Experimental Study on Concrete under Combined FRP–Steel Confinement

Abstract

The confinement of reinforced concrete (RC) compression members by fiber-reinforced polymers (FRPs) is an effective measure for the strengthening and retrofitting of existing structures. Thus far, extensive research on the stress–strain behavior and ultimate limit state design of FRP-confined concrete has been conducted, leading to various design models. However, these models are significantly different when compared to one another. In particular, the use of certain empirical efficiency and reduction factors results in various predictions of load-bearing behavior. Furthermore, most experimental programs solely focus on plain concrete specimens or demonstrate insufficient variation in the material properties. Therefore, this paper presents a comprehensive experimental study on plain and reinforced FRP-confined concrete, limited to circular cross sections. The program included 63 carbon FRP (CFRP)-confined plain and 60 CFRP-confined RC specimens with a variation in the geometries and in the applied materials. The analysis showed a significant influence of the compressive strength of the confined concrete on the confinement efficiency in the design methodology, as well as the importance of the proper determination of individual reduction values for different FRP composites. Finally, applicable experimental test results from the literature were included, enabling the development of a modified stress–strain and ultimate condition design model.

1. Introduction

The confinement of axially loaded concrete members is an effective measure for improving load-bearing capacity and ductility. Apart from conventional transverse tie reinforcing steel in combination with shotcrete, fiber-reinforced polymers (FRPs) are becoming increasingly considered for the strengthening and rehabilitation of reinforced concrete (RC) structures. The composite material most commonly combines synthetic fibers (e.g., carbon fibers) and an epoxy-based resin matrix. In the application of confinement, the linear elastic FRP jacket resists the concrete’s lateral expansion, leading to a steadily increasing transverse pressure, σ_r. Regarding circular cross sections, the transverse pressure distributes evenly along the FRP jacket, as shown in Figure 1. The resulting confining pressure is carried by the mostly unidirectionally arranged FRP through tensile stresses σ_j in the hoop direction. Exceeding the initial compressive strength, an effective confinement leads to a multidimensional stress state of the concrete. Thereby, it is possible to increase its maximum bearing capacity and its ultimate strains without significantly affecting the dead loads.

The load-bearing behavior of short, plain concrete members confined with FRP composites has been extensively researched in the last two decades, leading to various experimental programs and design models, see, e.g., in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]. To date, these models have already been included in national standards, codes, and guidelines by several countries and institutions, providing frameworks for the design of the FRP confinement of RC columns for strengthening purposes, see, e.g., in [24,25,26,27,28,29,30].

In general, the ultimate confined concrete strength f_cc and the accompanying axial strain ε_ccu are derived by Equations (1) and (2):

$${\mathit{f}}_{\mathrm{cc}}{ = \mathit{f}}_{\mathrm{c}0}{ + \mathit{k}}_1 ·{\mathit{f}}_{\mathrm{lj}},$$

(1)

$${\epsilon }_{\mathrm{ccu}}{=\epsilon }_{\mathrm{c}0}·{\mathit{k}}_2{+\epsilon }_{\mathrm{c}0}·{\mathit{k}}_3·\frac{{\mathit{f}}_{\mathrm{lj}}}{{\mathit{f}}_{\mathrm{c}0}}·{\left(\frac{{\epsilon }_{\mathrm{ju}}}{{\epsilon }_{\mathrm{c}0}}\right)}^{{\mathit{k}}_4},$$

(2)

where f_c0 is the mean value of the unconfined concrete strength, ε_c0 is the peak strain of the unconfined concrete, f_lj is the confinement pressure provided by the FRP jacket, ε_ju is the rupture strain of the FRP jacket in the application of confinement, and k₁–k₄ are factors affecting the impact of f_lj on f_cc and ε_ccu.

The prediction of the ultimate condition of the confined concrete is directly dependent on the confining pressure f_lj provided by the FRP jacket. The commonly used form for the calculation of the confining pressure is given by Equation (3):

$${\mathit{f}}_{\mathrm{lj}}=\frac{1}{2}·{\rho }_{\mathrm{j}}·{\mathit{E}}_{\mathrm{j}}·{\epsilon }_{\mathrm{ju}}{=\mathit{E}}_{\mathrm{jl}}·{\epsilon }_{\mathrm{ju}}=\frac{2·{\mathit{t}}_{\mathrm{j}}·{\mathit{E}}_{\mathrm{j}}}{\mathit{D}}·{\epsilon }_{\mathrm{ju}},$$

(3)

where ρ_j is the confinement ratio, E_jl is the confinement modulus, E_j is the modulus of the composite material, t_j is the FRP thickness, and D is the diameter of the circular cross section.

The rupture strain of the carbon FRP (CFRP) jacket in the application of confinement, ε_ju, has a significant impact on the confinement pressure, f_lj. According to the current state-of-the-art, ε_ju is defined as the actual hoop rupture strain measured in the FRP jacket, as, in most cases, it is considerably smaller than the ultimate tensile strain found from flat coupon tensile tests ε_FRP. Therefore, Lam and Teng [6] established an FRP efficiency factor k_ε, defined by

$${\epsilon }_{\mathrm{ju}}{=\epsilon }_{\mathrm{FRP}}·{\mathit{k}}_{\mathsf{\epsilon }}.$$

(4)

Although most approaches are derived by the same basic functions, the design models show significant differences.

Table 1. Different approaches to predict f_cc and ε_ccu of confined concrete columns.

Authors	Confined Concrete Compressive Strength fcc	Ultimate Axial Compressive Strain εccu
Richart et al. (1928) [31]	${\mathit{f}}_{\mathrm{cc}}{=\mathit{f}}_{\mathrm{c}0}{+\mathit{k}}_1·{\mathit{f}}_{\mathrm{lj}}$	-
	${\mathit{k}}_1=4.1$
Samaan et al. (1998) [32]	${\mathit{f}}_{\mathrm{cc}}{=\mathit{f}}_{\mathrm{c}0}{+\mathit{k}}_1·{\mathit{f}}_{\mathrm{lj}}$ ${\mathit{k}}_1=6.0·{\mathit{f}}_{\mathrm{lj}}{}^{-0.3}$	${\epsilon }_{\mathrm{ccu}}=\frac{{\mathit{f}}_{\mathrm{cc}}{+\mathit{f}}_0}{{\mathit{E}}_2}$
		${\mathit{E}}_2=245.61·{\mathit{f}}_{\mathrm{c}0}^{0.2}+1.3456·\frac{{\mathit{E}}_{\mathrm{j}}{+t}_{\mathrm{j}}}{\mathit{D}}$
		${\mathit{f}}_0=0.872·{\mathit{f}}_{\mathrm{c}0}+0.371·{\mathit{f}}_{\mathrm{lj}}+6.258$
Xiao and Wu (2003) [13]	${\mathit{f}}_{\mathrm{cc}}=\alpha ·{\mathit{f}}_{\mathrm{c}0}{+\mathit{k}}_1·{\mathit{f}}_{\mathrm{lj}}$	${\epsilon }_{\mathrm{ccu}}=\frac{{\epsilon }_{\mathrm{ju}}}{{\mathit{v}}_2}=\frac{{\epsilon }_{\mathrm{ju}}}{10·{\left({\mathit{f}}_{\mathrm{c}0}/{\mathit{E}}_{\mathrm{jl}}\right)}^{0.9}}$
	${\mathit{k}}_1=4.1-0.45·{\left(\frac{{\mathit{f}}_{\mathrm{c}0}^2}{{\mathit{E}}_{\mathrm{jl}}}\right)}^{1.4}\mathrm{with}\alpha \approx 1.1$
Lam and Teng (2003) [6]	${\mathit{f}}_{\mathrm{cc}}{=\mathit{f}}_{\mathrm{c}0}{+\mathit{k}}_1·{\mathit{f}}_{\mathrm{lj}}$	${\epsilon }_{\mathrm{ccu}}{=\epsilon }_{\mathrm{c}0}·1.75{+\epsilon }_{\mathrm{c}0}·12·\frac{{\mathit{f}}_{\mathrm{lj}}}{{\mathit{f}}_{\mathrm{c}0}}·{\left(\frac{{\epsilon }_{\mathrm{ju}}}{{\epsilon }_{\mathrm{c}0}}\right)}^{0.45}$
	${\mathit{k}}_1=3.3$
Teng et al. (2009) [11]	${\mathit{f}}_{\mathrm{cc}}=\{\begin{array}{c}{\mathit{f}}_{\mathrm{c}0}{+\mathit{f}}_{\mathrm{c}0}·3.5·\left({\rho }_{\mathrm{k}}-0.01\right)·{\rho }_{\mathsf{\epsilon }}\\ {\mathit{f}}_{\mathrm{c}0}\end{array}\begin{array}{c}{\mathrm{if}\rho }_{\mathrm{k}}\ge 0.01\\ {\mathrm{if}\rho }_{\mathrm{k}}<0.01\end{array}$	${\epsilon }_{\mathrm{ccu}}{=\epsilon }_{\mathrm{c}0}·1.75{+\epsilon }_{\mathrm{c}0}·6.5·{\rho }_{\mathrm{k}}{}^{0.8}·{\rho }_{\mathsf{\epsilon }}{}^{1.45}$
	${\rho }_{\mathrm{k}}=\frac{2·{\mathit{E}}_{\mathrm{j}}·t_{\mathrm{j}}}{\left({\mathit{f}}_{\mathrm{c}0}/{\epsilon }_{\mathrm{c}0}\right)·\mathit{D}}{\mathrm{and}\rho }_{\mathsf{\epsilon }}=\frac{{\epsilon }_{\mathrm{ju}}}{{\epsilon }_{\mathrm{c}0}}$
Niedermeier (2009) [33]	${\mathit{f}}_{\mathrm{cc}}{=\mathit{f}}_{\mathrm{c}0}{+\mathit{k}}_1·{\mathit{f}}_{\mathrm{lj}}$	${\epsilon }_{\mathrm{ccu}}{=\epsilon }_{\mathrm{c}0}·1.75{+\epsilon }_{\mathrm{c}0}·19·\frac{{\mathit{f}}_{\mathrm{lj}}}{{\mathit{f}}_{\mathrm{c}0}}$
	${\mathit{k}}_1=3.66$

provides an overview of the selected, renowned models for the design of confined concrete.

