Confinement properties of circular concrete columns wrapped with prefabricated textile-reinforced fine concrete shells

Abstract

This paper proposes an innovative column composed of a core column (including both reinforced concrete (RC) and plain concrete (PC) columns) and a prefabricated textile-reinforced fine concrete (TRC) shell. To study the confinement properties of TRC shells on this novel type of concrete column, 20 circular specimens, including 12 PC columns and 8 RC columns, were prepared for axial compressive tests. Four key parameters, including the column size, reinforcing ratio of the carbon textile, concrete strength, and stirrup spacing, were evaluated. The results indicated that the compressive properties of the columns were improved by increasing the reinforcing ratio of the textile layers. In the case of TRC-confined PC columns, the maximum improvement in the peak load was 56.3%, and for TRC-confined RC columns, the maximum improvement was 60.2%. Based on the test results, an analytical model that can be used to calculate the stress–strain curves of prefabricated TRC shell-confined concrete columns has been proposed. The calculated curves predicted by the proposed model agreed well with the test results.

Graphical abstract

Keywords

textile-reinforced fine concrete / prefabricated shell / confined concrete column / confinement properties / stress–strain relationship

1 Introduction

A concrete column is usually regarded as a significant component of many buildings, and its main task is to withstand horizontal and axial forces. However, columns often lose their load-carrying capacity owing to strong earthquakes or environmental corrosion [1–6]. Therefore, the construction industry is constantly seeking techniques to strengthen or rehabilitate deteriorated or damaged concrete columns. Many researchers have attempted to wrap columns with composite materials, such as fiber-reinforced polymer (FRP) or steel tubes, to enhance the mechanical properties of deteriorated columns. Studies on the compressive properties of concrete columns strengthened by these composite materials have been conducted [7–9]. It was established that the confinement provided by composite materials or steel tubes significantly enhanced the axial load-bearing capacity of concrete columns. In recent years, some drawbacks of FRP, such as relatively high cost, poor aging resistance, and inapplicability to wet surfaces, have been highlighted [10–13]. Moreover, the use of steel tubes is limited in corrosive environments.

Textile-reinforced fine concrete (TRC), a new composite material, has been widely used in recent years. In TRC, textile materials manufactured using high-performance fibers, such as carbon, basalt, or glass fibers, are adopted as reinforcing materials, and high-performance fine concrete is used as the bond matrix. Owing to its good tensile strength, ductility capacity, and corrosion resistance, TRC has become popular for rehabilitating existing reinforced concrete (RC) structures over the past few decades [14–17]. Compared with traditional composite materials such as FRP, TRC can be used in wet or corrosive environments [11,18,19].

Recently, several studies have investigated the characteristics of TRC. The tensile and bending behaviors of TRC sheets were studied, and calculation models for predicting their mechanical properties were proposed [20,21]. Some researchers have also investigated the strengthening effectiveness of TRC-strengthened concrete columns [22–33]. Tsesarsky et al. [22], Bournas et al. [23], and Yin et al. [24] investigated the compressive properties of concrete columns strengthened with TRC jackets using axial compression tests. According to the test results, the bearing capacity of the concrete columns increased significantly when TRCs were used for strengthening. The confinement provided by the TRC had no effect under a small compressive load. The core concrete started to expand laterally when the load approached 80% of the peak load, and the extension was limited by the confinement. Moreover, the effects of all types of contributing factors on the strengthening effectiveness of TRC-strengthened columns have been investigated in recent years. Colajanni et al. [25] evaluated the compressive properties of columns wrapped with different textile layers. The test results indicated that the axial bearing capacity of the columns could be improved by increasing the number of textile layers. Tello et al. [26] and Yin et al. [27] obtained similar results. The improvement in the compressive strength was 36% for columns wrapped with four textile layers. Some researchers have studied the effectiveness of confinement when textiles made from different fibers, including carbon, basalt, and glass fiber textiles (CTRC, BTRC, and GTRC), were used [28–31]. It was found that CTRC provided great confinement to improve the compressive behavior of concrete specimens. Li et al. [32] added short polyvinyl alcohol (PVA) fibers to TRC composites to improve the compressive behavior of TRC-confined columns. It was found that these fibers increased the confinement effects of the TRC composites. To further analyze and predict the bearing capacity and corresponding strain of TRC-confined RC columns, confinement models have been developed based on axial compressive tests [33–35]. These studies on TRC applications for RC columns have mainly focused on improving mechanical properties. In these studies, the TRCs were wrapped around the columns as strengthening layers, which significantly improved the bearing capacity of the columns. TRC materials can also be used as permanent formworks for newly constructed RC members [36,37]. Papantoniou and Papanicolaou [38,39] examined the mechanical properties of TRC permanent formworks and found that the TRC permanent formwork and cast-in-place concrete structure formed a mixed-structure system. Li and Yin [40] designed a TRC permanent formwork composite square column and studied the mechanical performance of the columns using a compressive test. It was found that the TRC permanent formwork composite columns exhibited a high crack control performance. TRC materials can consist of permanent tubular formworks. This type of formwork can limit the lateral extension of concrete, thereby improving the axial compressive strength and strain of the core concrete. Moreover, TRC formwork contains no metal material and has outstanding anti-corrosion characteristics. However, most studies have focused on TRC permanent formwork to improve the mechanical performance of concrete flexural members. Few investigations have focused on TRC permanent formwork for strengthening concrete columns and increasing their compressive behavior. In particular, studies on permanent formwork used for circular concrete columns are relatively scarce.

