Analysis-Oriented Stress-Strain Model for Prestressed FRP-Confined Circular Concrete

1. Introduction

Fiber-reinforced polymer (FRP) confinement has been widely applied for strengthening concrete columns in bridge, marine, and rehabilitation engineering owing to its advantages of high strength-to-weight ratio, ease of installation, durability, and design flexibility [1,2,3]. After FRP confinement, the core concrete changes from a uniaxial compression state to a triaxial compression state, where lateral expansion is restrained and both compressive strength and deformation capacity are enhanced. Extensive experimental and theoretical investigations have been conducted on the axial compressive behavior of FRP-confined concrete, leading to the development of various stress–strain models. These models can generally be classified into design-oriented models and analysis-oriented models. The former mainly focus on key parameters such as peak strength and ultimate strain, offering simple formulations for engineering design. The latter describe the interaction between concrete and FRP confinement and are capable of reproducing the complete stress–strain response, making them more suitable for nonlinear finite element analysis and refined evaluation of structures under complex confinement conditions. Existing analysis-oriented models are generally developed based on the theory of actively confined concrete and assume that both stress path independence and strain path independence are applicable [2]. Accordingly, the stress–strain response of FRP-confined concrete can be derived based on models established for actively confined concrete.

However, conventional FRP confinement is essentially passive confinement, in which the FRP jacket is gradually activated only after considerable lateral dilation of concrete, resulting in a confinement delay effect [3,4,5,6]. To improve the utilization efficiency of FRP materials, various prestressing techniques have been developed in recent years, including expansive mortar methods [7,8], continuous filament winding methods [9,10,11], mechanical anchorage-based prestressing methods [12,13,14,15,16], and expansive concrete methods [17,18,19,20]. Prestressed FRP can provide lateral confinement from the initial loading stage, thereby restraining early cracking and lateral deformation and further improving the strength and ductility of concrete members. Existing studies have mainly focused on axial compression tests, strength enhancement mechanisms, and prediction of peak stress and ultimate strain of prestressed FRP-confined concrete, providing an important basis for understanding its mechanical behavior.

Nevertheless, several critical issues remain unresolved. First, existing models for prestressed FRP-confined concrete are generally developed under specific experimental conditions, and their parameters are calibrated based on particular material systems and prestressing techniques. The lack of a unified analytical framework limits their applicability to different prestressing systems. Second, the introduction of prestress changes the initial confinement state and its subsequent evolution during loading. Consequently, prestressed FRP-confined concrete exhibits characteristics of both active and passive confinement at different loading stages. However, most existing analytical models still directly adopt the path independence assumptions developed for conventional FRP-confined concrete, while the applicability of stress path and strain path assumptions under prestressed conditions has not been systematically examined. If these assumptions are invalid, the theoretical basis of existing analytical models may become questionable, leading to potential deviations in the prediction of peak parameters, dilation behavior, and the complete stress–strain response.

Moreover, the interaction mechanism between FRP and concrete varies among different prestressing techniques. Mechanical prestressing methods directly introduce initial lateral pressure through external tensioning, whereas expansive methods involve internal expansion processes that may influence the initial damage state and axial stiffness of concrete. Such differences have received limited attention, and a unified analytical model capable of considering various prestressing techniques is still lacking. This limitation restricts not only the development of constitutive models for prestressed FRP-confined concrete but also their further application in nonlinear finite element analysis, nonuniform confinement evaluation, and structural performance assessment.

Therefore, this study investigates the fundamental issues associated with the development of an analysis-oriented model for prestressed FRP-confined circular concrete. First, the applicability of stress path and strain path assumptions under different prestressing techniques is systematically examined by comparing the confinement mechanisms of actively confined concrete and prestressed FRP-confined concrete. Subsequently, the effects of initial lateral confinement on axial stiffness and lateral dilation behavior are considered, and unified modifications are introduced for the peak stress, peak strain, and lateral strain–axial strain relationship. Based on these modifications, an iterative analytical framework is established to develop a complete stress–strain model for prestressed FRP-confined circular concrete. The proposed model is further validated using independent experimental datasets, providing a theoretical basis and analytical tool for the advanced analysis and engineering application of prestressed FRP-confined concrete.