Most design models are used to determine the ultimate stress and strain conditions of a column under concentric compression or with comparatively small eccentricities. However, proper confinement can also provide significant strength enhancement for members subjected to combined compression and flexure. For the design of eccentrically loaded, FRP-confined columns, proper material models are essential. In general, these models use stress (σ_c)–strain (ε_c) curves with a parabolic first portion and a straight line second portion (second modulus). An example is given by the stress–strain model of Lam and Teng [6]:

$${\sigma }_{\mathrm{c}}=\{\begin{array}{c}{\mathit{E}}_{\mathrm{c}}·{\epsilon }_{\mathrm{c}0}-\frac{{\left({\mathit{E}}_{\mathrm{c}}{-\mathit{E}}_2\right)}^2}{4·{\mathit{f}}_{\mathrm{c}0}}·{\epsilon }_{\mathrm{c}0}{}^2\\ {\mathit{f}}_{\mathrm{c}0}{+\mathit{E}}_2·{\epsilon }_{\mathrm{c}0}\end{array}\begin{array}{c}\mathrm{if}0\le {\epsilon }_{\mathrm{c}0}\le {\epsilon }_{\mathrm{t}}\begin{array}{c}\\ \end{array}\\ {\mathrm{if}\epsilon }_{\mathrm{t}}\le {\epsilon }_{\mathrm{c}0}\le {\epsilon }_{\mathrm{ccu}}\end{array},$$

(5)

where E₂ is the second modulus, E_c is the modulus of elasticity, and ε_t is the strain value at the transition between the parabolic curve and the straight-line second portion. A graphical representation of Lam and Teng’s stress–strain model is given in Figure 2.

The empirical approaches for the development of design-oriented models (Table 1) mostly follow the concept of Richart et al. [31], introducing empirical confinement effectiveness coefficients k₁ (ultimate stress) and k₂–k₄ (ultimate strain). In the majority of cases, k₁ and k₂–k₄ are defined as constant values or are solely dependent on the maximum confining pressure f_lj. These concepts lead to considerable discrepancies regarding the prediction of confined columns with different initial concrete strengths, f_c0. Figure 3 shows a graphical comparison of stress–strain curves, predicted by the models listed in Table 1, for two specimens—one with a normal (30 MPa) and one with a high (60 MPa) unconfined concrete strength. Particularly for a high initial concrete strength, remarkable differences between the calculated stress–strain curves and the ultimate condition values of f_cc and ε_ccu can be seen. The discrepancies between the predicted results tend to increase significantly alongside the unconfined concrete strength.

The relatively good correlations of the exemplary calculations with f_c0 = 30 MPa may be due to the fact that most empirical design models use experimental investigations on normal-strength concrete for the derivation of the confinement effectiveness, k₁ and k₂–k₄ (Figure 4).

Furthermore, the presented models and equations only concern the confinement effect of the CFRP jacket. The contribution of the internal transverse steel reinforcement and other effects, such as the buckling of the longitudinal steel reinforcement, are not taken into account. Only a few confinement models, e.g., Hu et al. [5], Eid and Paultre [3], Rousakis and Karabinis [35], Pellegrino and Modena [8], Teng et al. [12], or Niedermeier [33], consider the interaction between the internal lateral steel reinforcement and the external FRP jacket. The most common proposals are shown in

Table 2. Different approaches to predict f_cc and ε_ccu of CFRP-confined reinforced concrete (RC) columns.

Authors	Confined Concrete Compressive Strength fcc	Ultimate Axial Compressive Strain εccu
Eid and Paultre (2008) [3]	${\mathit{f}}_{\mathrm{cc}}{=\mathit{f}}_{\mathrm{c}0}{+\mathit{k}}_1·\left({\mathit{f}}_{\mathrm{lj}}+f_{\mathrm{l},\mathrm{wy}}\right)$	${\epsilon }_{\mathrm{ccu}}{=\epsilon }_{\mathrm{c}0}·1.56{+\epsilon }_{\mathrm{c}0}·12·\left(\frac{{\mathit{f}}_{\mathrm{lj}}}{{\mathit{f}}_{\mathrm{c}0}}+\frac{{\mathit{f}}_{\mathrm{l},\mathrm{wy}}}{{\mathit{f}}_{\mathrm{c}0}}\right)·{\left(\frac{{\epsilon }_{\mathrm{ju}}}{{\epsilon }_{\mathrm{c}0}}\right)}^{0.45}$
	${\mathit{k}}_1=3.3$
Pellegrino and Modena (2010) [8]	${\mathit{f}}_{\mathrm{cc}}{=\mathit{f}}_{\mathrm{c}0}{+\mathit{k}}_1·\left({\mathit{f}}_{\mathrm{lj}}{+\mathit{f}}_{\mathrm{l},\mathrm{wy}}·\frac{{\mathit{A}}_{\mathrm{cc}}}{{\mathit{A}}_{\mathrm{c}}}\right)$	${\epsilon }_{\mathrm{ccu}}{=\epsilon }_{\mathrm{c}0}·{2+\epsilon }_{\mathrm{c}0}·B·\frac{\left({\mathit{f}}_{\mathrm{lj}}{+\mathit{f}}_{\mathrm{l},\mathrm{wy}}·\frac{{\mathit{A}}_{\mathrm{cc}}}{{\mathit{A}}_{\mathrm{c}}}\right)}{{\mathit{f}}_{\mathrm{c}0}}$
	${\mathit{k}}_1=\mathit{A}·{\left[\frac{\left({\mathit{f}}_{\mathrm{lj}}{+\mathit{f}}_{\mathrm{l},\mathrm{wy}}·\frac{{\mathit{A}}_{\mathrm{cc}}}{{\mathit{A}}_{\mathrm{c}}}\right)}{{\mathit{f}}_{\mathrm{c}0}}\right]}^{-\alpha }$
Niedermeier (2009) [33]	${\mathit{f}}_{\mathrm{cc}}{=\mathit{f}}_{\mathrm{c}0}{+\mathit{k}}_1·\left[{\mathit{f}}_{\mathrm{lj}}+\left({\mathit{f}}_{\mathrm{l},\mathrm{wy}}-\Delta p\right)·{\left(\frac{{\mathit{D}}_{\mathrm{c}} -\mathrm{s}/2}{D}\right)}^2\right]$	${\epsilon }_{\mathrm{ccu}}{=\epsilon }_{\mathrm{c}0}·1.75{+\epsilon }_{\mathrm{c}0}·19·\left(\frac{{\mathit{f}}_{\mathrm{lj}}}{{\mathit{f}}_{\mathrm{c}0}}+\frac{{\mathit{f}}_{\mathrm{l},\mathrm{wy}}}{{\mathit{f}}_{\mathrm{c}0}} -\frac{\Delta p}{{\mathit{f}}_{\mathrm{c}0}}\right)$
	${\mathit{k}}_1=3.66$

Abbreviations: f_l,wy = confining pressure provided by transverse reinforcement; A_cc = area of core of section enclosed by the center lines of the perimeter spiral or tie; A_c = column cross section; A, B, and α = empirical parameters; D_c = horizontal center distance of the spiral or tie reinforcement; Δp = reduction of confinement pressure between the core section and the concrete cover; s = vertical spacing between spiral or tie bars.

. These models are mostly based on the basic function of Richart et al. [31] where the increase in strength and strain is not dependent on the unconfined concrete strength, f_c0.

Despite the extensive research efforts carried out in the field of FRP confinement of RC columns, there is still a substantial need for research. Particularly research regarding the determination of the confinement effectiveness coefficients as well as the interaction between the FRP-confining jacket and the internal steel reinforcement, which has thus far been considered contradictory by different design models. Furthermore, the literature lacks experimental investigations of FRP-confined RC specimens with adequate variation in different material parameters and sufficient documentation.

2. Experimental Investigations

2.1. Experimental Program

The main objective of this research program was to resolve the pending issues and knowledge gaps regarding the modeling of FRP-confined concrete revealed during the literature review. Primarily, the interaction between the FRP jacket and the transverse steel reinforcement formed part of the investigations. As described in Section 1, the existing design-oriented approaches for dual FRP–steel confinement (see, e.g., in [3,7,8,36]) show significant discrepancies. Furthermore, most experimental programs lack adequate variation in the material properties used.

Therefore, a test program of CFRP-confined plain and RC cylinders, including the following variation parameters, was conceived:

• Diameter of the concrete cylinders
• Concrete mixture/mechanical properties of the core concrete
• Shape of the transverse steel reinforcement (i.e., tie/spiral)
• Diameter and volumetric ratio of the transverse steel reinforcement
• Mechanical properties of the transverse steel reinforcement
• Surface texture of the transverse steel reinforcement
• Volumetric ratio of the longitudinal steel reinforcement
• CFRP material
• Volumetric ratio of the CFRP jacket

In total, the program included 63 CFRP-confined plain concrete specimens and 60 CFRP-confined RC specimens with circular cross sections.

2.2. Materials

The following materials were used for the production of the test specimens.

2.2.1. Concrete

The concrete specimens were produced using different concrete mixtures. Each series was made of concrete from the same batch. All series used CEM II 32.5 cement according to EN 197-1:2011 [37], natural aggregates with a maximum grain size of 16 mm and fly ash. The concrete mixtures were mainly designed to meet the requirements of a standard concrete with a compressive strength f_c0 between 25 and 40 MPa. The properties of the hardened concrete were determined on cylinders with a diameter of 150 mm according to EN 12390-3:2009 [38].

2.2.2. Steel Reinforcement

Table 3. Properties of the used steel reinforcement (mean values).

Type	Nominal Diameter	Ribbing	Yield Strength fym	Tensile Strength ftm	Modulus of Elasticity	Rupture Strain
	[mm]	[-]	[MPa]	[MPa]	[GPa]	[%]
T4	4	yes	550	610	196	8
T6	6
T8	8
T10	10
T12	12		500	608	194	14
T5	5		670	725	205	-
T6NR	6	no	730	760	-	12

shows the experimentally determined properties of the applied internal steel reinforcement. In most cases, steel reinforcement B500 in accordance with the German standard DIN 488-1:2009-08 [39] was used (i.e., T4, T6, T8, T10, and T12).

The variation in the mechanical properties of the transverse steel reinforcement was realized using bars with differing yield strengths (i.e., T5 and T6NR) and without ribbing (i.e., T6NR).

2.2.3. Carbon Fiber-Reinforced Polymer

The confining jackets consisted of unidirectional carbon fiber (CF) sheets and a two-component, thixotropic impregnating epoxy adhesive. To ensure the variation of the material properties, three different sheets from two different manufacturers were used.

CF sheets M1 and M2 showed approximately the same material characteristics, as they originated from one manufacturer, but had a different arrangement of the carbon fibers. CF sheet M3 had a considerably higher tensile strength and rupture strain. The exact material properties, as provided by the manufacturer, are shown in

Table 4. Properties of used CFRP materials.