As discussed above, an innovative prefabricated TRC shell-confined RC column is presented in the current study. A prefabricated TRC shell was used to enhance the bearing capacity of plain concrete (PC) and RC columns. Axial compressive tests were performed, and the confinement effectiveness of the prefabricated TRC shell was studied. The effects of the reinforcing ratio of carbon textiles, column sizes, and stirrup spacing on the confinement properties were explicitly considered. Finally, a theoretical model for the stress–strain relationship of confined concrete is presented to predict the compressive strengths of the columns.

2 Experimental programs

2.1 Specimen preparation

To study the compressive properties of prefabricated TRC shell-confined concrete columns, four test parameters were considered and evaluated: column size, number of carbon fiber textile layers, concrete strength, and stirrup spacing. Twenty circular specimens, including 12 PC columns and 8 RC columns, were prepared for the axial compressive test. In this study, scale specimens were used as test columns. The design of the specimens was based on a standard [41]. The experimental program for the concrete columns is listed in Tab.1. For series 1, ‘200-x’ and ‘160-x’ represent control columns without a prefabricated TRC shell. The ‘xPVC-Lx-Cx’ specimens represent the strengthened columns that were confined with a TRC shell, where the first number is the column diameter, the middle number ‘Lx’ represents the number of textile layers, and the last number ‘Cx’ represents the concrete strength. For series 2, similar to series 1, ‘xPVC’ represents the diameter of the specimens, ‘Lx’ represents the number of textile layers, ‘Cx’ represents the strength grade of the concrete, and ‘Sx’ represents the stirrup spacing.

The prefabricated TRC shell-confined RC column can be divided into two parts: core concrete and TRC shell. The TRC shell consists of three components: polyvinyl chloride (PVC) pipe, fiber textile, and high-performance fine concrete (Fig.1). It should be noted that PVC has outstanding deformation performance and excellent anti-corrosion characteristics. PVC pipes have been widely used in engineering applications [42]. Thus, PVC pipes were selected as the liners of the prefabricated TRC shells in this study. To prepare the specimens, the first 3–5 mm fine concrete layer was manually troweled on the PVC pipe. Subsequently, as shown in Fig.2(a), the first textile layer was wrapped onto the surface and the second fine concrete layer was pressed onto it. These production steps were repeated until the outermost fine concrete layer was wrapped. Finally, the last layer of fine concrete was smoothed, as shown in Fig.2(b). Before the concrete was applied, six cutting lines were carved, and 32 stainless steel screws were inserted into the surface of the PVC pipes. Epoxy glue was also applied to the surface to improve the adhesion between the PVC pipes and TRC.

After the TRC shells were prepared and cured for 28 d, the concrete core was poured into the shells with continuous shaking. It should be noted that for series 2, the reinforcement cages were placed into the shells before the concrete was poured, as shown in Fig.2(c). After the specimens were cured at laboratory temperature for 28 d, white paste and grids were painted on the specimens to observe the cracks, as shown in Fig.2(d).