2. Stress–Strain Relationship of Confined Concrete

According to whether the lateral confinement stress varies during the loading process, the confinement mechanisms of concrete can be classified into active confinement and passive confinement. Active confinement refers to the condition where the externally applied lateral confinement stress remains constant throughout loading. In contrast, for FRP-confined concrete, the lateral confinement stress provided by the FRP jacket is activated by the lateral expansion of concrete and progressively increases with the development of dilation deformation. Therefore, FRP confinement is generally categorized as passive confinement.

The axial stress–strain curves of actively confined concrete can be obtained through triaxial compression tests, and corresponding stress–strain models can be established by calibrating the model parameters. Ozbakkaloglu et al. [21] reviewed the experimental database of non-prestressed FRP-confined concrete and evaluated existing models, indicating that most available stress–strain analytical models were developed based on the axial stress–strain relationship and lateral strain–axial strain relationship of actively confined concrete. These models have various mathematical forms, and their parameters are calibrated based on specific experimental datasets. Essentially, these approaches employ actively confined concrete models to predict the axial stress under prescribed axial strain and lateral confinement pressure.

When actively confined concrete models are applied to FRP-confined concrete, their applicability mainly depends on the validity of two assumptions: stress path independence and strain path independence. The stress path independence assumption indicates that, under identical axial strain and lateral confinement pressure conditions, actively and passively confined concrete exhibit the same axial stress response, implying that the axial stress is independent of loading history. The strain path independence assumption indicates that the lateral strains of actively and passively confined concrete are identical under the same conditions.

Jiang and Ozbakkaloglu et al. [21,22] pointed out that most existing analytical models assume the validity of these two assumptions for FRP-confined concrete. Accordingly, the lateral strain–axial strain relationship and axial stress–strain relationship of actively confined concrete are adopted as the basis for model development, and an incremental approach is subsequently employed to obtain the complete analytical response of FRP-confined concrete.

Based on this framework, the stress–strain curve of FRP-confined concrete can be obtained through the following procedures:

(1) A lateral strain is prescribed, and the corresponding axial strain is determined according to the lateral strain–axial strain relationship;

(2) Based on the compatibility between the deformation of concrete and FRP, the FRP confinement stress corresponding to the prescribed lateral strain is calculated;

(3) The obtained axial strain and confinement stress are substituted into the axial stress–strain model for actively confined concrete to determine the corresponding axial stress, thereby obtaining one point on the stress–strain curve.

By repeating this procedure, the complete stress–strain curve can be generated.

2.1. Lateral Strain–Axial Strain Relationship

During axial compression of FRP-confined concrete columns, the core concrete undergoes axial shortening accompanied by lateral expansion. The lateral expansion induces tensile deformation in the FRP jacket, thereby generating lateral confinement on the concrete. Since FRP is generally bonded tightly to the concrete surface through resin impregnation, a perfect bond condition without relative slip or separation can be assumed between the FRP jacket and concrete.

Based on this confinement mechanism, and considering the constitutive relationship under triaxial stress conditions together with deformation compatibility, when an initial prestress-induced tensile strain is applied to the FRP and the lateral strain state of concrete after prestressing is defined as the reference zero point, the relationship between the subsequent lateral strain of concrete ${\epsilon }_1$ and the hoop strain of FRP ${\epsilon }_{\mathrm{h}}$ during loading can be expressed as Equation (1).

$${\epsilon }_{\mathrm{h}}=-{\epsilon }_{\mathrm{l}}+{\epsilon }_{\mathrm{f},\mathrm{p}}$$

(1)

The hoop tensile stress/strain of FRP is defined as positive, whereas the compressive stress/strain of concrete is defined as positive. The negative sign is introduced to ensure consistency in the strain direction and maintain the numerical compatibility between the two materials.

