Prediction of Flexural Strength of RC Circular Columns Considering Lateral Confinement Effects of FRCM and Transverse Steel Reinforcement

Abstract

There has recently been growing interest in making a sustainable and durable fiber reinforced cementitious matrix (FRCM) to improve the seismic performance of RC column members. However, most studies evaluating the lateral confinement effect on FRCM jacketing concrete have excluded the confinement effect of transverse steel reinforcement and focused solely on mechanical properties. This paper, based on existing studies, proposes a peak axial stress formula that considers the lateral confinement effects of FRCM composite and transverse steel reinforcement. Additionally, the study assesses the structural performance of FRCM composites with flexural strengthening in actual size RC circular columns and predicts the maximum flexural strength by applying the proposed formula. The proposed peak axial stress formula, considering the influence of transverse reinforcement, was compared with the experimental value (databases) and the predicted value, and the suitability was confirmed with a standard deviation of 27.6% and a coefficient of variation of 0.856. In addition, the maximum flexural strength of actual size RC circular columns predicted by applying this formula ranged from 0.97 to 1.02, which effectively predicted the experimental values.

1. Introduction

Environmental factors, such as abnormal temperatures and earthquakes, have recently increased attention to the safety of structures, which has led to a growing demand for improved strengthening systems. In particular, axially loaded column members are subject to more stringent structural standards and require increased load-carrying capacity to compensate for damage caused by design and construction errors and lack of maintenance [1]. Traditionally, fiber-reinforced polymer (hereinafter, “FRP”) jackets, due to their high strength-to-weight ratio, resistance to fatigue and corrosion, and ease of construction have been used for column reinforcement [2]. The FRP jacket is applied in the transverse direction (circumference) of the column and delays the compressive failure of the core concrete, increasing the compressive strength and ultimate strain, thereby improving ductility and energy dissipation. In areas with high-seismic risk, FRP jacket reinforcement can improve structural performance by strengthening the plastic hinge zone. However, issues have been raised, such as high cost, due to the use of epoxy resins, difficulty in applying to wet surfaces or low temperatures, lack of permeability, and lack of usability with concrete surfaces [3].

To overcome these problems, fiber reinforced cementitious matrix composites (hereafter, “FRCM”), which consist of a sustainable and durable cement-based mortar, have recently gained attention [4,5,6,7]. FRCMs consist of an inorganic matrix that is responsible for stress transfer between the concrete surfaces and fiber reinforcement embedded in the matrix. FRCM composites apply an open grid of fiber reinforcement to increase mechanical bonding with the matrix [8]. FRCM composites have (1) excellent resistance to fire and high temperature, (2) excellent durability against UV rays, (3) application to wet surfaces, (4) ability to increase tensile strength and bending tensile strength of mortar, which is an inorganic matrix, and (5) ability for use in continuous repair and reinforcement. However, these composites have disadvantages, such as difficulty, in preventing microcracks in response to external conditions such as dryness and vibration of the inorganic matrix and low adhesion performance compared to organic polymers.

Previous experimental studies have shown that FRCMs can be effectively applied in the reinforcement of conventional reinforced concrete (RC) and masonry members. In addition to being extensively studied in the mechanical properties of FRCM composites [8], it has been used as an externally bonded reinforcement in bending [9,10,11] and shear [12,13,14] members of RC beams, showing increases in strength, stiffness, and ductility, as well as decreases in crack width and deflection. FRCMs have also been used as external confinement to increase the strength and deformation performance of axially loaded members [15]. When a pure compressive stress is applied to an FRCM confined column, the column gradually expands and the jacket confines the transverse deformation [16]. The internal confining pressure caused by the external confining is applied uniformly along the perimeter of the circular cross-section column. The study of the compressive behavior of FRCM-confined concrete has received increasing attention in recent years, but this material’s behavior when used as lateral confinement is not yet fully understood and more research is needed. Experimental studies published in the literature on the compressive behavior of FRCM-confined concrete column have suggested that FRCMs improve responses of confined elements in terms of both strength and deformability [17,18,19].

The ACI committee 549 (hereafter, “ACI 549.4R”) [20] requires that peak axial stress be evaluated by applying a compressive force to a concrete specimen to account for the lateral confinement effect of FRCM in the design. Since FRCMs are used as reinforcement in conventional RC structures, their lateral confinement effect should be considered simultaneously with that of the transverse steel reinforcement present in conventional RC structures. However, there is a lack of previous research, and ACI 549.4R considers only the lateral confinement effect of FRCM, making it difficult to accurately predict the peak axial stress.

One previous study proposed a peak axial stress formula for concrete cylinders that considers variables such as the type of concrete cylinder cross-section (round, square), size, strength of concrete, and type of fibers [21]. However, the peak axial stress formula is limited to the evaluation of material properties, and applicability to actual size RC columns is minimal.

In this study, a peak axial stress formula that simultaneously considers the confinement effects of transverse steel reinforcement and FRCM is proposed using an experimental database of previous studies of laterally confined concrete. Furthermore, to verify the reliability of the proposed peak axial stress formula, the structural performance of RC circular columns reinforced with FRCM was evaluated and its applicability at the member level was assessed.

2. Research Significance

The objectives of this work are to:

• Analyze the existing lateral confinement theories (Plain, RC) and propose a peak axial stress formula for concrete considering the lateral confinement effects of FRCM and transverse steel reinforcement using an experimental database.
• Predict the ultimate flexural strength of an actual size FRCM-reinforced RC circular column by applying the proposed peak axial stress formula.

To reach the objectives of this study, the approach used in this paper is described below.

In Section 3, a database of compression tests of results of concrete cylinders containing transverse steel reinforcement and externally reinforced with FRP and FRCM was assembled. Based on this, the analysis and reliability of the equations for calculating the peak axial stress in concrete due to lateral confinement in previous studies were evaluated. The database of various references was used for the evaluation and, due to the lack of research on specimens consisting of FRCM-reinforced concrete columns (FRCM-steel Reinforced Concrete, hereinafter “FMRC”) with transverse reinforcement, a large number of FRP-reinforced concrete columns (FRP-steel Reinforced Concrete, hereinafter “FPRC”) with the same confinement model were included.