2.2 Material properties

2.2.1 Concrete

In this study, all columns were constructed from normal concrete, consisting of 42.5 ordinary Portland cement, water, fine aggregate sand, and coarse aggregate. The mixing proportions of the normal concrete with different strength grades are listed in Tab.2. For the prefabricated TRC shell, the fine-grain concrete included a mixture of cement, fly ash, silica fume, fine sand, and Q8081-PCA (I) water-reducing agent, with the mixing proportions of cement:sand:fly ash:silica fume:water:water-reducing agent = 1:1.5:0.2:0.07:0.38:0.018. Compressive and bending tests were carried out, and of the resulting compressive and bending strength values of the fine concrete were 58.6 and 13.7 MPa.

In this study, 12 mm PVA fiber was added to the matrix of the TRC shell to improve its tensile strength. The short fiber content was chosen according to a previous study by Zhang et al. [43]. This study investigated the effect of short-fiber content on the mechanical properties of fine concrete. It was found that the mechanical properties of the fine concrete first increased and then decreased with increasing short-fiber content. A content of 1.5% by volume of short fibers resulted in the maximum improvement in the mechanical properties. Therefore, the amount of short PVA fibers used in this study was 1.5% by volume. The mechanical properties of the short PVA fibers were provided by the manufacturer. The density, tensile strength, elastic modulus, and yarn diameter were 1300 g/cm³, 1500 MPa, 29 GPa, and 35 μm, respectively.

2.2.2 Textile layer

The fiber textile used in this research was a high-performance textile grid composed of carbon fiber bundles as warp threads and alkali-free glass fiber bundles as weft threads, as shown in Fig.3(a). When used for the TRC shell, the tensile load is borne by the warp thread. Both the carbon and alkali resistant glass (AR-glass) fiber textiles had a spacing of 10 mm between the threads. Tab.3 shows the main mechanical properties of the carbon fiber bundles provided by the manufacturer. In addition, the actual tensile strength of the carbon fiber was measured using tensile tests, and the mean value was 2237.8 MPa, as shown in Fig.3(b).

2.2.3 Steel bars

For series 2 specimens, steel bars were used to reinforce the concrete core. HRB400 steel bar with a diameter of 12 mm was chosen as the longitudinal steel bar, and HPB300 steel bar with a diameter of 6 mm was used for the stirrups. All of the RC columns were reinforced using four longitudinal bars. The steel bars used to reinforce the columns were tested according to the code [44]. The tensile test results for the steel bars are shown in Tab.4. Note that, according to the tensile test results of the steel bars, the elastic modulus of the steel bars is almost equal to the value of 2.0 × 10⁵ N/mm² provided by the code [44]. Therefore, in this study, the elastic modulus of the steel bars was taken as 2.0 × 10⁵ N/mm².

2.3 Test setup and instrumentation

In this study, axial compressive tests were performed using a 300T hydraulic compression testing machine (YAW-3000). A force transducer above the loading platen was used to measure the load and two displacement gauges were used to measure the displacement during the tests. The test device is shown in Fig.4. To mount the displacement gauges, a metal band was placed on each side of the columns prior to testing. The compressive test was performed under displacement control at a rate of 1 mm/min.

3 Experimental results

3.1 Typical failure modes

The typical failure modes for the column specimens were observed, as shown in Fig.5. For the specimens without prefabricated TRC shells (160-L0-C30, 200-L0-C30, and 200-L0-C30-S100), no significant cracking or lateral expansion displacement was observed at the start. Subsequently, a thin crack along the axial direction appeared and grew more rapidly as the load increased. Vertical split failure occurred when the core concrete reached its compressive strength, as shown in Fig.5(a). For columns confined with prefabricated TRC shells, two failure modes were observed (Fig.5(b) and Fig.5(c)). For confined columns without textile layers, a similar phenomenon was observed when the load was small. Subsequently, cracks occurred and propagated with the increase in the lateral displacement. Finally, the PVC fractured owing to fatigue crack growth, and considerable spalling of fine concrete on the TRC shell could be observed, as shown in Fig.5(b). Columns with two or four textile layers exhibited a different failure mode. The lateral extension of the concrete caused by the axial compression was confined by the TRC shell, and the bearing capacity was improved. When the axial load reached approximately 80% of the peak load, cracks appeared and then propagated. As the cracks propagated, slight crushing was observed, and the fine concrete of the TRC shell spalled gradually. Finally, the carbon fiber bundles were torn and the columns were destroyed, as shown in Fig.5(c).

Fig.5(d) and Fig.5(e) show the failure modes of RC specimens with two textile mesh layers. The TRC-confined RC columns exhibited almost identical modes of failure to the TRC-confined PC columns. It was observed that the cracks on the RC columns appeared later compared to those without steel bars. In addition, more spalling of the concrete on the surface of the RC specimens was observed compared with the PC columns. This can be explained by the fact that the bearing capacity of the concrete core was increased and a higher axial load was applied to the core concrete when the fiber bundles ruptured, which led to more cracks and spalling in the concrete.