For circular cross-sections, the lateral confinement stress provided by FRP can be assumed to be uniformly distributed along the hoop direction. Based on the deformation compatibility between FRP and concrete, the confinement stress can be calculated using Equation (2).

$${\sigma }_{\mathrm{l}}={\displaystyle \frac{2E_{\mathrm{f}}{\epsilon }_{\mathrm{h}}{t}_{\mathrm{f}}}{D}}$$

(2)

where $E_{\mathrm{f}}$ is the elastic modulus of FRP,  $t_{\mathrm{f}}$ is the total thickness of FRP, and $\mathit{D}$ is the diameter of the confined concrete core.

The lateral strain–axial strain relationship is one of the key factors governing the accuracy of analytical models for FRP-confined concrete. Based on a systematic investigation of the dilation behavior of both unconfined and confined concrete, Teng et al. [23] proposed a lateral strain–axial strain relationship applicable to unconfined concrete, actively confined concrete, and FRP-confined concrete, as expressed in Equation (3).

$${\displaystyle \frac{\epsilon }{{\epsilon }_{\mathrm{o}}}}=0.85{[1+0.75\left({\displaystyle \frac{-\epsilon }{{\epsilon }_{\mathrm{o}}}}\right)]}^{0.7}-\mathrm{e}\mathrm{p}[-7\left({\displaystyle \frac{-\epsilon }{{\epsilon }_{\mathrm{o}}}}\right)]\times [1+8\left({\displaystyle \frac{\sigma }{f_{\mathrm{o}}}}\right)]$$

(3)

where ${\epsilon }_{\mathrm{c}}$ represents the axial strain of confined concrete, while $f_{\mathrm{c}\mathrm{o}}$ and ${\epsilon }_{\mathrm{c}\mathrm{o}}$ denote the compressive strength of unconfined concrete and the corresponding strain, respectively.

Lim et al. [24] established and validated an expression capable of uniformly describing the dilation behavior of both actively confined concrete and FRP-confined concrete based on experimental data, as given in Equations (4)–(5).

$${ϵ}_{\mathrm{c}}={\displaystyle \frac{{ϵ}_{\mathrm{l}}}{\nu [1+(\frac{{ϵ}_{\mathrm{l}}}{\nu {ϵ}_{{\mathrm{c}}_0}}{)}^n{]}^{1/n}}}+0.04{ϵ}_{\mathrm{l}}^{0.7}[1+21({\displaystyle \frac{{\sigma }_{\mathrm{l}}}{f_{{\mathrm{c}}_0}^{\prime }}}{)}^{0.8}]$$

(4)

$$n=1+0.03f_{\mathrm{c}\mathrm{o}}^{\prime }$$

(5)

Yang and Feng [25] recalibrated the parameters in the lateral strain–axial strain relationship proposed by Teng et al. [23] using collected experimental data, resulting in the following expression:

$${\displaystyle \frac{\epsilon }{{\epsilon }_o}}=0.85[1+075({\displaystyle \frac{-\epsilon }{{\epsilon }_o}}\left)\right]-\mathrm{e}\mathrm{p}[-7({\displaystyle \frac{-\epsilon }{{\epsilon }_o}}\left)\right]\times [1+19({\displaystyle \frac{\sigma }{{\rho }_{\sigma }^{\prime }}}{)}^{12}{]}^{18}$$

(6)

2.2. Actively Confined Concrete Models

The prediction of the stress–strain curve of actively confined concrete is generally based on a stress–strain function describing the overall curve shape, together with a set of equations defining the peak stress and the corresponding strain. Among existing analytical models, the model proposed by Popovics et al. [26] has been widely adopted to describe the stress–strain relationship of actively confined concrete, which is expressed as Equation (7).

$${\displaystyle \frac{{\sigma }_{\mathrm{c}}}{f_{\mathrm{c}\mathrm{c}}^{*}}}={\displaystyle \frac{({\epsilon }_{\mathrm{c}}/{\epsilon }_{\mathrm{c}\mathrm{c}}^{*})r}{r-1+{({\epsilon }_{\mathrm{c}}/{\epsilon }_{\mathrm{c}\mathrm{c}}^{*})}^r}}$$