In Section 4, the formula proposed by Wang et al. [22], based on experimental results, and the existing formula used by researchers for lateral-confined concrete were used to calculate certain parameters. As a result, a new prediction formula for the peak axial stress of laterally confined concrete with FRCM composites is proposed. Previous studies were limited to evaluating the reliability of the equations in terms of material properties, so their applicability to actual RC columns was further evaluated in Section 5 of this paper.

In Section 5, an actual size RC column reinforced with FRCM was subjected to a cyclic loading test to evaluate the structural performance; this included analysis of failure modes and crack patterns, load–displacement relationship curves, ultimate strength, and ductility. In addition, the formula proposed in Section 4 was applied to evaluate the ultimate strength at the member level; the appropriateness was evaluated by comparison with the available predictive formula.

3. Experimental Databases and Available Predictive Formula

3.1. Experimental Databases

The experimental database used in this study is shown in

Table 1. Database of axial compression tests on FRP or FRCM confined circular RC columns.

Source	Specimen	D (mm)	H (mm)	Ef (GPa)	tf (mm)	s (mm)	Ast (mm2)	fyf (MPa)	fyt (GPa)	fco (GPa)	flf (GPa)	fls (GPa)	κf	Type
Benzaid et al. [23]	I.RCC.1.1L	160	320	34	1.0	140	50.3	450	235	29.5	5.6	1.11	5.1	CFRP + Steel
	I.RCC.2.1L	160	320	34	1.0	140	50.3	450	235	29.5	5.6	1.11	5.1	CFRP + Steel
	I.PCC.1.1L	160	320	34	1.0	140	50.3	450	235	25.9	5.6	1.11	5.1	CFRP + Steel
	II.RCC.1.1L	160	320	34	1.0	141	50.3	450	235	58.2	5.6	1.10	5.1	CFRP + Steel
	II.RCC.2.1L	160	320	34	1.0	142	50.3	450	235	58.2	5.6	1.09	5.1	CFRP + Steel
	II.RCC.1.3L	160	320	34	3.0	143	50.3	450	235	58.2	16.9	1.09	15.5	CFRP + Steel
	II.RCC.2.3L	160	320	34	3.0	140	50.3	450	235	58.2	16.9	1.11	15.2	CFRP + Steel
	II.PCC.1.3L	160	320	34	3.0	140	50.3	450	235	49.5	16.9	1.11	15.2	CFRP + Steel
Pessiki et al. [24]	C4	508	1830	21.6	3.0	356	70.9	571.5	502	32.8	6.9	0.40	16.8	CFRP + Steel
Eid et al. [25]	A5NP2 C	303	1200	78	0.762	150	70.9	1045.2	602	29.4	5.3	1.94	2.7	CFRP + Steel
	A3NP2 C	303	1200	78	0.762	70	70.9	1045.2	602	31.7	5.3	4.15	1.3	CFRP + Steel
	A1NP2 C	303	1200	78	0.762	45	70.9	1045.2	602	31.7	5.3	6.46	0.8	CFRP + Steel
	C4NP2 C	303	1200	78	0.762	100	100.3	1045.2	456	31.7	5.3	3.14	1.7	CFRP + Steel
	C4N1P2 C	303	1200	78	0.762	100	100.3	1045.2	456	36	5.3	3.14	1.7	CFRP + Steel
	C4NP4 C	303	1200	78	1.524	100	100.3	1045.2	456	31.7	10.5	3.14	3.4	CFRP + Steel
	B4NP2 C	303	1200	78	0.762	100	100.3	1045.2	456	31.7	5.3	3.14	1.7	CFRP + Steel
	C2NP2 C	303	1200	78	0.762	65	100.3	1045.2	456	31.7	5.3	4.82	1.1	CFRP + Steel
	C2N1P2 C	303	1200	78	0.762	65	100.3	1045.2	456	36	5.3	4.82	1.1	CFRP + Steel
	C2N1P4 C	303	1200	78	1.524	65	100.3	1045.2	456	36	10.5	4.82	2.2	CFRP + Steel
	C2N1P2 N	303	1200	78	0.762	65	100.3	1045.2	456	36	6.3	5.82	1.1	CFRP + Steel
	C2MP2 C	303	1200	78	0.762	65	100.3	1045.2	456	50.8	5.3	4.82	1.1	CFRP + Steel
	C2MP4 C	303	1200	78	1.524	65	100.3	1045.2	456	50.8	10.5	4.82	2.2	CFRP + Steel
	C2MP2 N	303	1200	78	0.762	65	100.3	1045.2	456	50.9	6.3	5.82	1.1	CFRP + Steel
Wang et al. [22]	C1H1L1M	305	915	240	0.167	80	28.3	4340	397	24.5	4.8	0.94	5.1	CFRP + Steel
	C1H1L2M	305	915	240	0.334	80	28.3	4340	397	24.5	9.5	0.94	10.1	CFRP + Steel
	C1H2L1M	305	915	240	0.167	40	28.3	4340	397	24.5	4.8	1.88	2.5	CFRP + Steel
	C1H2L2M	305	915	240	0.334	40	28.3	4340	397	24.5	9.5	1.88	5.1	CFRP + Steel
	C2H1L1M	204	612	240	0.167	150	28.3	4340	397	24.5	7.1	0.76	9.4	CFRP + Steel
	C2H1L2M	204	612	240	0.334	150	28.3	4340	397	24.5	14.2	0.76	18.8	CFRP + Steel
	C2H2L1M	204	612	240	0.167	60	28.3	4340	397	24.5	7.1	1.89	3.8	CFRP + Steel
	C2H2L2M	204	612	240	0.334	60	28.3	4340	397	24.5	14.2	1.89	7.5	CFRP + Steel
Zhang et al. [26]	CF0.5T300	350	1300	242	0.0155	300	50.3	3751	430	33	3.7	0.42	8.7	CFRP + Steel
	CF1T90	350	1300	242	0.0155	90	50.3	3751	358	46	7.2	1.17	6.2	CFRP + Steel
	CF1T150	350	1300	242	0.0155	150	50.3	3751	358	46	7.2	0.70	10.3	CFRP + Steel
	S6F1	150	300	250	0.11	60	19.6	4510	1200	36.2	6.6	5.42	1.2	CFRP + Steel
	S6F2	150	300	250	0.22	60	19.6	4510	1200	36.2	13.2	5.42	2.4	CFRP + Steel
	S6F4	150	300	250	0.44	60	19.6	4510	1200	36.2	26.5	5.42	4.9	CFRP + Steel
	S6F5	150	300	250	0.55	60	19.6	4510	1200	36.2	33.1	5.42	6.1	CFRP + Steel
	S4F1	150	300	250	0.11	40	19.6	4510	1200	36.2	6.6	8.12	0.8	CFRP + Steel
Lee et al. [27]	S6F1	150	300	250	0.11	60	19.6	4510	1200	36.2	6.6	5.42	1.2	CFRP + Steel
	S6F2	150	300	250	0.22	60	19.6	4510	1200	36.2	13.2	5.42	2.4	CFRP + Steel
	S6F4	150	300	250	0.44	60	19.6	4510	1200	36.2	26.5	5.42	4.9	CFRP + Steel
	S6F5	150	300	250	0.55	60	19.6	4510	1200	36.2	33.1	5.42	6.1	CFRP + Steel
	S4F1	150	300	250	0.11	40	19.6	4510	1200	36.2	6.6	8.12	0.8	CFRP + Steel
	S4F2	150	300	250	0.22	40	19.6	4510	1200	36.2	13.2	8.12	1.6	CFRP + Steel
	S4F3	150	300	250	0.33	40	19.6	4510	1200	36.2	19.8	8.12	2.4	CFRP + Steel
	S4F4	150	300	250	0.44	40	19.6	4510	1200	36.2	26.5	8.12	3.3	CFRP + Steel
	S4F5	150	300	250	0.55	40	19.6	4510	1200	36.2	33.1	8.12	4.1	CFRP + Steel
	S2F1	150	300	250	0.11	20	19.6	4510	1200	36.2	6.6	16.25	0.4	CFRP + Steel
	S2F2	150	300	250	0.22	20	19.6	4510	1200	36.2	13.2	16.25	0.8	CFRP + Steel
	S2F3	150	300	250	0.33	20	19.6	4510	1200	36.2	19.8	16.25	1.2	CFRP + Steel
	S2F4	150	300	250	0.44	20	19.6	4510	1200	36.2	26.5	16.25	1.6	CFRP + Steel
	S2F5	150	300	250	0.55	20	19.6	4510	1200	36.2	33.1	16.25	2.0	CFRP + Steel
Ilki et al. [28]	NSR-C -050-3	250	500	230	0.495	50	50.3	3430	476	27.6	13.6	3.95	3.4	CFRP + Steel
	NSR-C -100-3	250	500	230	0.495	100	50.3	3430	476	27.6	13.6	1.98	6.9	CFRP + Steel
	NSR-C -145-3	250	500	230	0.495	145	50.3	3430	476	27.6	13.6	1.36	10.0	CFRP + Steel
	NSR-C -050-5	250	500	230	0.825	50	50.3	3430	476	27.6	22.6	3.95	5.7	CFRP + Steel
	NSR-C -100-5	250	500	230	0.825	100	50.3	3430	476	27.6	22.6	1.98	11.4	CFRP + Steel
	NSR-C -145-5	250	500	230	0.825	145	50.3	3430	476	27.6	22.6	1.36	16.6	CFRP + Steel
Faleschini et al. [29]	C20-1	300	1000	242	0.047	200	50.3	1487	485	16.0	0.5	0.83	0.6	CFRCM + Steel
	C20-2	300	1000	242	0.094	200	50.3	1487	485	16.0	0.9	0.83	1.1	CFRCM + Steel
	C33-1	300	1000	242	0.047	330	50.3	1487	485	16.0	0.5	0.51	0.9	CFRCM + Steel
	C33-2	300	1000	242	0.094	330	50.3	1487	485	16.0	0.9	0.51	1.8	CFRCM + Steel

