Experimental Study on Concrete under Combined FRP–Steel Confinement

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.


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 . 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 fcc and the accompanying axial strain εccu are derived by Equations (1) and (2): where fc0 is the mean value of the unconfined concrete strength, εc0 is the peak strain of the unconfined concrete, flj is the confinement pressure provided by the FRP jacket, εju is the rupture strain of the FRP jacket in the application of confinement, and k1-k4 are factors affecting the impact of flj on fcc and εccu. The prediction of the ultimate condition of the confined concrete is directly dependent on the confining pressure flj provided by the FRP jacket. The commonly used form for the calculation of the confining pressure is given by Equation (3): where ρj is the confinement ratio, Ejl is the confinement modulus, Ej is the modulus of the composite material, tj 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, εju, has a significant impact on the confinement pressure, flj. According to the current state-of-the-art, εju 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 εFRP. Therefore, Lam and Teng [6] established an FRP efficiency factor kε, defined by Although most approaches are derived by the same basic functions, the design models show significant differences. Table 1 provides an overview of the selected, renowned models for the design of confined concrete. Table 1. Different approaches to predict fcc and εccu of confined concrete columns.

Authors Confined Concrete Compressive Strength fcc
Ultimate Axial Compressive Strain εccu Richart et al. (1928) [31] f cc = f c0 + k 1 • f lj k 1 = 4.1 Samaan et al. (1998) [32] f cc = f c0 + k 1 • f lj  In general, the ultimate confined concrete strength f cc and the accompanying axial strain ε ccu are derived by Equations (1) and (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 k 1 -k 4 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): 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 Although most approaches are derived by the same basic functions, the design models show significant differences. Table 1 provides an overview of the selected, renowned models for the design of confined concrete. 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 Xiao and Wu (2003) [13] Lam and Teng (2003) [6] f Niedermeier (2009) [33] f 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 (σc)-strain (εc) 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]: where E2 is the second modulus, Ec is the modulus of elasticity, and εt 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 flj. These concepts lead to considerable discrepancies regarding the prediction of confined columns with different initial concrete strengths, fc0. 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 Figure 2. Stress-strain model for FRP-confined concrete according to Lam and Teng [6].
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 k 1 (ultimate stress) and k 2 -k 4 (ultimate strain). In the majority of cases, k 1 and k 2 -k 4 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.
Materials 2020, 13, x FOR PEER REVIEW 4 of 35 εccu 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 fc0 = 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  [6,11,13,19,32,34].
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, k 1 and k 2 -k 4 ( Figure 4). εccu 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 fc0 = 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). Number of specimens as a function of the initial concrete strength, fc0, used for the derivation of empirical design models for FRP-confined concrete by the authors of [6,11,13,32,33]. 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 Figure 4. Number of specimens as a function of the initial concrete strength, f c0 , used for the derivation of empirical design models for FRP-confined concrete by the authors of [6,11,13,32,33]. 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. 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 . Eid and Paultre (2008) [3] f cc = f c0 +k 1 · f lj + f l,wy ε ccu = ε c0 · 1.56+ε c0 · 12 · flj fc0 + fl,wy fc0 · εju εc0 0.45 Pellegrino and Modena (2010) [8] f cc = f c0 +k 1 · f lj + f l,wy · Acc 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; ∆p = reduction of confinement pressure between the core section and the concrete cover; s = vertical spacing between spiral or tie bars.
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.

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

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

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]. Table 3 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).

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, 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.

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.

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).

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.

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.

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).

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).    Table 5 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 fc0 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.     Table 5 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 fc0 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.  Table 5 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.

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 (E 2 ) 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 E 2 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 ).
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 (E2,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 (fcc) and strain (εccu).   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 (E2,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 (fcc) and strain (εccu).   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) 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 axialconfinement 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. Table 6 shows the results obtained from the CFRP-confined plain concrete specimens without internal reinforcement. 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 k 1 (cf. Equation (1)) and the second Poisson's ratio of the confined member ν 2 . Typical examples are shown in Figure 12. 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) 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 axialconfinement 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. Table 6 shows the results obtained from the CFRP-confined plain concrete specimens without internal reinforcement. 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 ν 2 . Furthermore, the axial-confinement stress response explains the design factor, k 1 . 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 k 1 . Table 6 shows the results obtained from the CFRP-confined plain concrete specimens without internal reinforcement.

CFRP-Confined Concrete Specimens
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 c0 2 , and f lj /f c0 can be defined (Table 7). 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, ∆f cc (∆f cc = f cc − f c0 ) and the ultimate strain, ε ccu , on the initial concrete strength, f c0 . 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, ρj. The volumetric ratio and the material properties of the CFRP jacket define its maximum confinement pressure, flj, as shown in Equation (3). As expected, flj had a significant impact on fcc and εccu. Furthermore, the investigations indicated that the unconfined concrete strength, fc0, is a second impact factor. Figure 13 illustrates the dependence of the strength enhancement, Δfcc (Δfcc = fcc − fc0) and the ultimate strain, εccu, on the initial concrete strength, fc0. For this comparison, only fc0 was changed. Only test specimens with equal diameters (150 mm) and properties of the applied CFRP system were used, while the concrete strength, fc0, varied. An impact of fc0 on fcc and εccu 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 fl is set in relation to fc0, satisfying regressions for the prediction of fcc and εccu 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, Δfcc, and the ultimate strain, εccu.
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 Ejl to the divisor fc0 enables the prediction of E2,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 E2,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 Ejl and the calculated confinement pressure flj are sufficient for the consideration of the varying diameter. 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, ∆f 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 ν 2 , . 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, ν 2 . 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

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 kε < 1.0 should be mandatory. An overview of different approaches to determine kε is given in Table 8. Table 8. Suggested approaches to determine kε.