(7)

where ${\sigma }_{\mathrm{c}}$ represents the axial stress of confined concrete,  $f_{\mathrm{c}\mathrm{c}}^{*}$ denotes the peak stress of actively confined concrete, and ${\epsilon }_{\mathrm{c}\mathrm{c}}$ is the corresponding peak strain. The constant $r$ in Equation (8) reflects the brittleness characteristics of concrete. Carreira et al. [27] proposed the following equation to determine this parameter:

$$r={\displaystyle \frac{E_{\mathrm{c}}}{E_{\mathrm{c}}-f_{\mathrm{c}\mathrm{c}}^{*}/{\epsilon }_{\mathrm{c}\mathrm{c}}^{*}}}$$

(8)

where $E_{\mathrm{c}}$ represents the initial elastic modulus of unconfined concrete.

For the peak stress $f_{\mathrm{c}\mathrm{c}}^{*}$ of actively confined concrete, the expression proposed by Mander et al. [28] is currently one of the most widely adopted formulations, as given in Equation (9).

$$f_{\infty }^{*}=f_{\infty }^{\prime }(2.254\sqrt{1+7.94{\displaystyle \frac{{\sigma }_l}{f_{\infty }^{\prime }}}}-2{\displaystyle \frac{{\sigma }_l}{f_{\infty }^{\prime }}}-1.254)$$

(9)

The corresponding peak strain ${\epsilon }_{\mathrm{c}\mathrm{c}}^{*}$ was originally proposed by Richart et al. [29], and its classical expression is given in Equation (10).

$${\displaystyle \frac{{\epsilon }_{\mathrm{c}\mathrm{c}}}{{\epsilon }_{\mathrm{c}\mathrm{o}}}}=1+5({\displaystyle \frac{f_{\mathrm{c}\mathrm{c}}^{*}}{f_{\mathrm{c}\mathrm{o}}^{\prime }}}-1)$$

(10)

Furthermore, Teng et al. [23] suggested using the simplified Equations (11) and (12) instead of Equations (9) and (10) to define the failure state of actively confined concrete.

$${\displaystyle \frac{f_{\mathrm{c}\mathrm{c}}^{*}}{f_{\mathrm{c}\mathrm{o}}^{\prime }}}=1+3.5{\displaystyle \frac{{\sigma }_{\mathrm{l}}}{f_{\mathrm{c}\mathrm{o}}^{\prime }}}$$

(11)

$${\displaystyle \frac{{\epsilon }_{\mathrm{c}\mathrm{c}}^{*}}{{\epsilon }_{\mathrm{c}\mathrm{o}}}}=1+17.5{\displaystyle \frac{{\sigma }_1}{f_{\mathrm{c}\mathrm{o}}^{\prime }}}$$

(12)

2.3. Actively Confined Concrete Models

Figure 1 compares the typical lateral strain–axial strain relationships and axial stress–strain curves of actively confined concrete and prestressed FRP-confined concrete. The curves of prestressed FRP-confined concrete are obtained from the experimental results reported in Ref. [10], whereas the curves of actively confined concrete are generated using the aforementioned actively confined concrete model.

As shown in Figure 1, the failure state of actively confined concrete is characterized by its peak stress $f_{\mathrm{c}\mathrm{c}}^{*}$ and the corresponding peak strain ${\epsilon }_{\mathrm{c}\mathrm{c}}^{*}$ . In contrast, the ultimate state of prestressed FRP-confined concrete is determined by the compressive strength $f_{\mathrm{c}\mathrm{c}}^{\prime }$ and the corresponding ultimate axial strain ${\epsilon }_{\mathrm{c}\mathrm{u}}$ when the FRP jacket reaches its rupture strain ${\epsilon }_{\mathrm{h},\mathrm{r}\mathrm{u}\mathrm{p}}$ .

The comparison indicates that the two confinement systems exhibit different confinement stress paths, resulting in distinct characteristics of their axial stress–strain responses. For actively confined concrete, the stress–strain curve initially exhibits a linear ascending stage under a constant confinement stress, followed by a parabolic stage until reaching the peak stress. After the peak point, the curve gradually decreases. During the descending branch, the residual strength generated by the internal friction of concrete is reflected as a relatively stable stress plateau, namely the residual stress $f_{\mathrm{c},\mathrm{r}\mathrm{e}\mathrm{s}}$ .