. The database was formed using data from tests on 58 circular compressive cylinders containing transverse steel reinforcement and reinforced with FRP or FRCM [22,23,24,25,26,27,28,29]. All experimental data was collected using carbon fiber reinforcement. The FMRC specimens accounted for about 7%, with four specimens; most of the experimental data was obtained from FPRC specimens because most of the FRCM jacketed cylinders were concrete cylinders without transverse steel reinforcement, so we included a large number of FRP-jacketed cylinders.

The specimens were collected in a circular cross-sectional shape to exclude the contribution of lateral confining pressure to the corner geometry of the cross-section. The diameter (D) of the cylinder cross-sections ranged from 160 mm to 508 mm and the height (H) from 300 mm to 1300 mm, with an aspect ratio (D:H) of 1:2 in most cases, but 1:3 was also present. The compressive strength (f_co) of the unconfined concrete cylinders was collected mainly from experimental data using normal strength concrete; values varied from 16.0 MPa to 58.2 MPa. The yield strength of the transverse reinforcement was not more than 400 MPa, but high-strength reinforcement values of 600 MPa and 1200 MPa were also included. The lateral confining pressure (f_lf) of the FRCM was based on ACI 549. 4R [20] and the work of Teng et al. [30]. The transverse confining pressure of the transverse beam was calculated by applying the work of Richart et al. [31].

In addition, the lateral confining pressure ratio (κ_f) of FRP and transverse steel reinforcement varied from 0.8 to 18.8, considering the interaction of the stiffness ratio of FRP and transverse steel reinforcement presented by J.G. Teng et al. in [30]; the variation of the lateral confining pressure ratio of FRP and transverse steel reinforcement was also included.

3.2. Available Predictive Formula

Although various studies have been conducted to characterize the mechanical behavior of FRCM [17,18,32,33,34], there is a lack of research on strength prediction formulas for FRCM-confined columns (with transverse steel reinforcement). Peak axial stress formulas for evaluating the compressive strength of available confined concrete cylinders are shown in

Table 2. Available predictive formula for the compressive strength of confined columns.