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 kε < 1.0 should be mandatory. An overview of different approaches to determine kε is given in Table 8. Table 8. Suggested approaches to determine kε.

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. Table 8. Suggested approaches to determine k ε .
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. Toutanji et al. [41] kε = 0.6 no information Smith et al. [21] kε = 0.8 no information Pellegrino and Modena [8] Abbreviations: Rc = corner radius; Es = elastic modulus steel reinforcement; ρl = 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 kε = 0.49 and kε = 0.70. The use of a mean value kε, 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, kεk. 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 kε on the used CFRP material. Furthermore, the findings enabled the derivation of particular partial factors γj for the used CFRP materials. The approach introduced in the fib bulletin 80 [43] was used for the calculation: where αR is the sensitivity factor (αR = 0.8), Vx is the presumed coefficient of variation of the rupture strain εFRP, β is the reliability factor (β = 3.8), γRd1 is a factor considering model uncertainties, and γRd2 is a factor considering geometrical uncertainties. As shown in Table 9, the variation coefficients Vx vary remarkably between the used CFRP materials. Hence, γj 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), γRd1 was predicted with a value of 1.20 because model uncertainties are comparable to that of models for shear design. In contrast, γRd2 was determined with a value of 1.0. For columns with a circular cross section, the geometrical uncertainties are negligible, as kε persisted at a constant value independent of the column 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: 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, 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. 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.  Table 11 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]:

CFRP-Confined Reinforced Concrete Specimens
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. 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 ∆f cc is defined as ∆f 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.  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 E 2 observed in confined plain concrete, as further strength enhancement depends on the linear elastic CFRP jacket. 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).
Materials 2020, 13, x FOR PEER REVIEW 21 of 35 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 fcc and εccu. However, the E2 reached is almost similar. In addition, Figures 18 and 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 εst increased more slowly compared to the CFRP jacket, εj. 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 εj and εst. Figure 20 shows the deviations in the axial-transverse strain responses and the axial-confinement stress responses for series D30-SR-M1-2L-2. The transition zone between the first linear increase and second linear branch, E 2 , 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 E 2 reached is almost similar. In addition, Figures 18 and 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

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 kε. Niedermeier [33,40] followed this proposal and suggested a mean value kε = 0.50 and a characteristic value kεk = 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, εccu, was reached. A strong impact of the longitudinal reinforcement on εju should influence the confinement pressure, fl; because of this, the diagram on the left of Figure 21 explains the determination of kε for the three longitudinal bar configurations by using the proposal of Pellegrino and Modena [8]. As the number of bars increases, kε should decrease and, therefore, reduce εccu; however, the tests could not confirm these assumptions.
In conclusion, the reduction factor kε remains constant independent of the applied longitudinal reinforcement. Low reduction values such as kεk = 0.25 are highly conservative and may provoke an unnecessary loss of load-bearing capacity.

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.

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

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 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 Tables 14 and 15, the collected test data regarding CFRP-confined plain and reinforced concrete specimens were collated. In addition, Table 16 shows the collected data concerning ν 2 and k 1 from Xiao and Wu [13].

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, k 1 , to predict f cc . In Figure 23, all of the gathered results concerning k 1 are presented as a function of the ratio f l /f c0 .
Obviously, no established approach for the prediction of k 1 can fit the test database, exhibiting a considerable scatter. In conclusion, the design factor k 1 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.   (a) (b) Figure 22. E2,t (a) and ν2 (b) as functions of the ratio between the confinement modulus and the unconfined concrete strength including the databases in [4,13,46,48].

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 fcc and εccu. 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 fcc and εccu. Figure 25 shows the determined dependency of Δfcc and εccu on the ratio between the total confinement pressure fl(j+w) and the unconfined concrete strength fc0.

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 ∆f cc and ε ccu on the ratio between the total confinement pressure f l(j+w) and the unconfined concrete strength f c0 . longitudinal and transverse reinforcement as well as detailed information on the reached fcc and εccu. 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 fcc and εccu. Figure 25 shows the determined dependency of Δfcc and εccu on the ratio between the total confinement pressure fl(j+w) and the unconfined concrete strength fc0.  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. where fck is the characteristic concrete compressive strength, εjuk is the characteristic rupture strain of the FRP jacket in the application of confinement (εjuk = εFRP ‧ kεk), and fyk is the characteristic yield stress of the steel reinforcement. The limitations ensure that the calculation is within boundaries of the gathered experimental results.   Tables 14 and 15).