In contrast, the stress–strain curve of prestressed FRP-confined concrete exhibits a higher initial stress level in the linear elastic stage due to the existence of initial lateral confinement stress. With increasing axial load, the FRP confinement stress continuously develops, resulting in a transition into a linear hardening stage. Ultimately, the curve reaches the ultimate state due to rupture of the FRP jacket.

3. Development of the Stress–Strain Model

3.1. Stress Path Dependency

In existing studies on the stress–strain relationship of confined concrete, the stress path independence assumption is generally adopted, where the influence of different confinement mechanisms and loading paths on the axial stress response is neglected [23]. However, recent investigations have indicated that the stress–strain response of confined concrete may depend on the stress path [30,31,32].

Li et al. [31] reported that the stress path dependency of FRP-confined concrete was insignificant under monotonic loading, whereas it became more pronounced under cyclic loading. Through comparative analyses of experimental data, Lim et al. [32] found that, under identical axial strain and confinement stress conditions, the axial stress of FRP-confined concrete was generally lower than that of actively confined concrete. This observation indicates that the axial stress response is influenced by the loading path of confinement pressure, and this phenomenon is particularly evident in high-strength concrete. Similar conclusions were obtained by Lai et al. [30], who incorporated the influence of stress path by introducing a confinement pressure gradient prediction equation and a modified peak stress formulation, respectively.

As discussed above, under monotonic axial compression, particularly for FRP-confined high-strength concrete, the axial stress–strain response exhibits a certain degree of stress path dependency. Unlike actively confined concrete, where the confinement pressure remains constant, the confinement stress in FRP-confined concrete gradually develops with increasing deformation. Therefore, under the same axial stress level, FRP-confined concrete generally exhibits a higher axial stiffness, corresponding to a smaller axial strain, which is attributed to the slower development of internal cracking [33,34]. In other words, under identical axial strain and confinement stress conditions, the axial stress of FRP-confined concrete tends to be lower than that of actively confined concrete.

For the prestressed FRP-confined concrete investigated in this study, the confinement mechanism exhibits distinctive characteristics. At the initial stage of loading, the prestressed FRP provides an initial lateral confinement stress, which enhances the axial stiffness of the core concrete. With increasing axial load, the confinement stress progressively increases due to the development of internal cracking and accelerated lateral dilation of concrete, resulting in continuous changes in axial stiffness. Therefore, the confinement mechanism can be regarded as a transition from an initial state with certain active confinement characteristics toward a passive confinement state.

To establish a more accurate analytical model for prestressed FRP-confined concrete based on actively confined concrete models, the applicability of the stress path independence assumption must first be examined under such conditions.

Accordingly, the stress path independence assumption was evaluated by comparing the curves predicted by actively confined concrete models with experimental stress–strain curves of prestressed FRP-confined concrete. Axial stress–strain test data of prestressed FRP-confined concrete reported in Refs. [10,11,17,18] were selected (solid lines in Figure 2(a)–(d)) and compared with a series of curves generated using the actively confined concrete equations (Equations (7), (8), (11), and (12)) (dashed lines). The corresponding axial stress points under identical axial strain and confinement stress conditions were marked in the figures and connected by dashed lines.

The differences between the two responses were quantified using the axial stress ratio ${\sigma }_{\mathrm{c}}/{\sigma }_{\mathrm{c}}^{*}$ and relative error $\delta =({\sigma }_{\mathrm{c}}-{\sigma }_{\mathrm{c}}^{*})/{\sigma }_{\mathrm{c}}\times 100\%$ , where ${\sigma }_{\mathrm{c}}$ represents the experimental axial stress of prestressed FRP-confined concrete and ${\sigma }_{\mathrm{c}}^{*}$ represents the prediction from the actively confined concrete model.

Figure 2(a) and (b) present the experimental results obtained using the expansive concrete method, whereas Figure 2(c) and (d) show the results obtained using the continuous filament winding method. The comparison demonstrates that different prestressing techniques lead to distinct mechanical responses of confined concrete.