Paper	Confining Pressure	Compression Strength
Richart et al. [31]	$f_{ls}=\frac{2A_{st}{f}_{yt}}{d_{c}s}$	$\frac{f_{cc}}{f_{co}}=1+4.1\frac{f_{ls}}{f_{co}}$
Mander et al. [35]	$f_{ls}=\frac{1}{2}{\rho }_s{f}_{yt}{k}_e$	$\frac{f_{cc}}{f_{co}}=2.254\sqrt{1+7.94\frac{f_{ls}}{f_{co}}}-2\frac{f_{ls}}{f_{co}}-1.254$
ACI 549.4R [20]	$f_{lf}=\frac{2{nE}_f{\epsilon }_f{t}_f}{D_c}$	$\frac{f_{cc}}{f_{co}}=1+3.3\frac{f_{lf}}{f_{co}}$
Teng et al. [30]	$\begin{array}{l}{f}_{ls}=\frac{2A_{st}{f}_{yt}}{d_{c}s}\\ f_{lf}=\frac{2{t_{f}E}_f{\epsilon }_f}{D_c}\end{array}$	$\frac{f_{cc}}{f_{co}}=2.254\sqrt{1+7.94\frac{f_{ls}}{f_{co}(1+0.202{\rho }_f^{\prime 0.145})}}-2\frac{f_{ls}}{f_{co}\left(1+0.202{\rho }_f^{\prime 0.145}\right)}-1.254+3.5\frac{f_{lf}}{f_{co}}$

. The peak axial stress formulas assume that the compressive strength of confined concrete (f_cc) is equal to the compressive strength of unconfined concrete (f_co) plus the lateral confining pressures (f_ls, f_lf) caused by the reinforcement (transverse steel reinforcement and FRP, FRCM). The lateral confining pressure caused by the transverse steel reinforcement placed inside the concrete and the fiber reinforcement placed outside is assumed to be a function of the diameter of the cylinder (D), the cross-sectional area of the transverse steel reinforcement (A_st), the yield strength of the transverse steel reinforcement (f_yt), the thickness of the fiber reinforcement (t_f), the number of reinforcement layers (n), and the elastic modulus of fiber (E_f).

Richart et al. [31] calculated the force to expand laterally core concrete when a reinforced concrete column member was subjected to compressive force as the lateral confining pressure (f_ls) of the transverse steel reinforcement. The pressure of the transverse steel reinforcement considers the mechanical properties and the influence factor of the reinforcement ratio; the peak axial stress is calculated based on the equilibrium between the transverse expansion force of the core concrete and the confinement force induced by the transverse steel reinforcement in the laterally confined concrete cross section. This is the basic theory of lateral confinement of transverse steel reinforcement and has been in general use to date.

Mander et al. [35] determined that the size and shape of the cross-section of the laterally confined concrete affects the lateral confining pressure, and defined this as the effective lateral confining pressure (f_ls). f_ls is expressed in terms of the lateral confinement coefficient (k_e), which is the ratio of the effective cross-sectional area of the core concrete (A_e) to the total cross-sectional area of the concrete confined by the transverse steel reinforcement (A_cc), assuming that delamination of the laterally confined concrete cylinder occurs in the form of a quadratic equation, it is the equation that is at an inclination of approximately 45°.

ACI 549.4R [20] is the first international code for predicting the compressive strength of concrete cylinders confined laterally by FRCM composites. A linear relationship between compressive strength and maximum lateral confining pressure is proposed. In the peak axial stress calculation, the modulus of elasticity of FRCM is determined by the clevis-type direct tensile test presented in AC434 [36], which is not consistent with the modulus of the fibers [9]. The contribution of the confinement of the transverse steel reinforcement is not included.

J.G. Teng et al. [30] proposed a peak axial stress formula for concrete confined by transverse steel reinforcement and FRP. The peak axial stress formula is based on the transverse confining pressure of FRP and the formula of Mander et al. [35]. It was experimentally evaluated by adding the lateral confining pressure of the transverse steel reinforcement calculated. In this case, the lateral confinement interaction of the transverse steel reinforcement and FRP was included in the ratio (κ_f) of the lateral confining pressure of the transverse steel reinforcement and FRP.

To verify the performance of the preceding peak axial stress calculation method for confined concrete, the database in Table 1 was used to plot the relationship of predicted values to experimental values; results are shown in Figure 1.

The predictive formulas of Richart et al. [31] and Mander et al. [35], shown in Figure 1a,b, showed a low prediction performance for the experimental values, with coefficients of variation of 0.256 and 0.269, and standard deviations of 42.4% and 37.9%, respectively. These poor results may be due to the tendency to underestimate the experimental results because the studies did not consider the effect of lateral confinement on fiber reinforcement.

The prediction formula of ACI 549.4R [20], shown in Figure 1c, had a high-prediction performance, with a coefficient of variation of 0.891 and a standard deviation of 27.7% compared to the experimental values. Based on these results, it can be concluded that the lateral confinement effect of the fiber reinforcement is more important than that of the transverse steel reinforcement when calculating the peak axial stress because the peak axial stress is determined by fracturing the fiber reinforcement in the case of transverse steel reinforcement and FRCM.

The peak axial stress formula of J.G. Teng et al. [30], shown in Figure 1d, has a lower performance than that of ACI 549, with a coefficient of variation of 0.883 and a standard deviation of 37.7%. The peak stress formula of J.G. Teng et al. [30] was used to evaluate the stress contribution of the transverse reinforcement at the peak stress of the confined concrete with the formula proposed by Mander et al. [35]. To improve the accuracy of the experimental results, the confining pressure ratio expansion factors a and b were used in regression analysis. Also, this is because the lateral confining pressure was overestimated due to the influence of high-strength reinforcement when considering the confinement effect of transverse reinforcement [30].

4. Predicted Peak Axial Stress Formula

Figure 2 shows the axial stress–strain curve based on the experimental results in the study by Wang et al. [22]. The transverse steel reinforcement used had a yield strength of 397 MPa and a transverse steel reinforcement ratio (ρ_s) of 1.0%. The compressive strength of the FPRC specimen was higher than that of the steel-reinforced concrete (hereinafter, “SRC”) specimen. Also, the first linear slopes of the stress–strain curves for both SRC and FPRC specimens showed identical behavior. However, the stress in the FPRC specimen increased after the yielding of the transverse steel reinforcement. Based on these results, it was confirmed that the confining pressure of the transverse steel reinforcement plays a major role in the initial elastic modulus, and the lateral confinement contribution of the FRP increases after the yielding of the transverse steel reinforcement. Therefore, the form of the peak axial stress formula presented in this study was designed to represent (1) the effective lateral confining pressure induced by the transverse steel reinforcement as the initial linear slope, and (2) the linear slope after the yielding of the transverse steel reinforcement through the effective lateral confining pressure of the FRCM.