CFRP type	Density	Axial Tensile Strength	Axial Modulus of Elasticity	Rupture Strain (axial)	Weight Per Square Meter
[-]	[g/m3]	[MPa]	[GPa]	[%]	[g/m2]
M1	1.80	3900	230	1.70	200
M2	1.80	4100	230	1.78	220
M3	1.79	4800	240	2.00	200

, while the arrangement of the fibers of the different sheets can be seen in Figure 5. A two-component, high-strength (33.8 MPa), high-modulus (3.5 GPa) impregnating epoxy resin was used as adhesive and primer.

2.3. Preparation of the Test Specimens

Prior to the strengthening process, the concrete surface was ground until aggregates >4 mm could be seen. Additionally, the top and bottom of the cylinders were ground plane and parallel to ensure uniform load distribution. Seven days prior to the compression tests, the CFRP jacket was applied in a dry lay-up process; after the application of a primer coat to the surface of the concrete, the CF sheets were laminated continuously around the cylinders. The overlap length of the CFRPs was 100 mm, as specified by the manufacturers. The application process is shown in Figure 6.

2.4. Test Setup and Instrumentation

The specimens were tested under uni-axial compression through monotonically applied loading using a hydraulic press with a 5000 MPa load-carrying capacity. The testing machine was set to a displacement-controlled mode with a constant rate of 0.01 mm/s. The axial displacements were measured using linear variable differential transformers (LVDTs). Lateral strains of the CFRP jacket were measured using strain gauges bonded to the specimens at mid-height. In cases where the specimens have internal reinforcement, steel strain gauges were applied on the rebar surface of the transverse reinforcement test specimen at mid-height (Figure 7).

Figure 8 provides a schematic description and a picture of the setup during testing.

2.5. Test Matrix

Table 5. Experimental program.

Series (3 specimens)	Concrete Strength	Dia Meter	Height	CFRP Confinement			Transverse Reinforcement
	fc0	D	h	Material	Layers	tj	Type	s	Geometry
	[MPa]	[mm]	[mm]		[-]	[mm]		[mm]
D15-P-M1-1L-1	36.9	150	300	M1	1	0.111	-	-	-
D15-P-M1-1L-2	36.9	150	300	M1	1	0.111	-	-	-
D15-P-M1-2L-1	36.9	150	300	M1	2	0.222	-	-	-
D15-P-M2-2L-2	16.5	150	300	M2	2	0.244	-	-	-
D15-P-M2-2L-3	34.7	150	300	M2	2	0.244	-	-	-
D15-P-M2-2L-4	42.3	150	300	M2	2	0.222	-	-	-
D15-P-M2-2L-5	52.7	150	300	M2	2	0.244	-	-	-
D15-P-M2-2L-6	39.8	150	300	M2	2	0.244	-	-	-
D15-P-M1-3L-1	36.9	150	300	M1	3	0.333	-	-	-
D15-TR-M1-2L-1	42.3	150	300	M1	2	0.222	T6	100	Tie
D15-TR-M1-2L-2	42.3	150	300	M1	2	0.222	T6	50	Tie
D20-P-M1-1L-1	27.0	200	400	M1	1	0.111	-	-	-
D20-P-M3-1L-2	24.5	200	400	M3	1	0.112	-	-	-
D20-P-M1-2L-1	27.0	200	400	M1	2	0.222	-	-	-
D20-P-M3-2L-2	24.5	200	400	M3	2	0.223	-	-	-
D20-P-M1-3L-1	27.0	200	400	M1	3	0.444	-	-	-
D20-P-M3-3L-2	24.5	200	400	M3	3	0.447	-	-	-
D20-TR-M1-2L-1	27.0	200	400	M1	2	0.222	T4	175	Tie
D20-TR-M1-2L-2	27.0	200	400	M1	2	0.222	T6	175	Tie
D20-TR-M2-2L-3a	28.0	200	400	M2	2	0.244	T6	100	Tie
D20-TR-M2-2L-3b	28.0	200	400	M2	2	0.244	T6	100	Tie
D20-TR-M2-2L-3c	28.0	200	400	M2	2	0.244	T6	100	Tie
D20-TR-M2-2L-4	28.0	200	400	M2	2	0.244	T6	50	Tie
D20-TR-M2-1L-1	24.5	200	400	M2	1	0.122	T6	75	Tie
D20-TR-M2-1L-2	24.5	200	400	M2	1	0.122	T6NR	75	Tie
D20-TR-M2-1L-3	24.5	200	400	M2	1	0.122	T5	50	Tie
D25-P-M1-1L-1	28.1	250	500	M1	1	0.111	-	-	-
D25-P-M1-2L-1	38.0	250	500	M1	2	0.222	-	-	-
D25-P-M1-3L-1	38.0	250	500	M1	3	0.333	-	-	-
D25-P-M1-4L-1	33.0	250	500	M1	4	0.444	-	-	-
D25-SR-M1-1L-1	33.0	250	500	M1	1	0.111	T8	40	Spiral
D25-SR-M1-2L-1	39.0	250	500	M1	2	0.222	T8	40	Spiral
D25-SR-M1-2L-2	28.1	250	500	M1	2	0.222	T10	40	Spiral
D25-SR-M1-2L-3	31.2	250	1000	M1	2	0.222	T8	40	Spiral
D25-SR-M1-3L-1	39.0	250	500	M1	3	0.333	T8	40	Spiral
D25-TR-M1-2L-1	33.0	250	500	M1	2	0.222	T6	100	Tie
D25-TR-M1-2L-2	31.2	250	1000	M1	2	0.222	T6	100	Tie
D30-P-M1-2L-1	30.8	300	600	M1	2	0.222	-	-	-
D30-P-M1-3L-1	30.8	300	600	M1	3	0.333	-	-	-
D30-SR-M1-2L-1	31.0	300	600	M1	2	0.222	T10	40	Spiral
D30-SR-M1-2L-2	31.0	300	600	M1	2	0.222	T10	55	Spiral

shows an overview of the experimental program. The reinforced series with a diameter of 150 mm (i.e., D15-TR) were equipped with six longitudinal reinforcing bars of Type T8 according to Table 3. Series D20-TR-M2-2L-3 was split into three subseries including four (a), six (b), and eight (c) longitudinal reinforcing bars of type T12. Any further reinforced series (D20-TR, D25-SR, D25-TR, and D30-SR) were equipped with 6 longitudinal reinforcing bars of the type T12. In all reinforced series, the concrete cover was 15 mm. In series D15-P-M2-2L-2 to D-15-P-M2-2L-5, the targeted compressive strength was altered deliberately through different concrete mixtures to assess the impact of f_c0 on the material behavior of the confined specimens. Furthermore, series D15-P-M2-2L-6 additionally contained a grit aggregate to examine the impact of the aggregate form and type.

3. Experimental Findings

3.1. Evaluation Methods

The evaluation focused on the stress–strain behavior of the confined plain and RC specimens. Therefore, the axial stress was determined by the ratio of the applied load to the cross-sectional area of the concrete, disregarding the thickness of the CFPR and its possible axial resistance. Axial and lateral strains were obtained from the applied LVTDs and strain gauges. The stress–strain behavior (longitudinal and transverse) of the CFRP-confined specimens was bilinear in general, and consisted of a three-phase behavior like that predicted by the material model illustrated in Figure 2. The second modulus could be observed in the longitudinal (E₂) as well as in the transverse (E_2,t) direction. As an example, Figure 9 shows the stress–strain curves of single specimens of series D15-P-M1-1L-1, D15-P-M1-2L-1, and D15-P-M1-3L-1, illustrating the interrelation between E₂ and the volumetric ratio of the CFRP jacket. An increase in the applied CFRP layers led to higher second moduli and higher ultimate states of strength (f_cc) and strain (ε_ccu).

The failure of the CFRP-confined plain or steel reinforced specimens was caused by a sudden and noisy fracture of the CFRP sheets at ultimate strength, f_cc, and strain, ε_ccu. Typical examples of failed confined plain and RC specimens can be seen in Figure 10 and Figure 11.

In addition to the stress–strain relationships, the development in the comparative diagrams showing the axial–transverse strain responses and the axial–confinement stress responses of the CFRP-confined concrete specimens was an important aspect of the evaluation process. These diagrams enable the analysis of the factor k₁ (cf. Equation (1)) and the second Poisson’s ratio of the confined member ν₂. Typical examples are shown in Figure 12.

In most cases, the initial slopes of the axial strain and transverse strain relationships matched well the typical initial Poisson’s ratio for concrete of 0.2. As the axial strain increased, the ratio between the transverse and axial strain also increased, indicating the acceleration of the expansion of the concrete. This second linear slope describes the second Poisson’s ratio ν₂. Furthermore, the axial–confinement stress response explains the design factor, k₁. Once the axial stress exceeds the unconfined concrete strength, the curves converge to flatter linear relationships compared to that of the initial behavior, expressing the empirical confinement effectiveness coefficient k₁.

3.2. CFRP-Confined Concrete Specimens

Table 6. Test results of CFRP-confined plain concrete specimens.

