• 3.The proposed CFS-confined concrete significantly improved both compressive strength and corresponding compressive strains. Subgroup 2A demonstrated the highest enhancement with a 246 % increase in compressive strength and a 1477 % increase in strain. Subgroup 2B also showed substantial improvements, highlighting the effectiveness of multiple cotton rope layers in handling higher compressive loads compared to single-layer reinforcement. These findings underscore the influence of CFS layers and cotton ropes on enhancing concrete strength and ductility.
• 4.The efficiency of the proposed CFS strengthening was reduced as the unconfined compressive strength enhanced. Moreover, the compressive strength, the peak strain, and the ultimate strain increased significantly by the increase in the confinement ratio. However, this increase was not linear. The elastic modulus of concrete did not vary in the presence of CFS confinement.
• 5.The idealized two-branch curves of CFS-confined concrete were predicted. Regression-based expressions were proposed for the compressive strength, the peak strain, the ultimate strain, and elastic modulus. The initial parabolic branch was predicted by the modification of the model by Popovics [65]. The post-peak degrading branch was proposed by modifying the model by Fafitis and Shah [66]. The two modified models, combined, produced compressive curves that resembled closely the experimental results.

CRediT authorship contribution statement

Panumas Saingam: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. Chaitanya Krishna Gadagamma: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. Qudeer Hussain: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. Ali Ejaz: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. Hnin Hnin Hlaing: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. Rawirot Suwannatrai: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. Kaffayatullah Khan: Writing – review & editing, Writing – original draft, Methodology, Conceptualization. Suniti Suparp: Writing – review & editing, Writing – original draft, Methodology, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.