Based on the experimental results of Wang et al. [22], Figure 3 shows the axial stress ratio according to amount of transverse steel reinforcement estimated by Teng et al. [30]. It can be seen that the difference in the axial stress ratio between FPRC and FR- reinforced concrete (hereinafter, “FPC”) columns after the yielding of the transverse steel reinforcement did not change significantly with the FRP confinement level (f_lf/f′_co); however, this difference increased with the amount of transverse steel reinforcement (ρ_s: 0%, 0.5%, 1.0%).

In Figure 2 and Figure 3, it can be seen that the initial modulus of elasticity changed depending on the contribution of the transverse steel reinforcement, and the axial stress ratio increased as the amount of transverse steel reinforcement increased. Based on these previous studies, this study used the peak axial formula of Mander et al. [35] in the primary modulus area and the formula of ACI 549.4R [20] in the secondary modulus area. As the axial stress increased with the transverse steel reinforcement ratio, as shown in Figure 3, an additional factor was required in the maximum stress calculation formula of Mander et al. [35]; the following conditions were satisfied.

(1)

The peak axial stress is reflected to change according to the amount of transverse steel reinforcement.

(2)

To consider the peak axial stress of SRC columns without fiber reinforcement.

To satisfy the above conditions (1) and (2), a parameter concept involving the confining stiffness of the fiber and the transverse steel reinforcement (κ_f) proposed by J.G. Teng et al. [30] was introduced. The lateral confining pressures of the transverse steel and fiber reinforcement are expressed by Equations (1) and (2):

$$f_{ls}=\frac{2f_{ys}{A}_{st}}{d_{c}s}=\frac{1}{2}{f}_{ys}{\rho }_s$$

(1)

$$f_{lf}=\frac{2E_f{\epsilon }_f{t}_f}{D_c}=\frac{1}{2}{f}_{yf}{\rho }_f$$

(2)

where κ_f is the confining stiffness ratio of the fiber reinforcement to the transverse steel reinforcement, as shown in Equation (3).

$${\kappa }_f=\frac{f_{lf}}{f_{ls}}=\frac{2E_f{t}_f}{D}/\frac{2k_e{E}_s{A}_{st}}{s{d}_c}=\frac{E_f{t}_{f}s{d}_c}{k_e{E}_s{A}_{s}D}$$

(3)

The peak axial stress formula for this study, which includes κ_f, is constructed as Equation (4):

$$\frac{f_{cc,p}}{f_{co}}=\left(2.254\sqrt{1+7.94\frac{f_{ls}}{f_{co}\left(1+{\kappa }_f\right)}}-2\frac{f_{ls}}{f_{co}\left(1+{\kappa }_f\right)}-2.254\right)+1+\frac{{∆f}_{cc,f}}{f_{co}}$$

(4)

where ${∆f}_{cc,f}/f_{co}$ can be expressed as the ratio of the lateral confining pressure of the fiber reinforcement to that of the unconfined concrete, as shown in Equation (5); the confinement amplification factor (k) was calculated using the database in Table 1.

$$\frac{∆f_{cc,f}}{f_{co}}=k\frac{f_{lf}}{f_{co}}$$

(5)

Calculation of the confinement amplification factor (k) was performed by regression analysis, as follows, due to the lack of experimental data on FRCM reinforcement.

(1)

Calculate the value of confinement amplification factor (k₁) using the experimental database of FPRC (54ea).

(2)

Apply the k₁ value to Equation (4) to evaluate the suitability of FMRC (Faleschini et al. [29]).

(3)

Calculate the confinement amplification factor (k₂) using the experimental database (58ea) of FPRC and FMRC.

(4)

Apply the k₂ value to Equation (4) to verify the suitability of the proposed formula (Equation (6)).

Figure 4 shows the results of the confinement amplification factor determined through regression analysis and the suitability evaluation of the proposed Equation (4). As shown in Figure 4a, the value of k₁ is defined as 2.6; as a result of comparing the experimental and predicted values of FMRC (4ea) by applying k₁ to Equation (4), k₁ is effectively predicted with a standard deviation of 2.5% and a coefficient of variation of 0.873, as shown in Figure 4b. Also, as shown in Figure 4c, the value of k₂ is 2.5, which does not show a significant difference from the value of k₁ and, when the defined value of k₂ is applied to Equation (4) to compare the experimental and predicted values of all experimental data (58ea), the suitability is confirmed, with a standard deviation of 27.6% and a coefficient of variation of 0.856. Based on these results, the peak axial stress formula proposed in this study is shown in Equation (6).

$$\frac{f_{cc,p}}{f_{co}}=\left(2.254\sqrt{1+7.94\frac{f_{ls}}{f_{co}\left(1+{\kappa }_f\right)}}-2\frac{f_{ls}}{f_{co}\left(1+{\kappa }_f\right)}-2.254\right)+1+2.5\frac{f_{l,f}}{f_{co}}$$

(6)

5. Evaluation of Structural Performance of RC Circular Columns

5.1. Experimental Design

Experiments were carried out to verify the seismic performance of RC circular columns with FRCM composites. As shown in

Table 3. Design parameters of the tested columns.

Column Index	Strengthening Material	Number of Layer	Impregnation Material	Grid Size	Grid Surface Coating	Matrix
Ctrl	-	-	-	-	-	-
C-V-N	V-GRID	1	SBR	27	NON	Inorganic matrix
C-S-N	S-GRID	1	EPOXY	23	NON
C-HI-N	HI-GRID	1		20	NON
C-HI-AL		1		20	AL

, the variables of the test specimens were type of textile grid (V, S, HI-GRID) and Al powder surface coating (with, without). The reference specimen was designed by referring to the ACI 318-19 guidelines [37]. Its specimen was designed with a flexural strength lower than its shear strength, so as to induce flexural failure, as shown in Figure 5. In accordance with the laboratory environment, the cross-section of the column was circular with a diameter (D) of 350 mm, a height (H) of 2000 mm, and a shear span ratio (a/d) of 3.5. Eight D22 bars were placed in the main reinforcement, and D10 bars were placed in the transverse reinforcement at 125 mm intervals from the center of the column to the two ends so that the flexural failure of the Column was occurred first.