Series	Specimens	fc0	fcc	εccu	E2,t	E2	ν2	k1	kε
		[MPa]	[MPa]	[%]	[MPa]	[MPa]	[-]	[-]	[-]
D15-P-M1-1L-1	1	36.9	42.23	0.761	497	960	1.857	1.581	0.546
	2		45.34	0.939	750	1112	1.747	2.196	0.649
	3		47.39	1.017	647	1094	1.681	1.893	0.737
	Mean:		44.99	0.906	631	1055	1.762	1.890	0.644
D15-P-M1-1L-2	1	36.9	44.90	0.868	670	1039	1.532	1.974	0.590
	2		46.72	1.001	536	999	1.800	1.553	0.867
	3		44.11	0.890	517	1008	1.948	1.739	0.767
	Mean:		45.24	0.920	574	1015	1.760	1.755	0.741
D15-P-M1-2L-1	1	36.9	55.43	1.089	1996	2079	1.033	3.031	0.516
	2		61.87	1.450	2166	2018	0.897	3.210	0.625
	3		62.82	1.480	1932	2055	1.047	2.855	0.749
	Mean:		60.04	1.340	2031	2051	0.992	3.032	0.630
D15-P-M2-2L-2	1	16.5	54.16	3.138	3273	1209	0.394	4.270	0.600
	2		54.53	2.908	2854	1292	0.533	3.807	0.743
	3		47.02	2.730	3120	1266	0.395	4.295	0.522
	Mean:		51.90	2.925	3082	1256	0.441	4.124	0.622
D15-P-M2-2L-3	1	34.7	64.07	1.652	2553	1895	0.811	3.339	0.651
	2		67.37	1.920	2754	1862	0.956	3.674	0.729
	3		69.73	2.030	2634	1757	0.894	3.514	0.752
	Mean:		67.06	1.867	2647	1838	0.887	3.509	0.711
D15-P-M2-2L-4	1	42.3	72.68	1.570	1867	2023	1.115	2.715	0.885
	2		67.36	1.240	1750	2135	1.325	2.495	0.737
	3		68.36	1.390	1956	2221	1.253	2.789	0.758
	Mean:		69.47	1.400	1858	2126	1.231	2.666	0.793
D15-P-M2-2L-5	1	52.7	75.25	1.397	1255	1470	1.499	2.046	0.785
	2		71.07	1.235	989	1291	1.561	1.919	0.785
	Mean:		73.16	1.316	1122	1381	1.530	1.983	0.785
D15-P-M2-2L-6	1	39.8	69.55	1.820	1949	1758	1.009	2.514	0.505
	2		66.42	1.938	1773	1602	1.031	2.352	0.841
	3		67.85	1.926	2124	1672	0.987	2.676	0.774
	Mean:		67.94	1.895	1949	1677	1.009	2.514	0.707
D15-P-M1-3L-1	1	36.9	81.16	1.867	3180	2672	0.825	3.125	0.722
	2		80.43	1.869	3482	2432	0.754	3.497	0.699
	3		81.05	2.125	3137	2350	0.795	3.087	0.719
	Mean:		80.88	1.954	3266	2485	0.791	3.236	0.713
D20-P-M1-1L-1	1	27.0	36.68	1.128	559	928	1.626	2.189	0.802
	2		37.39	1.226	679	893	1.311	2.654	0.790
	3		36.66	1.000	625	1066	2.035	2.446	0.814
	Mean:		36.91	1.118	621	962	1.657	2.430	0.802
D20-P-M3-1L-2	1	24.5	39.17	0.824	563	1230	2.074	2.177	0.400
	2		42.25	0.949	932	1447	1.986	3.174	0.475
	3		39.73	0.741	1059	1816	1.920	3.303	0.420
	Mean:		40.38	0.838	851	1498	1.993	2.885	0.432
D20-P-M1-2L-1	1	27.0	45.81	1.266	1600	1810	1.089	3.253	0.661
	2		54.16	1.738	2220	2057	0.963	4.349	0.743
	3		53.99	1.681	2084	2017	0.961	4.150	0.767
	Mean:		51.32	1.562	1968	1961	1.004	3.917	0.724
D20-P-M3-2L-2	1	24.5	58.29	1.411	2126	2065	1.146	4.337	0.530
	2		61.90	1.653	2032	1977	1.218	4.048	0.640
	3		48.99	1.018	2399	2597	1.091	4.825	0.370
	Mean:		56.39	1.361	2186	2213	1.152	4.403	0.513
D20-P-M1-3L-1	1	27.0	71.72	2.140	3584	2705	0.752	4.509	0.729
	2		71.15	2.264	3136	2305	0.772	3.738	0.749
	3		71.30	2.350	3440	2254	0.648	4.077	0.721
	Mean:		71.39	2.251	3387	2421	0.724	4.108	0.733
D20-P-M3-3L-2	1	24.5	67.24	1.614	3151	2244	0.802	4.128	0.480
	2		68.77	1.570	2788	2457	1.004	3.597	0.500
	3		76.45	2.000	3156	2286	0.966	4.146	0.625
	Mean:		70.82	1.728	3032	2329	0.924	3.957	0.535
D25-P-M1-1L-1	1	28.1	30.11	0.834	600	1027	1.724	2.933	0.722
	2		29.92	0.893	660	1049	1.582	3.231	0.696
	3		29.85	0.894	1033	1202	1.130	5.088	0.484
	Mean:		29.96	0.874	764	1093	1.479	3.751	0.634
D25-P-M1-2L-1	1	38.0	44.87	0.798	675	991	1.994	1.650	0.413
	2		46.33	0.905	634	1000	1.584	1.550	0.590
	3		44.20	0.877	429	550	1.091	1.050	0.413
	Mean:		45.13	0.860	579	847	1.556	1.417	0.472
D25-P-M1-3L-1	1	38.0	59.54	1.511	1564	1820	1.151	2.551	0.678
	2		56.89	1.300	1692	1727	1.030	2.759	0.548
	3		56.94	1.195	1437	1709	1.224	2.343	0.590
	Mean:		57.79	1.335	1564	1752	1.135	2.551	0.605
D25-P-M1-4L-1	1	33.0	75.80	2.270	3140	2448	0.804	3.870	0.826
	2		66.20	1.840	2890	2249	0.850	3.571	0.708
	3		77.80	2.470	3314	2503	0.783	4.121	0.826
	Mean:		73.27	2.193	3115	2400	0.812	3.854	0.787
D30-P-M1-2L-1	1	30.8	41.50	1.206	719	1152	1.580	2.167	0.944
	2		40.85	1.115	1178	1476	1.146	3.690	0.578
	3		43.33	1.319	860	1371	1.432	2.909	0.885
	Mean:		41.89	1.213	919	1333	1.386	2.922	0.802
D30-P-M1-3L-1	1	30.8	50.75	1.459	1657	1859	1.126	3.280	0.740
	2		51.08	1.539	1852	1869	1.007	3.645	0.708
	3		47.68	1.345	1991	1876	0.880	3.957	0.546
	Mean:		49.84	1.448	1833	1868	1.004	3.627	0.665

shows the results obtained from the CFRP-confined plain concrete specimens without internal reinforcement.

For the following analysis, the specific values ρ_j, E_jl, and f_lj had to be determined for each series. Set in relation to the unconfined concrete strength, the ratios E_jl/f_c0, E_jl/f_c0², and f_lj/f_c0 can be defined (

Table 7. Specific values for the CFRP-confined plain concrete specimens.

Series	ρj	flj	Ejl	Ejl/fc0	Ejl/fc02	flj/fc0
	[%]	[MPa]	[MPa]	[-]	[-]	[-]
D15-P-M1-1L-1	0.296	4.00	340	9.24	0.250	0.109
D15-P-M1-1L-2	0.296	4.00	340	9.24	0.250	0.109
D15-P-M1-2L-1	0.593	8.01	682	18.474	0.501	0.217
D15-P-M2-2L-2	0.652	9.44	750	45.38	2.747	0.571
D15-P-M2-2L-3	0.652	9.44	750	21.63	0.624	0.272
D15-P-M2-2L-4	0.593	8.01	682	16.13	0.382	0.190
D15-P-M2-2L-5	0.652	9.44	750	14.22	0.270	0.179
D15-P-M2-2L-6	0.652	9.44	750	18.83	0.473	0.237
D15-P-M1-3L-1	0.889	12.02	1022	27.71	0.751	0.326
D20-P-M1-1L-1	0.222	3.00	256	9.48	0.352	0.111
D20-P-M3-1L-2	0.223	2.65	268	10.92	0.445	0.108
D20-P-M1-2L-1	0.444	6.00	511	18.96	0.703	0.223
D20-P-M3-2L-2	0.447	5.30	536	21.85	0.890	0.216
D20-P-M1-3L-1	0.733	10.62	843	31.28	1.160	0.394
D20-P-M3-3L-2	0.670	7.94	805	32.77	1.335	0.323
D25-P-M1-1L-1	0.178	2.40	204	7.28	0.259	0.086
D25-P-M1-2L-1	0.356	4.81	409	10.76	0.283	0.126
D25-P-M1-3L-1	0.533	7.21	613	16.14	0.425	0.190
D25-P-M1-4L-1	0.711	9.61	818	24.77	0.750	0.291
D30-P-M1-2L-1	0.296	4.00	341	11.06	0.359	0.130
D30-P-M1-3L-1	0.444	6.00	511	16.59	0.538	0.195

).

The variation in the diameter of the cylinder, as well as the thickness of the CFRP, led to varying volumetric ratios of the CFRP jackets, ρ_j. The volumetric ratio and the material properties of the CFRP jacket define its maximum confinement pressure, f_lj, as shown in Equation (3). As expected, f_lj had a significant impact on f_cc and ε_ccu. Furthermore, the investigations indicated that the unconfined concrete strength, f_c0, is a second impact factor. Figure 13 illustrates the dependence of the strength enhancement, Δf_cc (Δf_cc = f_cc − f_c0) and the ultimate strain, ε_ccu, on the initial concrete strength, f_c0.

For this comparison, only f_c0 was changed. Only test specimens with equal diameters (150 mm) and properties of the applied CFRP system were used, while the concrete strength, f_c0, varied. An impact of f_c0 on f_cc and ε_ccu can be recognized, but a sufficient correlation is pending. Therefore, the proposal of Xiao and Wu [13] was applied to involve the unconfined strength into the analysis. If f_l is set in relation to f_c0, satisfying regressions for the prediction of f_cc and ε_ccu can be found. Figure 14 shows the results of all plain test specimens defined using the CFRP system, as listed in Table 6, and the regression curves for the strength enhancement, Δf_cc, and the ultimate strain, ε_ccu.

The high coefficients of determination of the regression curves indicate the reliability of the ratio between confinement pressure and unconfined concrete strength to predict the load-bearing capacity of a CFRP-confined concrete member.

Further analysis confirmed that relating the confinement modulus E_jl to the divisor f_c0 enables the prediction of E_2,t, as well as ν₂^,. Figure 15 shows the results of all plain test specimens as listed in Table 6, as well as the regression curves for the second modulus E_2,t and the second Poisson’s ratio, ν₂.

The comparison of the variation in the cross-sectional diameter showed no significant size effect on the FRP-confined concrete. The use of the confinement modulus E_jl and the calculated confinement pressure f_lj are sufficient for the consideration of the varying diameter.

3.3. FRP Rupture Strain and Accompanied Partial Safety Factors

Regarding the CFRP’s rupture strain reached by the CFRP jacket, the investigations correspond with the findings of Lam and Teng [6,23]. In almost all cases, the rupture strain was considerably lower than the ultimate tensile strain found from flat coupon tensile tests. Therefore, a factor k_ε < 1.0 should be mandatory. An overview of different approaches to determine k_ε is given in

Table 8. Suggested approaches to determine k_ε.