For the expansive concrete method, the measured axial stress is generally higher than the prediction from the actively confined concrete model under identical confinement stress conditions. The axial stress ratio is approximately 1.2, corresponding to a relative error close to 20%. This indicates that the stress–strain response exhibits considerable dependency on the loading path.

In contrast, the results obtained using the continuous filament winding method show that the measured axial stress is generally consistent with the prediction of the actively confined concrete model under equivalent conditions. The axial stress ratio approaches unity, and the relative error is mostly within 10%. This difference demonstrates that the stress path dependency of prestressed FRP-confined concrete is closely associated with the prestressing technique.

For the continuous filament winding method, the results satisfy the stress path independence assumption, indicating that the axial stress–strain response is primarily governed by the instantaneous confinement stress state rather than the loading path used to reach that state.

For the expansive concrete method, however, the measured axial stress exceeds the prediction from the actively confined concrete model, indicating that the stress path independence assumption cannot be directly applied. A possible explanation is that the addition of expansive agents reduces the initial microcracking within concrete. Consequently, concrete exhibits higher axial stiffness under the same confinement stress level, and the transition threshold from the elastic stage to the nonlinear stage is increased.

For prestressed FRP-confined concrete, the initial lateral confinement stress $f_{\mathrm{e}\mathrm{l},\mathrm{p}}$ generated by the FRP prestress strain ${\mathcal{E}}_{\mathrm{f},\mathrm{p}}$ can be calculated using Equation (13).

$$f_{\mathrm{e}\mathrm{l},\mathrm{p}}={\displaystyle \frac{2E_{\mathrm{f}}{ϵ}_{\mathrm{f},\mathrm{p}}{t}_{\mathrm{f}}}{D}}$$

(13)

Previous studies [18,20,35] have indicated that when the applied load approaches the compressive strength of unconfined concrete $f_{\infty }^{\prime }$ , the development of internal microcracks activates the lateral confinement provided by FRP, causing the stress–strain curve to enter the nonlinear stage. Therefore, it is assumed that the boundary of the elastic stage of confined concrete is controlled by the development of microcracks, and the lateral strain of concrete at this point is equal to the ultimate lateral strain of unconfined concrete ${\epsilon }_{\mathrm{l}\mathrm{o}}$ , where ${\epsilon }_{\mathrm{l}\mathrm{o}}=-\nu f_{\mathrm{c}\mathrm{o}}^{\prime }/E_{\mathrm{c}}$ .

Based on Hooke’s law, the axial stress $f_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }$ corresponding to the elastic limit under the initial lateral confinement stress $f_{\mathrm{e}\mathrm{l},\mathrm{p}}$ can be derived, resulting in the following prediction equation:

$$f_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }=f_{\mathrm{c}\mathrm{o}}^{\prime }+({\displaystyle \frac{1-\nu }{\nu }})f_{\mathrm{e}\mathrm{l},\mathrm{p}}$$

(14)

where the Poisson’s ratio is calculated using the equation proposed by Candappa [36].

To extend the actively confined concrete model to the expansive concrete method, an equivalent prestress-induced axial stress $f_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }$ is introduced to increase the peak stress level of the model. Specifically,  $f_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }$ and its corresponding axial strain ${\epsilon }_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }$ are used to replace $f_{\infty }^{\prime }$ and ${\epsilon }_{\mathrm{c}\mathrm{o}}$ , respectively, in the equations for calculating peak stress $f_{\mathrm{c}\mathrm{c}}^{*}$ and peak strain ${\epsilon }_{\mathrm{c}\mathrm{c}}^{*}$ . The modified formulations are expressed as Equations (15) and (16).

$${\displaystyle \frac{f_{\mathrm{c}\mathrm{c}}^{*}}{f_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }}}=1+3.5{\displaystyle \frac{{\sigma }_1}{f_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }}}$$

(15)

$${\displaystyle \frac{{\epsilon }_{\mathrm{c}\mathrm{c}}^{*}}{{\epsilon }_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }}}=1+17.5{\displaystyle \frac{{\sigma }_1}{f_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }}}$$

(16)

where the axial strain ${\epsilon }_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }$ corresponding to $f_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }$ is calculated using ${\epsilon }_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }=0.000937\sqrt{f_{\mathrm{c}\mathrm{o},\mathrm{p}}^{\prime }}$  (unit: MPa) proposed by Popovics [26].