The re-bar used to fabricate the specimens was D22 with f_y = 500 MPa and D10 with f_y = 400 MPa.

Table 4. Measured concrete and steel reinforcement properties.

Material	Concrete	Steel Reinforcement
		D10	D22
Compressive strength, fck (MPa)	31.2	-	-
Yield stress, fy (MPa)	-	495	455
Yield strain, εy (%)	-	0.305	0.247
Modulus of elasticity, Es (GPa)	-	162	184

shows the mechanical properties measured by the test method given in ASTM A370 [38]. The yield strength of D10 re-bar was 495 MPa; the elastic modulus and strain at yield were 162 GPa and 0.305%, respectively. The yield strength of D22 re-bar was 455 MPa; the elastic modulus and strain at yield were 184 GPa and 0.247%.

Table 5. Mix proportions of concrete.

Design Strength (MPa)	W/B (%)	s/a (%)	Gmax (mm)	Weight of Unit Volume (kg/m3)
				W	C	S	G	AD
30	36.4	45.2	25	162	460	485	970	4.46

W/B: Water-binder ratio, s/a: Ratio of coarse to fine aggregate, G_max: maximum size of coarse aggregate, W: water, C: cement, S: fine aggregate, G: coarse aggregate, AD, admixtures.

shows the concrete mix proportions used for the column experiments. The same transit mixer was used to make all the RC column specimens at once. Cylindrical concrete specimens with a diameter of 100 mm and height of 200 mm were fabricated to evaluate the compressive strength of the concrete according to ASTM C39 [39]. The compressive strength of the cylinder was measured before and after the experiment; the average cylinder compressive strength was found to be 31.2 MPa. The mechanical properties of the re-bars and concrete used for this experiment are summarized in Table 4.

5.2. FRCM Composite Materials

The mechanical properties of the FRCM used for reinforcement are shown in

Table 6. Measured C-FRCM material properties.

Textile Type	Textile Grid			Inorganic Matrix
	V-Type	HI-Type	S-Type
Cross section area (mm2/yarn)	1.856	1.781	1.856	-
Tensile strength (MPa)	1758	2157	2500	-
Elastic modulus (GPa)	147	180	220	-
Compressive strength, (MPa)	-	-	-	74.6

. In addition, as shown in Figure 6, three types of textile grids (V, S, HI) were used as fiber reinforcement, and the matrix was an inorganic mortar. The V grid, S grid, and HI grid used in the investigation are commercial products and were purchased from the manufacturers. The V grid has crisscrossed carbon fibers and glass fibers, with the carbon fibers aligned in the warp direction. The fiberglass roving is 1200 TEX, while a value of 50 K is used for the carbon fiber roving. The weaving method involves the use of two sets of warp yarns, which are firmly connected using pillar stitching. The grid size is 27 mm × 27 mm; styrene-butadiene rubber (SBR) was used for impregnation. For the S grid, carbon fibers were used for warp and weft yarns. Furthermore, a value of 50 K was used for the carbon fiber roving comprising the textile. The same weaving method as that for the V grid was used. The grid size was 21 mm × 21 mm; epoxy was used for impregnation. As for the HI grid, the leno weave method, in which two warp threads twist around and bind up weft thread, was used. Composition of warp and weft yarns was the same as that for the V grid. The glass fiber roving is 2400 TEX and 50 K was used for the carbon fiber roving. The grid size is 20 mm × 20 mm; epoxy was used for impregnation. The mechanical properties of the textile grids were measured by tensile testing of carbon fiber rovings placed in the warp direction. Tests were carried out according to the specimen preparation and testing methods presented in ISO/FDIS 10406-2 [40].

The tensile strength and modulus of elasticity were high in the order of V, HI, and S. The mechanical property of the matrix was measured according to ISO 679: 2009 [41]; compressive strength was found to be 74.6 MPa.

5.3. FRCM Composite Installation and Wrapping Schemes

As shown in Figure 7, after curing for 28 days, RC columns were strengthened with FRCM at their tops and bottoms, where a plastic hinge area formed (1.5d = 465 mm); the strengthening was performed in the following order: (1) grinding of reinforcement surface to remove any impurities, after which surface was washed with water; (2) installation of anchors (rawlplug) to fix the textile grid; (3) placement of a 10 mm thick inorganic matrix flat on the column surface; (4) use of installed anchors to install textile grid on the column surface (1/4 perimeter of the development length) and attach it to the inorganic matrix; and (5) final placement of 15 mm thick inorganic matrix and its curing.

5.4. Test Setup, Instrumentation, and Loading Protocol

The loading device and experimental setup of the structure testing machines (Smart Natural Space Research Center) for cyclic loading of RC column experiments are shown in Figure 8. The strengthened test specimen was loaded with a vertical actuator with a capacity of 1000 kN to apply 10% (294 kN, 0.1f_ck·A_g) of the axial load. A horizontal actuator with a capacity of 1000 kN was used to apply a lateral load so that the same shear force was applied to the test section. In addition, leveling devices installed on both sides of the pre-tensioning plane were used to minimize the P-delta effect due to the axial force acting on the column.

The loading protocol was based on ACI 374.2R-13 [42]. Before yielding of the longitudinal reinforcement, the load was applied at 0.25% and 0.5% of the drift ratio; after yielding of the longitudinal reinforcement, the load was applied in the north (+)/south (−) directions in the order of 1Δ_y, 2Δ_y, 4Δ_y, 6Δ_y, and 7Δ_y for each displacement; the procedure was repeated twice according to the load program. The transverse displacement of the column member at yielding of the longitudinal reinforcement was taken as the time at which the strain gauge attached to the longitudinal reinforcement 62.5 mm from the top of the lower stub reached the yield strain. The test was stopped when the specimen was degraded to 85% of its ultimate load.

To measure the bending yield of the specimen and the strain of the transverse steel reinforcement, a strain gauge was attached to the lower part of the plastic hinge, as shown in Figure 7. Lateral displacement of the specimen was measured by installing an LVDT, as shown in Figure 8.