Source		FRP-Confined Plain Concrete	FRP-Confined Reinforced Concrete
Niedermeier	[33,40]	kε = 0.66, kεk = 0.50	kε = 0.50, kεk = 0.25
Lam and Teng	[6,23]	kε = 0.586 (Carbon), kε = 0.669 (Glass)	no information
Toutanji et al.	[41]	kε = 0.6	no information
Smith et al.	[21]	kε = 0.8	no information
Pellegrino and Modena	[8]	${\mathit{k}}_{\mathsf{\epsilon }}=0.25+0.25 · \left(\frac{2 ·{ \mathit{R}}_{\mathrm{c}}}{b}\right)$	${\mathit{k}}_{\mathsf{\epsilon }}=\gamma ·{ \mathit{C}}^{ -0.7} \le 0.8 \mathrm{with} \mathit{C}=\frac{{\mathit{E}}_{\mathrm{s}} ·{ \rho }_{\mathrm{l}}}{{\mathit{E}}_{\mathrm{j} }·{ \rho }_{\mathrm{j}}}$

Abbreviations: R_c = corner radius; E_s = elastic modulus steel reinforcement; ρ_l = longitudinal steel ratio.

.

While most approaches suggest a common, universally valid reduction factor for CFRP systems, the conducted experimental program shows significant differences, even between the used carbon fibers. The average value for the three different CFRP systems differed remarkably between k_ε = 0.49 and k_ε = 0.70. The use of a mean value k_ε, as mainly suggested in literature, can, therefore, be uncertain. Due to the large scattering of the test results, the conservative approach introduced by Niedermeier [33,40] was adopted, using characteristic values, k_εk. In accordance with EN 1990:2002 [42], characteristic values for the tested specimens were determined; the results can be seen in Figure 16. In summary, the evaluation revealed the dependence of the efficiency factors k_ε on the used CFRP material.

Furthermore, the findings enabled the derivation of particular partial factors γ_j for the used CFRP materials. The approach introduced in the fib bulletin 80 [43] was used for the calculation:

$${\gamma }_{\mathrm{j}}=\frac{\exp (-1.645·{\mathit{V}}_{\mathrm{x}})}{{\exp (-\alpha }_{\mathrm{R}}·\beta ·{\mathit{V}}_{\mathrm{x}})}·{\gamma }_{\mathrm{Rd}1}·{\gamma }_{\mathrm{Rd}2},$$

(6)

where α_R is the sensitivity factor (α_R = 0.8), V_x is the presumed coefficient of variation of the rupture strain ε_FRP, β is the reliability factor (β = 3.8), γ_Rd1 is a factor considering model uncertainties, and γ_Rd2 is a factor considering geometrical uncertainties.

As shown in

Table 9. Calculated partial factors γ_j for the CFRP materials used.

CFRP Sheet	Vx	γj
M1	0.200	1.59
M2	0.155	1.50
M3	0.189	1.57

, the variation coefficients V_x vary remarkably between the used CFRP materials. Hence, γ_j should be determined separately for each FRP system—for instance, within a technical approval procedure.

For the derivation of the displayed partial factors according to Equation (7), γ_Rd1 was predicted with a value of 1.20 because model uncertainties are comparable to that of models for shear design. In contrast, γ_Rd2 was determined with a value of 1.0. For columns with a circular cross section, the geometrical uncertainties are negligible, as k_ε persisted at a constant value independent of the column diameter.

In comparison, the calculated safety factors are significantly higher than those suggested by current recommendations, codes, and guidelines, as listed in

Table 10. Recommended FRP material safety factors γ_j.

Recommendation/Code		γj
CNR-DT 200 R1/2013	[27]	1.21
GB 50608-2010	[28]	1.40
DAfStb-Guideline	[30]	1.35
fib Technical Report	[44]	1.35

. These partial safety factors originated from flat coupon tests of CFRP laminates and were not conditional on the application. However, this is a potential unsafe approach, as γ_j depends on V_x of the FRP jacket’s hoop strain applied to the column perimeter. The same applies for the characteristic values of the FRP strength and rupture strain.

3.4. CFRP-Confined Reinforced Concrete Specimens

Table 11. Test results of the CFRP-confined RC specimens.

Series	Specimens	fc0	ke	fl(j+w)	fcc	Δfcc	εccu	E2,t	ν2
		[MPa]	[-]	[MPa]	[MPa]	[MPa]	[%]	[MPa]	[-]
D15-TR-M1-2L-1	1	42.3	0.352	9.93	83.80	36.70	1.254	5178	0.873
	2				89.46	42.36	1.680	5376	0.951
	3				86.15	39.05	1.720	4886	0.990
	Mean:				86.47	39.37	1.551	5147	0.938
D15-TR-M1-2L-2	1	42.3	0.182	8.51	83.25	36.16	1.620	3745	1.120
	2				81.92	34.82	1.430	3129	1.293
	3				73.03	25.94	1.180	4485	0.996
	Mean:				79.40	32.31	1.410	3786	1.136
D20-TR-M1-2L-1	1	27.0	0.154	6.08	65.08	27.08	1.980	3241	0.814
	2				69.37	31.37	2.176	2595	0.930
	3				67.76	29.76	2.106	2552	0.959
	Mean:				67.40	29.40	2.087	2796	0.901
D20-TR-M1-2L-2	1	27.0	0.146	6.17	64.99	26.99	1.977	3216	0.655
	2				64.43	26.43	1.915	2602	0.784
	3				60.75	22.75	1.746	2839	0.749
	Mean:				63.93	25.39	1.879	2886	0.729
D20-TR-M2-2L-3a	1	28.0	0.325	7.69	66.10	30.77	1.660	3945	0.647
	2				68.70	33.38	1.630	3476	0.736
	3				67.05	31.72	1.690	2860	0.971
	Mean:				67.28	31.96	1.660	3427	0.785
D20-TR-M2-2L-3b	1	28.0	0.325	7.69	72.80	33.75	1.690	3298	0.937
	2				75.91	36.85	1.860	3277	0.895
	3				72.84	33.78	1.660	3339	0.882
	Mean:				73.85	34.79	1.737	3305	0.905
D20-TR-M2-2L-3c	1	28.0	0.325	7.69	76.32	33.47	1.781	3631	0.811
	2				77.08	34.23	1.796	4370	0.769
	3				78.39	35.54	1.926	3524	0.781
	Mean:				77.26	34.41	1.834	3842	0.787
D20-TR-M2-2L-4	1	28.0	0.483	8.91	76.97	37.92	1.877	3738	0.727
	2				77.06	38.00	1.834	4424	0.654
	3				78.06	39.00	1.867	3973	0.709
	Mean:				77.36	38.31	1.859	4045	0.697
D20-TR-M2-1L-1	1	24.5	0.400	4.55	51.64	26.29	1.094	2830	0.880
	2				54.32	28.97	1.257	3190	0.865
	Mean:				52.98	27.63	1.176	3010	0.873
D20-TR-M2-1L-2	1	24.5	0.490	5.10	49.07	23.71	1.065	2452	0.941
	2				57.04	31.69	1.180	2043	1.228
	3				56.68	31.33	1.249	2303	1.072
	Mean:				54.26	28.91	1.165	2266	1.080
D20-TR-M2-1L-3	1	24.5	0.400	4.92	56.65	31.30	1.193	3871	0.783
	2				57.77	32.42	1.310	3129	0.921
	3				52.07	26.71	1.450	3621	0.891
	Mean:				55.50	30.14	1.318	3540	0.865
D25-SR-M1-1L-1	1	33.0	0.590	6.25	60.65	20.62	1.473	3125	0.799
	2				59.80	19.77	1.490	-	-
	3				60.84	20.81	1.616	3361	0.780
	Mean:				60.43	20.40	1.526	3243	0.790
D25-SR-M1-2L-1	1	39.0	0.590	8.65	76.51	30.50	1.850	3140	0.776
	2				75.79	29.78	1.966	3140	0.835
	3				76.69	30.68	2.036	3412	0.811
	Mean:				76.33	30.32	1.951	3230	0.807
D25-SR-M1-2L-2	1	28.1	0.578	10.75	-	-	-	5257	0.475
	2				-	-	-	4634	0.503
	3				-	-	-	4783	0.476
	Mean:				-	-	-	4891	0.485
D25-SR-M1-2L-3	1	31.2	0.590	8.65	68.08	29.86	1.911	3538	0.632
	2				68.96	30.74	2.214	4374	0.490
	Mean:				68.52	30.30	2.063	3956	0.561
D25-SR-M1-3L-1	1	39.0	0.590	11.06	87.95	41.94	2.350	4545	0.583
	2				87.25	41.24	2.220	4603	0.589
	3				85.88	39.87	2.100	4377	0.616
	Mean:				87.03	41.02	2.223	4508	0.596
D25-TR-M1-2L-1	1	33.0	0.430	5.43	60.90	20.86	1.800	2884	0.832
	2				57.57	17.54	1.605	2726	0.786
	3				50.83	10.80	1.258	2338	0.991
	Mean:				56.43	16.40	1.554	2649	0.870
D25-TR-M1-2L-2	1	31.2	0.430	5.43	54.02	15.80	1.466	2870	0.731
	2				50.83	12.61	1.289	2968	0.704
	3				54.64	16.42	1.564	2845	0.717
	Mean:				53.16	14.94	1.440	2894	0.717
D30-SR-M1-2L-1	1	31.0	0.651	7.44	-	-	-	4922	0.480
	2				-	-	-	4846	0.521
	3				-	-	-	4380	0.577
	Mean:				-	-	-	4716	0.526
D30-SR-M1-2L-2	1	31.0	0.601	7.63	-	-	-	4832	0.473
	2				65.20	29.34	1.880	3813	0.587
	3				-	-	-	3888	0.600
	Mean:				65.20	29.34	1.880	4178	0.553

shows the results obtained from the tests using the CFRP-confined concrete specimens with internal reinforcement, confirming a joint confinement effect by the external CFRP confinement and internal transverse reinforcement. Dual confinement strongly increases the load-bearing capacity in general. Therefore, the confinement pressures of the CFRP jacket and the transverse steel reinforcement have to be summed according to the work in [3]:

$${\mathit{f}}_{\mathrm{l}(\mathrm{j}+\mathrm{w})}{=\mathit{f}}_{\mathrm{lj}}{+\mathit{f}}_{\mathrm{l},\mathrm{wy}}=\frac{1}{2}·{\rho }_{\mathrm{j}}·{\mathit{E}}_{\mathrm{j}}·{\epsilon }_{\mathrm{ju}}+\frac{1}{2}·{\rho }_{\mathrm{st}}·{\mathit{f}}_{\mathrm{y}}·{\mathit{k}}_{\mathrm{e}}{\mathrm{with}\mathit{k}}_{\mathrm{e}}={\left(\frac{{\mathit{D}}_{\mathrm{c}}-\mathrm{s}/2}{\mathit{D}}\right)}^2{\mathrm{and}\rho }_{\mathrm{st}}=\frac{\pi ·{\varnothing }_{\mathrm{w}}{}^2}{{\mathit{D}}_{\mathrm{c}}·\mathit{s}},$$

(7)

where ρ_st is the transverse steel volumetric ratio, f_y is the yield stress, k_e is the coefficient of lateral and vertical efficiency of the transverse steel reinforcement according to Niedermeier [33], D_c is the horizontal center distance of the spiral or tie reinforcement, Ø_w is the diameter of the transverse steel reinforcement, and s is the vertical spacing between the spiral or tie bars.