Figure 3 compares the modified actively confined concrete model with the experimental stress–strain curves of prestressed FRP-confined concrete. The results indicate that, after modification, the axial stress ratio approaches unity and the relative error remains generally within 10%. This demonstrates that the stress path independence assumption can be reasonably satisfied within the proposed modification framework.

3.2 Strain Path Dependency

In analytical models for non-prestressed FRP-confined concrete, the strain path independence assumption is generally adopted [23,32]. This assumption indicates that actively confined concrete and FRP-confined concrete exhibit identical lateral strains under the same axial strain and confinement stress conditions.

To evaluate the applicability of this assumption to prestressed FRP-confined concrete, Figure 4 compares the lateral strain–axial strain relationships obtained from prestressed FRP-confined concrete tests reported in Refs. [10,11,17,18] with those calculated using Equation (3) for actively confined concrete. The solid lines represent the experimental results of prestressed FRP-confined concrete, whereas the dashed lines denote the curves generated from the actively confined concrete model. The intersection points indicate the corresponding confinement stresses under identical axial strain and lateral strain conditions.

The difference between the two responses is quantified by the confinement stress ratio $\$\$f_1/f_1^{*}\$\$$ , where $f_1$ represents the confinement stress of prestressed FRP-confined concrete and $f_1^{*}$ represents that of actively confined concrete. A confinement stress ratio close to unity indicates that the strain path independence assumption is satisfied.

Figure 4(a) and (b) present the results obtained using the expansive concrete method, whereas Figure 4(c) and (d) correspond to the continuous filament winding method. It can be observed that, under the initial reference condition, the lateral strain–axial strain curves of the two confinement systems intersect successively as the confinement stress increases. The confinement stress ratios at these intersection points are relatively large, indicating that the strain path independence assumption is not directly applicable.

Considering the influence of the initial lateral confinement stress $f_{\mathrm{e}\mathrm{l},\mathrm{p}}$ in prestressed FRP-confined concrete, Figure 5 presents the modified comparison curves, where the initial strain component corresponding to $f_{\mathrm{e}\mathrm{l},\mathrm{p}}$ is subtracted from the lateral strain of prestressed FRP-confined concrete. After this modification, the confinement stress ratios at the intersection points approach unity, indicating a strong consistency between the two relationships and confirming the existence of strain path dependency.

Therefore, to accurately describe the deformation behavior of prestressed FRP-confined concrete, the influence of the initial lateral confinement stress should be incorporated into the lateral strain–axial strain relationship. Accordingly, Equation (3) is modified, resulting in Equation (17).

$${\displaystyle \frac{\epsilon }{{\epsilon }_{\mathrm{o}}}}=0.85[1+0.75({\displaystyle \frac{\epsilon }{{\epsilon }_{\mathrm{o}}}}){]}^{17}-\mathrm{o}\mathrm{p}[7\left({\displaystyle \frac{\epsilon }{{\epsilon }_{\mathrm{o}}}}\right)\left]\right[1+8\left({\displaystyle \frac{\sigma -f_{\mathrm{d}\mathrm{p}}}{f_{\mathrm{o}}^{\prime }}}\right)]$$

(17)

3.3 Generation of Stress–Strain Curves

The axial stress, confinement stress, axial strain, and lateral strain of prestressed FRP-confined concrete are strongly interrelated, and the generation of its stress–strain curve involves an iterative procedure.

Based on the aforementioned analyses of stress path and strain path dependency, Figure 6 presents the flowchart for generating the stress–strain analytical model of prestressed FRP-confined concrete.