5.5. Test Results

5.5.1. Load Carrying Capacity, Ductility, and Skeleton Curves

Table 7. Experimental results of the columns.

Specimen	Vy (kN)	Δy (mm)	Vpeak (kN)	Δpeak (mm)	V0.85 (kN)	Δ0.85 (mm)	Gain in Vpeak (%)	Ductility (1)	Failure Mode (2)
Ctrl	−157.5	−22.5	157.7	44.1	134.0	79.5	-	3.7	(1)
			−178.6	−41.8	−151.8	−85.2
C-V-N	150.7	22.5	180.1	42.2	153.1	122.4	14	5.7	(2)
			−188.6	−43.8	−160.3	−135.0
C-S-N	167.7	25.0	195.4	49.0	166.1	132.5	24	5.5	(2)
			−193.5	−46.9	−164.5	−142.8
C-HI-N	−155.5	−20.5	195.8	70.9	166.4	133.8	24	6.5	(2)
			−187.4	−41.1	−159.3	−133.5
C-HI-Al	−168.6	−24.2	198.7	47.8	168.9	146.4	26	6.3	(2)
			−194.1	−48.4	−165.0	−153.7

Note; ₍₁₎ Ductility: ${∆}_{0.85}/{∆}_y$, ₍₂₎ Failure mode: (1) is concrete crushing after longitudinal rebar yielding, (2) is Textile grid rupture.

presents a summary of the test results involving all specimens. The lateral load–displacement hysteresis results of all test specimens considered as envelopes are shown in Figure 9. The x axis of the envelope curves represents the displacement ductility (Δ/Δ_y) because the displacement at yield for each specimen is different. All the FRCM-strengthened specimens exhibited a higher level of stiffness than the CTRL specimens until the yielding of the longitudinal steel reinforcement. After this, the CTRL specimen reached an ultimate load of 157.7 kN at about 2Δ_y, and the strengthened specimens reached maximum load at a higher level than the CTRL specimen at the same displacement ductility, except for the C-HI-N specimen. The maximum load of the C-HI-N specimen was about 3.5 Δ_y; this maximum load was reached at a higher level of displacement compared to the other strengthened specimens. After the maximum load, the load carrying capacity until the end of the test (0.85V_peak) showed a gradual decrease in load compared to the CTRL test, indicating that all the strengthened specimens had excellent load resistance capacity. For the C-HI-N and C-HI Al specimens with HI-type textile grids, the load-resistance capacity reached 85% of the maximum load at 7Δ_y; this was the best value achieved.

Columns 4 and 8 of Table 7 show the maximum load for each specimen and the percentage increase in load compared to the CTRL specimen. For the strengthened specimens, the C-V-N specimen with the V-type textile grid showed the lowest load increase, with a value of 14%. C-S-N, C-HI-N, and C-HI-Al with S-type and HI-type textile grids had similar load increases of 24–26%. The ductility indexes of each textile grid strengthened specimen are shown in the Column 9 of Table 7. The ductility index was defined as the ratio of the transverse displacement (Δ_0.85 at p_u) at 85% load reduction after reaching the maximum load to the transverse displacement (Δ_y) at a yield of the tensile reinforcement. Compared to the CTRL specimen, the ductility indexes of the strengthened specimens C-V-N, C-S-N, C-HI-N, and C-HI-Al increased by 149%, 154%, 176%, and 170%, respectively; all were high ductility indexes.

5.5.2. Crack Patterns and Failure Mode

The crack patterns and failure modes of the CTRL specimen and the FRCM-strengthened specimen at the end of the test are shown in Figure 10 and Figure 11. The CTRL specimen (Figure 10a) developed flexural cracks in the plastic hinge region. The first flexural crack occurred at a drift ratio of 0.25% along the tensile plane of the column in the north (+) direction. The longitudinal reinforcement then yielded in the plastic hinge region, and the crack propagated to the center when the maximum strength was reached. As shown in Figure 11a, final failure was caused by concrete crushing due to severe damage to the cover concrete at the top and bottom of the column and the core concrete inside the transverse steel reinforcement. The C-S-N specimen (Figure 10b) strengthened with the S-type textile grid and developed flexural cracks on the FRCM surface in the plastic hinge region (drift ratio 0.25%), identical to the results of the CTRL specimen. The number of cracks increased after the yielding of the longitudinal reinforcement, and the outer layer of the matrix in the plastic hinge region was delaminated when the maximum load was reached. However, the internal concrete before reinforcement remained sound. The final failure is shown in Figure 11b with the outer layer of the matrix delaminating at the bottom of the column and the textile grid breaking. For this reason, it is believed that the lateral confinement effect of FRCM can delay the failure of the core concrete and the bucking of the longitudinal reinforcement, thereby increasing the repetitive strain capacity and energy dissipation of RC column, as in the study of Bournas et al. [15]. The crack patterns and failure modes observed for the C-V-N, C-HI-N, and C-HI-AL specimens were almost identical to those of the C-S-N specimen.

5.5.3. Strain Distribution

The strain distribution of longitudinal and transverse bars with increasing load is shown in Figure 12 and Figure 13. In the figure, the x-axis represents the strain distribution of the reinforcement, and the y-axis represents the attachment location of the strain gauge. The strain distributions of the longitudinal bars in all experiments showed a monotonic behavior until the yielding of tensile bars. After yielding, the strain in the longitudinal bars increased rapidly. In addition, the FRCM reinforced specimen showed a higher longitudinal strain distribution at the same time point as that of the reference specimen. In the strain distributions of the transverse beams, all specimens failed to reach the yield strain by the end of the test; the strain distributions of the FRCM-reinforced specimens, like the strain distributions of the longitudinal beams, were lower than those of the reference specimens.

5.5.4. Energy Dissipation

When dealing with seismic actions, the ability of structures to dissipate energy is an important factor that characterizes the overall seismic behavior. Referring to existing study [43], the cumulative energy dissipation was calculated as shown in Equations (7) and (8).

$$E_{d,i}=\int F\left(∆\right)d∆$$

(7)

where F is the force attained at each displacement value Δ, while the cumulative energy dissipated during the loading history is:

$$\sum E_{d,i}=\sum _i^n{E}_{d,i}$$

(8)

where n is the total number of applied loading cycle.