For the following analysis, the provided confinement pressure and confinement stiffness had to be determined for each series. The specific values are shown in

Table 12. Specific values of the CFRP-confined RC specimens.

Series	flj	fl,wy	Asl	σsl	fl(j+w)/fc0
	[MPa]	[MPa]	[mm2]	[MPa]	[-]
D15-TR-M1-2L-1	8.01	1.92	170	4.85	0.235
D15-TR-M1-2L-2	8.01	0.50	170	4.85	0.201
D20-TR-M1-2L-1	6.01	0.07	679	11.04	0.226
D20-TR-M1-2L-2	6.01	0.16	679	11.04	0.229
D20-TR-M2-2L-3a	7.08	0.62	452	7.31	0.275
D20-TR-M2-2L-3b	7.08	0.62	679	11.04	0.275
D20-TR-M2-2L-3c	7.08	0.62	905	14.83	0.275
D20-TR-M2-2L-4	7.08	1.83	679	11.04	0.318
D20-TR-M2-1L-1	3.54	1.01	50	0.80	0.185
D20-TR-M2-1L-2	3.54	1.56	50	0.80	0.208
D20-TR-M2-1L-3	3.54	1.38	50	0.80	0.200
D25-SR-M1-1L-1	2.40	3.85	679	7.01	0.189
D25-SR-M1-2L-1	4.81	3.85	679	7.01	0.222
D25-SR-M1-2L-2	4.81	5.94	679	7.01	0.383
D25-SR-M1-2L-3	4.81	3.85	679	7.01	0.277
D25-SR-M1-3L-1	7.21	3.85	679	7.01	0.283
D25-TR-M1-2L-1	4.81	0.63	679	7.01	0.164
D25-TR-M1-2L-2	4.81	0.63	679	7.01	0.174
D30-SR-M1-2L-1	4.01	3.43	679	4.85	0.240
D30-SR-M1-2L-2	4.01	3.63	679	4.85	0.246

. Additionally, the cross-sectional area of the longitudinal reinforcement A_sl and the maximum stress carried by the longitudinal reinforcement during the compression test σ_sl are specified. The strength enhancement Δf_cc is defined as Δf_cc = f_cc − f_c0 − σ_sl.

In the diagrams of Figure 17, the experimental results for the strength enhancement, as well as the ultimate strain reached for both the confined plain and the RC cylinders are shown as functions of the ratio between f_l(j+w) and f_c0. As for the results of the sole confined plain concrete specimens, satisfying regressions for the prediction of f_cc and ε_ccu can be found.

As observed for the plain concrete, the bearing behavior of the confined RC is defined by a decrease in the specimens’ axial rigidity. However, the transition zone is smoother and prolonged.

Figure 18 shows the differences in bearing behavior, comparing a CFRP-confined plain concrete specimen and a column dually confined by a transverse spiral reinforcement and a CFRP jacket. In detail, a single specimen of series D30-SR-M1-2L-2 with a diameter of 300 mm and a spiral (Ø = 10 mm, s = 55 mm) was compared to a specimen of the same diameter and confinement but without reinforcement (series D30-P-M1-2L-1). As explained by Equation (7), a constant confining pressure of the yielding steel transverse reinforcement can be assumed. The second modulus is similar to E₂ observed in confined plain concrete, as further strength enhancement depends on the linear elastic CFRP jacket.

In addition to the amount of transverse reinforcement, the reinforcement type was varied by the application of normal ties and heavy spirals. A comparison between both reinforcement types is given in Figure 19. Herein, a CFRP-confined specimen of series D25-SR-M1-2L-3 with a diameter of 250 mm and a spiral (Ø = 8 mm, s = 40 mm) was compared to a specimen of series D25-TR-M1-2L-2 with the same diameter and CFRP confinement but with tie reinforcement (Ø = 6 mm, s = 100 mm).

The transition zone between the first linear increase and second linear branch, E₂, of the spiral reinforced specimen is more extended. Until its yielding strength is reached, the spiral reinforcement can activate a significantly higher confinement pressure, leading to a higher f_cc and ε_ccu. However, the E₂ reached is almost similar. In addition, Figure 18 and Figure 19 reveal a discrepancy between the strain development of the CFRP jacket and the transverse reinforcement. Exceeding the elastic range of the concrete, the strain of the transverse reinforcement ε_st increased more slowly compared to the CFRP jacket, ε_j. This behavior is contradictory to the assumptions of most material models, e.g., Hu et al. [5] or Eid and Paultre [3]. These models suppose an equal strain distribution of ε_j and ε_st. Figure 20 shows the deviations in the axial–transverse strain responses and the axial–confinement stress responses for series D30-SR-M1-2L-2.

3.5. Impact of the Longitudinal Reinforcement on the CFRP Jacket’s Rupture Strain

Previous investigations on the impact of longitudinal reinforcement on the CFRP jacket’s rupture strain, e.g., by Pellegrino and Modena [8] and Bai et al. [45], suppose additional effects of the buckling steel bars on the reduction factor k_ε. Niedermeier [33,40] followed this proposal and suggested a mean value k_ε = 0.50 and a characteristic value k_εk = 0.25. This procedure was adopted by the German Guideline for FRP Strengthening of Concrete Structures by DAfStb [30].

The experimental investigations did not confirm the assumption suggested in [8]. In general, the longitudinal reinforcement had no impact on the ultimate rupture strain of the CFRP jacket. Figure 21 shows a comparison of series D20-TR-M2-2L-3a, D20-TR-M2-2L-3b, and D20-TR-M2-2L-3c. Therein, CFRP-confined specimens with a diameter of 200 mm and the same tie configuration (Ø = 6 mm, s = 100 mm) with a different number of longitudinal reinforcing bars (Ø = 12 mm) were compared, showing that the number of bars differed between 4, 6, and 8. In all cases, approximately the same maximum axial strain, ε_ccu, was reached. A strong impact of the longitudinal reinforcement on ε_ju should influence the confinement pressure, f_l; because of this, the diagram on the left of Figure 21 explains the determination of k_ε for the three longitudinal bar configurations by using the proposal of Pellegrino and Modena [8]. As the number of bars increases, k_ε should decrease and, therefore, reduce ε_ccu; however, the tests could not confirm these assumptions.

In conclusion, the reduction factor k_ε remains constant independent of the applied longitudinal reinforcement. Low reduction values such as k_εk = 0.25 are highly conservative and may provoke an unnecessary loss of load-bearing capacity.

4. Implementation of the Experimental Results from the Literature

4.1. Included Experimental Programs

The obtained test database was enlarged with the test results of Eid et al. [4], Xiao and Wu [13], Lee et al. [46], Matthys et al. [47], Lam and Teng [48,49] and Ilki et al. [50]. The sufficient documentation, including all geometrical and mechanical parameters needed for analysis, was the main reason for the specific selection. Furthermore, the listed experimental programs provide an adequate variation in initial concrete strengths and properties of the used CFRP composites. In addition, the investigations contained several CFRP-confined RC specimens and large-scaled tests.

Table 13. Included experimental programs from the literature.

Authors			Used Materials	Number of Specimens 1
Xiao and Wu	(2003)	[13]	CFRP 1:	14 (U), 42 (U) k1 and ν2 analysis only
			Ej = 96 GPa, εFRP = 1.64 %, tj,n=1 = 0.39 mm
			CFRP 2:
			Ej = 78 GPa, εFRP = 1.59 %, tj,n=1 = 0.56 mm
Lee et al.	(2004)	[46]	CFRP:	5 (U), 15 (R)
			Ej = 250 GPa, εFRP = 1.80 %, tj,n=1 = 0.11 mm
			Spiral Reinforcement:
			fy = 1200 MPa, Dc = 130 mm
			No Longitudinal Reinforcement
Matthys et al.	(2005)	[47]	CFRP 1 (C240):	5 (R)
			Ej = 198 GPa, εFRP = 1.31 %
			CFRP 2 (C640):
			Ej = 480 GPa, εFRP = 0.23 %
			GFRP (TU600/25):
			Ej = 60 GPa, εFRP = 1.30 %
			Hybrid (TU360G160C/27G):
			Ej = 120 GPa, εFRP = 0.92 %
			Transverse Reinforcement:
			fy = 560 MPa, Dc = 370 mm
			Longitudinal Reinforcement:
			fy = 620 MPa, n = 10, Ø = 12 mm
Lam et al.	(2004/2006)	[48,49]	CFRP (C):	18 (U)
			Ej = 230 GPa, εFRP = 1.49 %, tj,n=1 = 0.165 mm
			GFRP (G):
			Ej = 22 GPa, εFRP = 2.00 %, tj,n=1 = 1.27 mm
Ilki et al.	(2008)	[50]	CFRP:	4 (R)
			Ej = 230 GPa, εFRP = 1.50 %, tj,n=1 = 0.165 mm
			Transverse Reinforcement:
			fy = 476 MPa, Dc = 200 mm
			Longitudinal Reinforcement:
			fy = 367 MPa, n = 6, Ø = 10 mm
Eid et al.	(2009)	[4]	CFRP:	36 (U), 15 (R)
			Ej = 78 GPa, εFRP = 1.35 %, tj,n=1 = 0.38 mm
			Transverse Reinforcement:
			fy = 456 MPa, Dc = 253 mm
			Longitudinal Reinforcement:
			fy = 423 MPa, n = 6, Ø = 16 mm

¹ U, unreinforced specimens; R, reinforced specimens.

specifies the general properties of the used materials for those experiments.

The implemented databases enabled the consideration of different FRP materials (particularly different E_j), concrete mixtures with variable unconfined concrete strengths (until a high-performance area >100 MPa), and different reinforcement approaches. In

Table 14. Summarized results regarding the tests of the CFRP-confined plain concrete specimens.