The procedure starts from the linear elastic constitutive relationship of FRP, where the confinement stress can be calculated based on the hoop strain ${\epsilon }_{\mathrm{h}}$ and Equation (2). Subsequently, for each increment of lateral strain ${\epsilon }_1$ and the corresponding confinement stress ${\sigma }_1$ , the axial strain ${\epsilon }_{\mathrm{c}}$ is determined using Equation (17). The peak stress $f_{\mathrm{c}\mathrm{c}}^{*}$ and peak strain ${\epsilon }_{\mathrm{c}\mathrm{c}}^{*}$ are then obtained using Equations (11)–(16), and the corresponding axial stress ${\sigma }_{\mathrm{c}}$ is calculated using Equation (7).

The above procedure is repeated until the hoop strain of FRP reaches its rupture strain ${\epsilon }_{\mathrm{h},\mathrm{r}\mathrm{u}\mathrm{p}}$ , at which point the iteration terminates. The complete stress–strain curve of prestressed FRP-confined concrete can therefore be obtained.

4. Model Validation

To evaluate the applicability of the proposed analytical model, experimental stress–strain curves of prestressed FRP-confined concrete reported in Refs. [10,17,18,37] were selected for validation. The experimentally obtained axial stress–strain curves and lateral strain–axial strain relationships were compared with the corresponding model predictions, as presented in Figure 7 and Figure 8. Furthermore, the predicted compressive strengths were compared with the experimental values, as shown in Figure 9.

4.1. Axial Stress–Strain Curves

Figure 7 compares the predicted stress–strain curves with the experimental results. The comparison demonstrates that the proposed model provides good agreement with most experimental data. In particular, the transition region, compressive strength, and ultimate axial strain are reasonably predicted, indicating that the proposed model can effectively capture the overall axial stress–strain response of prestressed FRP-confined concrete.

4.2. Lateral Strain–Axial Strain Curves

Figure 8 compares the predicted and experimental lateral strain–axial strain relationships. The predicted curves generally follow the experimental trends, further verifying the capability of the proposed model in describing the dilation behavior of concrete under different prestressing techniques.

4.3. Compressive Strength

Figure 9 compares the predicted compressive strengths with the corresponding experimental values. Most data points fall within the ±15% error range. The mean absolute error (MAE) between the predicted and experimental values is 8.9%, demonstrating that the proposed model provides reliable prediction accuracy for the compressive strength of prestressed FRP-confined concrete.

5. Conclusions

This study systematically investigated the differences between prestressed FRP-confined circular concrete and actively confined concrete in terms of stress path and strain path behavior, and established a unified stress–strain analytical model. The main conclusions are summarized as follows:

(1) The stress path dependency of prestressed FRP-confined concrete is closely related to the prestressing technique. For the continuous filament winding method, the axial stress–strain response is primarily governed by the instantaneous confinement state, and the stress path independence assumption can be reasonably adopted. In contrast, expansive methods exhibit apparent path dependency due to the influence of initial lateral confinement on the axial stiffness of concrete. By incorporating the initial confinement effect into the modification of peak parameters, the differences caused by various prestressing techniques can be considered within a unified analytical framework.

(2) Prestressed FRP-confined concrete possesses an initial lateral confinement stress that cannot be neglected. After removing the effect of this initial confinement, the lateral strain–axial strain relationship shows strong consistency with that of actively confined concrete. Based on this observation, the lateral strain–axial strain relationship was modified to more accurately describe the evolution of lateral dilation under prestressed confinement conditions.

(3) Based on the identified path-dependent mechanisms, an iterative analytical framework consisting of the FRP confinement relationship, modified peak parameter models, and modified lateral strain–axial strain relationship was established. The developed stress–strain model provides a unified description of the relationships among axial stress, axial strain, lateral strain, and confinement stress throughout the entire loading process of prestressed FRP-confined circular concrete.

(4) The proposed model was evaluated using multiple independent experimental datasets. The results demonstrate that the model can reasonably predict the axial stress–strain response, lateral dilation behavior, and compressive strength of prestressed FRP-confined concrete. The proposed analytical framework provides a theoretical basis and an effective tool for nonlinear analysis and engineering applications of prestressed FRP-confined concrete members.