Table 8. Cumulative energy dissipation.

Specimens	Cumulative Energy Dissipation (kN-m)
	Drift Ratio 0.25%	Drift Ratio 0.50%	1Δy	2Δy	4Δy	6Δy	7Δy
Ctrl	0.41	1.37	5.00	14.41	37.83	72.44
C-V-N	0.53	1.72	5.67	15.66	41.35	79.01
C-S-N	0.48	1.61	6.17	17.96	48.04	91.46
C-HI-N	0.53	1.73	5.16	13.79	36.85	70.90	106.91
C-HI-Al	0.50	1.67	6.24	17.22	45.60	88.58	135.32

shows the calculated energy dissipation for all specimens. Compared to Ctrl, the FRCM-composite-reinforced specimen showed a higher level of energy dissipation. In the displacement of the subject at the end of the loading, 72.44 kN m for Ctrl (6Δ_y), 79.01 kN m for C-V-N (6Δ_y), and 91.46 kN m for C-S-N (6Δ_y), indicating high-energy dissipation. In particular, the energy dissipation of C-HI-N (7Δ_y) and C-HI-Al (7Δ_y), which applied the HI grid, showed the best energy dissipation with 106.91 kN m and 135.32 kN m, respectively.

5.6. Evaluation of Predicted Peak Axial Stress Formula at Member Level

The bending moment (M_ult) at the ultimate stage was calculated by cross-section analysis of an RC circular column, as shown in Figure 14. The yield strain (ε_y) of the longitudinal reinforcement was applied to the material test results, and the strain of concrete (ε_cu) in the compression zone at the ultimate stage was applied to the strain at failure of lateral-confined concrete proposed by previous researchers. In the formula presented in this study, the strain at failure of concrete presented in ACI 549.4R [20] was used. Based on the center of the cross-section, the depth of the central axis was calculated according to the force equilibrium condition using Equations (7)–(10).

$$M_c=0.85f_{cc}·A·Y$$

(9)

$$M_s=\sum _{i=1}^n\left(N_{si}·\left(\frac{h}{2}-d_i\right)\right)$$

(10)

$$M_f=\frac{1}{2}{E}_f{\epsilon }_f{t}_f·(h-d_{mortar}-c)\left(\frac{2\left(h-d_{mortar}-c\right)}{3}-\left(\frac{h}{2}-c\right)\right)$$

(11)

$$M_{ult}=M_c+M_s+M_f$$

(12)

where M_c, M_s, and M_f = the resistance moments of concrete and longitudinal reinforcement, and the FRCM at ultimate stage; M_ult = moment of ultimate stage; f_cc = compressive strength of confined concrete; A = effective concrete compression area; Y = centroid of cross-section under compressive force; N_si = stress of rebar in row i; d_i = distance of rebar in row I; E_f = modulus of elasticity of FRCM; ε_f = strain of FRCM; t_f = thickness of FRCM; d_mortar = thickness of mortar; c = depth of neutral axis at ultimate stage; and T_tube = tensile force of FRCM.

The results of cross-sectional analysis at flexural failure (M_ult) are shown in

Table 9. Comparison between analytical and experimental results at ultimate stage.

Specimens	${\mathit{M}}_{\mathit{e}\mathit{x}\mathit{p}}$ $(\mathbf{k}\mathbf{N}·\mathbf{m})$	$\mathbf{Comparison}\left(\frac{{\mathit{M}}_{\mathit{a}\mathit{n}\mathit{a}}}{{\mathit{M}}_{\mathit{e}\mathit{x}\mathit{p}}}\right)$
		Mander et al. [35]	ACI 549.4R	J.G.Teng et al. [30]	Proposed Equation
CTRL	169	1.01	0.89	1.01	0.97
C-V-N	184	1.01	0.98	1.06	1.02
C-S-N	195	0.95	0.96	1.02	0.99
C-HI-N	192	0.97	0.96	1.02	0.99
C-HI-Al	196	0.95	0.94	1.00	0.98
Mean		0.98	0.95	1.02	0.99

and Figure 15. The results are expressed as the ratio of the analyzed value to the test value. The analytical results using the Mander et al. [35] lateral confining pressure formula were well-predicted at 1.01 for CTRL specimens; however, the FRCM-strengthened specimens were underestimated at 0.95~0.97 except for the C-V-N specimens. This is likely due to the lack of consideration of the lateral confinement effect of FRCM. For ACI 549.4R [20], the analyzed values tended to underestimate the test values by 0.89 to 0.98 due to exclusion of the confining effect of the transverse steel reinforcement in the calculation of the lateral confining pressure of concrete.

In comparison, the formula proposed in this study showed a very effective prediction of the test values, which had a range from 0.97 to 1.02. These good results are judged to be due to effective lateral confining pressure ratio (κ_f), as applied by J.G. Teng et al. [30].

6. Conclusions

In this study, the structural performance and maximum flexural strength prediction of RC circular columns strengthened with FRCM were evaluated based on experimental results. Prediction of the maximum flexural strength was performed by applying the peak axial stress formula, derived by considering the lateral confinement effect of the transverse steel reinforcement and FRCM composite. Based on experimental and analytical results, the following conclusions were drawn.

(1)

The FRCM-strengthened specimen reached the maximum load after the yielding of the longitudinal reinforcing bars; then, the load gradually decreased until final failure due to the rupture of the textile grid.

(2)

The strength of the FRCM-strengthened specimens increased by about 14~26% compared to the reference specimens due to increases in concrete strength via the lateral restraint effect; the ductility index improved by 49~76%.

(3)

The proposed peak axial stress formula used to consider the influence of transverse reinforcement was compared with the experimental value (Data base) and the predicted value; the suitability was confirmed, with a standard deviation of 27.6% and a coefficient of variation of 0.856; however, it is considered necessary to conduct further research by securing additional FRCM data.

(4)

Predictions of maximum flexural strength of the RC circular columns, performed by cross-sectional analysis, led to excellent theoretical predictive results for the experimental values, which were in a range of 0.98-1.03, reflecting the lateral confinement effects of transverse reinforcement and FRCM.