Series	Specimens	D	fc0	tj	flj	fcc	εccu	E2,t	kε	k1	ν2
		[mm]	[MPa]	[mm]	[MPa]	[MPa]	[%]	[MPa]	[-]	[-]	[-]
Xiao and Wu (2003) [13]
CFRP1-1L	1	152	33.7	0.39	4.68	48.0	1.35	1250	0.58	-	-
	2					50.0	1.24	1417	0.70	-	-
	3					50.0	1.40	1583	0.61	-	-
	Mean:					49.3	1.33	1417	0.63	-	-
CFRP1-2L	1	152	33.7	0.78	9.35	64.0	1.64	3167	0.55	-	-
	2					72.0	2.17	3300	0.61	-	-
	3					75.0	2.25	3750	0.61	-	-
	Mean:					70.3	2.02	3406	0.59	-	-
CFRP1-3L	1	152	33.7	1.17	14.03	83.0	2.48	5333	0.50	-	-
	2					87.0	2.45	6000	0.49	-	-
	3					95.5	3.00	6500	0.55	-	-
	Mean:					88.5	2.64	5944	0.51	-	-
CFRP2-1L	1	152	43.6	0.56	4.22	52.0	0.65	900	0.47	-	-
	2					54.5	0.78	1000	0.48	-	-
	3					-	-	-	-	-	-
	Mean:					53.25	0.72	950	0.48	-	-
CFRP2-1,5L	1	152	43.6	0.84	6.33	67.8	1.13	3150	0.45	-	-
	2					72.5	1.24	3350	0.41	-	-
	3					76.0	1.37	3760	0.50	-	-
	Mean:					72.1	1.25	3420	0.45	-	-
Lee et al. (2004) [46]
S0F	1	150	36.2	0.11	4.05	41.7	1.00	517	0.64	1.41	-
	2			0.22	8.10	57.8	1.50	2381	0.51	3.25	0.67
	3			0.33	12.14	69.1	2.00	3311	0.55	3.01	0.47
	4			0.44	16.19	85.4	2.70	3854	0.69	2.63	0.54
	5			0.55	20.24	104.3	3.10	5477	0.67	2.99	0.38
Lam et al. (2004/2006) [48,49]
C1	1	152	35.9	0.165	4.88	50.4	1.27	1375	0.65	2.75	0.91
	2					47.2	1.11	1375	0.67	2.75	1.09
	3					53.2	1.29	1813	0.77	3.63	0.83
	Mean:					50.3	1.22	1521	0.70	3.04	0.94
C2	1	152	35.9	0.330	9.76	68.7	1.68	3125	0.67	3.13	0.53
	2					69.9	1.96	3125	0.65	3.13	0.54
	3					71.6	1.85	3438	0.69	3.44	0.55
	Mean:					70.1	1.83	3229	0.67	3.23	0.54
C3	1	152	34.3	0.495	14.64	82.6	2.05	5625	0.54	3.75	0.38
	2					90.4	2.41	5363	0.61	3.58	0.42
	3					97.3	2.52	5938	0.66	3.96	0.40
	Mean:					90.1	2.33	5642	0.60	3,76	0.40
G1	1	152	38.5	1.27	6.36	56.2	-	-	-	-	-
	2					51.9	1.32	800	0.71	2.41	1.25
	3					58.3	1.46	900	0.96	2.13	1.33
	Mean:					55.5	1.39	850	0.84	2.27	1.29
G2	1	152	38.5	2.54	12.72	75.7	2.46	2000	0.83	2.66	0.95
	2					77.3	2.19	2227	0.88	2.97	0.89
	3					75.2	-	-	-	-	-
	Mean:					76.1	2.32	2114	0.86	2.82	0.92
CII-M	1	152	38.9	0.33	9.76	76.8	1.91	-	-	-	-
	2					79.1	2.08	-	-	-	-
	3					65.8	1.25	-	-	-	-
	Mean:					73.9	1.75	-	-	-	-
Eid et al. (2009) [4]
N1	1	152	32.1	0.381	3.83	39.0	1.00	1000	0.60	2.56	0.80
	2					41.0	1.08	1083	0.62	2.77	0.92
	3					41.0	1.08	1083	0.62	2.77	0.92
	Mean:					40.3	1.05	1055	0.61	2.70	0.88
N2	1	152	32.1	0.762	7.65	58.0	2.00	2617	0.74	3.35	0.48
	2					57.5	1.79	2500	0.67	3.20	0.50
	3					57.5	1.79	2583	0.69	3.30	0.51
	Mean:					57.7	1.86	2567	0.70	3.28	0.50
N3	1	152	33.6	1.143	11.48	72.5	2.23	4333	0.63	3.69	0.39
	2					75.0	2.32	4417	0.65	3.77	0.40
	3					77.0	2.43	4583	0.65	3.91	0.40
	Mean:					74.8	2.33	4444	0.64	3.79	0.40
M1	1	152	48.0	0.381	3.83	57.0	0.62	500	0.58	1.28	-
	2					60.5	0.66	500	0.66	1.28	1.75
	3					62.0	0.78	700	0.63	1.79	1.79
	Mean:					59.8	0.69	567	0.62	1.45	1.77
M2	1	152	48.0	0.762	7.65	79.5	1.23	2050	0.82	2.62	1.10
	2					79.5	1.23	2050	0.82	2.62	1.14
	3					81.0	1.18	2500	0.98	3.20	1.03
	Mean:					80.0	1.21	2200	0.87	2.81	1.09
M3	1	152	48.0	1.143	11.48	97.0	1.48	3200	0.88	2.73	0.94
	2					101.0	1.60	3200	1.06	2.73	1.04
	3					102.0	1.70	3200	1.06	2.73	1.07
	Mean:					100.0	1.59	3200	1.00	2.73	1.02
H11	1	152	67.7	0.381	3.83	57.5	0.63	-	0.59	-	-
	2					61.5	0.67	-	0.73	-	-
	3					66.0	0.69	-	0.77	-	-
	Mean:					61.7	0.66	-	0.70	-	-
H12	1	152	67.7	0.762	7.65	72.5	0.89	-	0.71	-	-
	2					83.0	1.08	417	0.91	0.53	1.90
	3					84.0	1.14	667	1.00	0.85	1.44
	Mean:					79.8	1.04	542	0.87	0.69	1.67
H13	1	152	75.9	1.143	11.48	89.0	1.01	-	0.87	-	-
	2					97.0	1.08	750	0.74	0.64	1.56
	3					97.0	1.20	1083	0.89	0.92	1.19
	Mean:					94.3	1.10	917	0.83	0.78	1.38
H21	1	152	107.7	0.381	3.83	91.0	0.52	-	0.56	-	-
	2					91.0	0.52	-	0.56	-	-
	3					92.5	0.54	-	0.53	-	-
	Mean:					91.5	0.53	-	0.55	-	-
H22	1	152	107.7	0.762	7.65	88.0	0.85	-	0.81	-	-
	2					95.5	0.73	-	0.56	-	-
	3					105.5	0.79	-	0.67	-	-
	Mean:					96.3	0.79	-	0.68	-	-
H23	1	152	107.7	1.143	11.48	105.0	1.00	-	0.74	-	-
	2					112.5	0.71	-	0.53	-	-
	3					117.0	0.88	-	0.65	-	-
	Mean:					111.5	0.86	-	0.64	-	-

and

Table 15. Summarized results regarding the tests of the CFRP-confined RC specimens.

Series	D	fc0	tj	flj	s	Øw	ke	fl,wy	fcc	εccu
	[mm]	[MPa]	[mm]	[MPa]	[mm]	[mm]	[-]	[MPa]	[MPa]	[%]
Lee et al. (2004) [46]
S6F1	150	36.2	0.110	4.05	60	5.5	0.44	3.25	50.37	1.70
S6F2	150	36.2	0.220	8.10	60	5.5	0.44	3.25	68.52	2.50
S6F4	150	36.2	0.440	16.19	60	5.5	0.44	3.25	99.49	3.40
S6F5	150	36.2	0.550	20.24	60	5.5	0.44	3.25	114.64	3.60
S4F1	150	36.2	0.110	4.05	40	5.5	0.54	5.90	60.00	1.90
S4F2	150	36.2	0.220	8.10	40	5.5	0.54	5.90	74.77	2.30
S4F3	150	36.2	0.330	12.14	40	5.5	0.54	5.90	73.85	2.90
S4F4	150	36.2	0.440	16.19	40	5.5	0.54	5.90	104.15	3.00
S4F5	150	36.2	0.550	20.24	40	5.5	0.54	5.90	123.64	3.60
S2F1	150	36.2	0.110	4.05	20	5.5	0.64	14.04	72.87	2.20
S2F2	150	36.2	0.220	8.10	20	5.5	0.64	14.04	92.68	3.60
S2F3	150	36.2	0.330	12.14	20	5.5	0.64	14.04	108.01	3.90
S2F4	150	36.2	0.440	16.19	20	5.5	0.64	14.04	115.72	3.80
S2F5	150	36.2	0.550	20.24	20	5.5	0.64	14.04	150.80	4.30
Matthys et al. (2005) [47]
K2	400	34.3	0.585	4.64	140	8	0.53	0.59	59.36	1.20
K3	400	34.3	0.940	5.89	140	8	0.53	0.59	59.60	0.43
K4	400	39.3	1.800	4.21	140	8	0.53	0.59	60.32	0.69
K5	400	39.3	0.600	1.40	140	8	0.53	0.59	42.38	0.38
K8	400	39.1	0.492	1.49	140	8	0.53	0.59	49.58	0.60
Ilki et al. (2008) [50]
NSR-C-050-3	250	27.6	0.495	9.51	50	8	0.45	2.22	77.59	3.40
NSR-C-100-3	250	27.6	0.495	9.51	100	8	0.32	0.80	72.60	2.80
NSR-C-145-3	250	27.6	0.495	9.51	145	8	0.23	0.39	71.95	3.30
NSR-C-145-5	250	27.6	0.825	15.85	145	8	0.23	0.39	94.45	4.50
Eid et al. (2009) [4]
A5NP2C	303	29.4	0.762	3.84	150	9.5	0.31	0.72	46.13	0.63
A3NP2C	303	31.7	0.762	3.84	70	9.5	0.47	2.37	60.06	1.24
A1NP2C	303	31.7	0.762	3.84	45	9.5	0.53	4.14	63.39	1.51
C4NP2C	303	31.7	0.762	3.84	100	11.3	0.40	1.51	51.37	0.77
C4N1P2C	303	36.0	0.762	3.84	100	11.3	0.40	1.51	56.87	0.84
C4NP4C	303	31.7	1.524	7.68	100	11.3	0.40	1.51	75.83	2.08
B4NP2C	303	31.7	0.762	3.84	100	11.3	0.40	1.51	58.00	1.36
C4MP2C	303	50.8	0.762	3.84	100	11.3	0.40	1.51	75.36	0.88
C2NP2C	303	31.7	0.762	3.84	65	11.3	0.48	2.78	55.94	1.32
C2N1P2C	303	36.0	0.762	3.84	65	11.3	0.48	2.78	62.44	1.03
C2N1P4C	303	36.0	1.524	7.68	65	11.3	0.48	2.78	75.71	1.84
C2N1P2N	303	36.0	0.762	4.60	65	11.3	0.68	3.98	75.57	1.55
C2MP2C	303	50.8	0.762	3.84	65	11.3	0.48	2.78	78.90	1.04
C2MP4C	303	50.8	1.524	7.68	65	11.3	0.48	2.78	97.94	1.64
C2MP2N	303	50.8	0.762	4.60	65	11.3	0.68	3.98	62.45	1.29

, the collected test data regarding CFRP-confined plain and reinforced concrete specimens were collated.

In addition,

Table 16. Additional data concerning ν₂ and k₁.

Ejl/fc0	ν2	Ejl/fc02	k1
[-]	[-]	[-]	[-]
47.00	0.30	1.30	3.80
47.00	0.35	1.30	4.00
47.00	0.35	1.30	4.40
36.00	0.40	0.88	3.20
36.00	0.42	0.88	3.40
36.00	0.45	0.88	4.00
31.00	0.41	0.80	3.35
31.00	0.42	0.80	3.75
31.00	0.49	0.80	4.20
28.50	0.55	0.78	3.25
28.50	0.61	0.78	3.80
28.50	0.61	0.78	3.80
26.50	0.39	0.53	3.20
26.50	0.44	0.53	3.50
26.50	0.60	0.53	3.35
24.00	0.55	0.50	2.70
24.00	0.61	0.50	3.00
24.00	0.73	0.50	3.20
19.50	0.55	0.48	3.25
19.50	0.60	0.48	3.25
19.50	0.60	0.48	3.40
17.50	0.58	0.43	3.70
17.50	0.65	0.43	3.90
17.50	0.73	0.43	4.20
16.00	1.25	0.42	2.55
16.00	1.30	0.42	2.75
16.00	1.68	0.42	3.05
15.50	0.75	0.31	0.45
15.50	0.80	0.31	0.70
15.50	0.85	0.31	1.00
13.00	1.34	0.30	0.45
13.00	1.71	0.30	1.20
13.00	1.85	0.30	2.20
10.50	1.45	0.28	-0.95
10.50	1.82	0.28	0.05
8.50	1.10	0.28	1.75
8.50	1.42	0.25	0.30
6.00	1.45	0.25	0.75
6.00	2.09	0.25	0.90
6.00	2.45	0.16	-4.30
-	-	0.16	-1.00
-	-	0.16	0.65

shows the collected data concerning ν₂ and k₁ from Xiao and Wu [13].

4.2. CFRP-Confined Plain Concrete Specimens

With the collected data, the database could be significantly extended. In Figure 22, the factors E_2,t and ν_2, which are crucial for the description of the stress–strain behavior, are shown as functions of the ratio between the confinement modulus and the unconfined concrete strength. In both cases, the collected data validate the findings described in Section 3.2. Furthermore, the higher diversity of the results allowed for the assessment of a constant design factor, k₁, to predict f_cc. In Figure 23, all of the gathered results concerning k₁ are presented as a function of the ratio f_l/f_c0.

Obviously, no established approach for the prediction of k₁ can fit the test database, exhibiting a considerable scatter. In conclusion, the design factor k₁ has to be reflected critically in general. The gathered data indicates an advantage in using the ratio between the confinement pressure and unconfined concrete strength to predict f_cc and ε_ccu, as seen in Figure 24.

4.3. CFRP-Confined Reinforced Concrete Specimens

Only few references regarding tests with CFRP confined RC specimens offer sufficient and comprehensive data concerning the applied CFRP system, the arrangement and construction of the longitudinal and transverse reinforcement as well as detailed information on the reached f_cc and ε_ccu. However, the considered data sets regarding CFRP confined RC columns only included 39 test results. Nevertheless, combined with the experimental results described in Section 3.4, the gathered database enabled satisfying regressions for the prediction of f_cc and ε_ccu. Figure 25 shows the determined dependency of Δf_cc and ε_ccu on the ratio between the total confinement pressure f_l(j+w) and the unconfined concrete strength f_c0.

The extent of the tested ratios f_l(j+w)/f_c0 covered by the experimental results could be enlarged to values close to f_l(j+w)/f_c0 = 1.0. In this case, the confinement pressure exceeded the unconfined concrete strength. The correlations in Figure 25 show the applicability of the ratio between the confinement pressure and the unconfined concrete strength for the description of the behavior of the CFRP-confined RC material.

5. Model for CFRP-Confined Plain and Reinforced Concrete

5.1. Ultimate Concrete Strength and Accompanied Axial Strain

For an overall evaluation of the achievable ultimate concrete strength, f_cc, and strain, ε_ccu, the results of the CFRP-confined plain concrete specimens, as well as the CFRP-confined RC specimens, were considered in a unified regression analysis. The database and the regression results are presented in Figure 26. In conclusion, general equations for the prediction of f_cc and ε_ccu could be determined as the following,

$${\mathit{f}}_{\mathrm{cc}}{=\mathit{f}}_{\mathrm{c}0}+30·\ln \left(\frac{{\mathit{f}}_{\mathrm{l}(\mathrm{j}+\mathrm{w})}}{{\mathit{f}}_{\mathrm{c}0}}\right)+75\left[\mathrm{MPa}\right],$$

(8)

$${\epsilon }_{\mathrm{ccu}}{=\epsilon }_{\mathrm{c}0}·1.75+0.05·\frac{{\mathit{f}}_{\mathrm{l}(\mathrm{j}+\mathrm{w})}}{{\mathit{f}}_{\mathrm{c}0}}[\%].$$

(9)

To allow the implementation of the results in modern limit state design concepts, Equation (10) presents an approach for the calculation of the characteristic strength, f_cck:

$${\mathit{f}}_{\mathrm{cck}}{=\mathit{f}}_{\mathrm{ck}}+30·\ln \left(\frac{{\mathit{f}}_{\mathrm{lk}(\mathrm{j}+\mathrm{w})}}{{\mathit{f}}_{\mathrm{c}0}}\right)+63\mathrm{if}0.75\ge \frac{{\mathit{f}}_{\mathrm{lk}(\mathrm{j}+\mathrm{w})}}{{\mathit{f}}_{\mathrm{c}0}}\ge {0.125\mathrm{with}\mathit{f}}_{\mathrm{lk}(\mathrm{j}+\mathrm{w})}{=\mathit{E}}_{\mathrm{jl}}·{\epsilon }_{\mathrm{juk}}+\frac{1}{2}·{\rho }_{\mathrm{st}}·{\mathit{f}}_{\mathrm{yk}}·{\mathit{k}}_{\mathrm{e}}\left[\mathrm{MPa}\right].$$

(10)

where f_ck is the characteristic concrete compressive strength, ε_juk is the characteristic rupture strain of the FRP jacket in the application of confinement (ε_juk = ε_FRP · k_εk), and f_yk is the characteristic yield stress of the steel reinforcement.

The limitations ensure that the calculation is within boundaries of the gathered experimental results.

5.2. Stress–Strain Relationships

For the design of a stress–strain model, the stress–strain relationships proposed by Lam and Teng [6] (Equation (5)) were adopted. Analysis of the experimental results revealed a significant dependency between the second modulus in the transverse direction, E_2,t, the second Poison’s ratio, ν₂, and the second modulus in the axial direction, E₂. Therefore, the following equations for the prediction of E₂ can be proposed,

$${\mathit{E}}_{2,\mathrm{t}}=135·\frac{{\mathit{E}}_{\mathrm{jl}}}{{\mathit{f}}_{\mathrm{c}0}} 550\left[\mathrm{MPa}\right],$$

(11)

$${\mathit{v}}_2=7·{\left(\frac{{\mathit{E}}_{\mathrm{jl}}}{{\mathit{f}}_{\mathrm{c}0}}\right)}^{-0.7},$$

(12)

$${\mathit{E}}_2{=\mathit{E}}_{2,\mathrm{t}}·{\mathit{v}}_2.$$

(13)

Furthermore, the transition point between the parabolic curve and the straight-line second portion, ε_t, can be described by the following equations,

$${\mathit{f}}_{\mathrm{c}}^{*}{=\mathit{f}}_{\mathrm{cc}}{-\mathit{E}}_2·{\epsilon }_{\mathrm{ccu}},$$

(14)

$${\epsilon }_{\mathrm{t}}=\frac{2·{\mathit{f}}_{\mathrm{c}}^{*}}{{\mathit{E}}_{\mathrm{c}} {-\mathit{E}}_2}.$$

(15)

Finally, the stress–strain relationship is given as follows,

$${\sigma }_{\mathrm{c}}=\{\begin{array}{c}{\mathit{E}}_{\mathrm{c}}·{\epsilon }_{\mathrm{c}}-\frac{{\left({\mathit{E}}_{\mathrm{c}}{-\mathit{E}}_2\right)}^2}{4·{\mathit{f}}_{\mathrm{c}}^{*}}·{\epsilon }_{\mathrm{c}}{}^2\\ {\mathit{f}}_{\mathrm{c}}^{*}{+\mathit{E}}_2·{\epsilon }_{\mathrm{c}}\end{array}\begin{array}{c}\mathrm{if}0\le {\epsilon }_{\mathrm{c}}\le {\epsilon }_{\mathrm{t}}\begin{array}{c}\\ \end{array}\\ {\mathrm{if}\epsilon }_{\mathrm{t}}\le {\epsilon }_{\mathrm{c}}\le {\epsilon }_{\mathrm{ccu}}\end{array},$$

(16)

6. Conclusions

FRP materials are gaining importance in construction. Especially for strengthening purposes, fiber-reinforced polymers show great potential [51,52]. FRP confinement can significantly increase the strength and ductility of concrete and RC. The present study confirmed the bilinear stress–strain model proposed by Lam and Teng [6] for confined plain and reinforced concrete. For enhancement of the ultimate strength and accompanied axial strains, the proposal of Xiao and Wu [13] using the ratio between the confinement modulus, E_jl, and the unconfined concrete strength, f_c0, proved to be the most correlated approach. The effect of a dual confinement on the stress–strain behavior could be explained by the individual confinement pressure provided by the CFRP jacket and the transverse steel reinforcement. Based on the model of Lam and Teng, an approach for the calculation of f_cc, ε_ccu, and E₂ could be developed. Furthermore, the findings led to additional knowledge concerning the prediction (in accordance with the limit state method) of the CFRP’s hoop strain, ε_ju, and the related partial factor, γ_j. However, further research efforts are still pending. In particular, the confinement of low-strength concrete, as well as substandard concrete, was not examined in the current study. Furthermore, the effect of particularly high confinement pressures exceeding the unconfined concrete strength has yet not been sufficiently considered.