3.2 Load–deformation curves

The relationship between the axial load and displacement (i.e., load–displacement curve) for the test columns is shown in Fig.6 (PC columns) and 7 (RC columns). It can be observed that for the control specimens, the load increased linearly at first and declined rapidly after the peak point. For the columns confined with the TRC shell, three stages can be observed: the linear elastic, nonlinear hardening, and failure stages. At the start of loading, the load increased linearly until the cracking point was reached. A linear response was observed and the slope was similar to that of the unconfined columns. This is because the compressive strength of the core concrete has not been reached, and TRC shells are not fully activated. In the second stage, the load–displacement curves showed a nonlinear increase until the peak point was reached. At this point, the core concrete reached its maximum compressive strength, and the TRC confinement started to play a role as the load further increased. In the last stage, the curves begin to decrease. The rate of decrease was rapid for the unconfined concrete. However, the load of the TRC-confined columns declined slowly because of the improvement in ductility compared with the columns without confinement.

Fig.6 and Fig.7 also show the effect of the number of textile layers, stirrup ratio, and concrete grade on the load–displacement curves of the columns. From these figures, it can be inferred that the compression properties of the specimens increased with an increase in the number of textile layers. However, the columns confined by shells with no textile layer (160PVC-L0-C30, 200PVC-L0-C30, and 200PVC-L0-C30-S100) exhibited the same peak load as the control specimens. In other words, the PVC pipes in the prefabricated TRC shells did not enhance the load-bearing capacity of the columns. This can be explained by the fact that PVC pipes exhibit a large elastic deformation under lateral stress, which limits the confinement effectiveness of the prefabricated shell. As the axial load increased, the lateral deformation of the PVC pipe increased until it fractured. In this process, PVC could not stop the expansion of the core concrete. Therefore, in this study, the effect of PVC pipes on the strength of the core concrete could be ignored.

For the 160 mm diameter columns, the load–deformation curves decreased more rapidly than those of the 200 mm diameter columns. This was attributed to the more pronounced confinement effectiveness of the TRC shell in columns with smaller diameters, which led to a larger increase in the bearing capacity of the concrete core, and more rapid failure of the core concrete after the rupture of the fiber bundles.

3.3 Load and deformation

3.3.1 Load-bearing capacity

Tab.5 presents the main test results of the prefabricated TRC shell-confined columns, including the initial cracking load P_cr, peak load P_p, ultimate axial displacement Δ_u, displacement ductility factor µ , and deformation energy E_d. As shown in the table, the PC columns confined with prefabricated TRC shells had significantly improved results for the cracking load and peak load, and the improvement was proportional to the number of textile layers. In the cases of 160 and 200 mm diameter PC columns, the maximum improvement of the peak load reached 56.3% and 52.4%, respectively, when four textile meshes were wrapped on the column. This is because the lateral deformation of the concrete was confined by the TRC shell. Confinement effectiveness was improved by increasing the number of textile layers, which enhanced the bearing capacity of the concrete columns.

The same conclusions were obtained for TRC-confined RC columns. The maximum increase in cracking and peak loads reached 58.1% and 60.2%, respectively, when four textile layers were used. However, the stirrup spacing had no significant effect on the peak load of the columns because the constraint of the stirrup could be ignored compared with the constraint of the prefabricated TRC shell.

The column diameter also significantly affected the bearing capacity of the columns. The cracking load and peak load of the 200 mm diameter columns (200PVC-L0-C30, 200PVC-L2-C30, and 200PVC-L4-C30) were higher than those of the 160 mm diameter columns (160PVC-L0-C30, 160PVC-L2-C30, and 160PVC-L4-C30). Meanwhile, for the 200 mm diameter columns, the increase in load-bearing capacity after confinement with TRC shells was less than that for the 160 mm diameter columns. This finding confirms that the confinement of columns with a small diameter leads to a greater increase in strength compared to those with a larger diameter.

The effect of the core concrete strength grade on the load-bearing capacity of the columns was also evaluated. As listed in Tab.5, for columns with different concrete strengths (C20, C30, and C40), the peak loads were almost the same. It can be concluded that the concrete strength had only a small influence on the load-bearing capacity of the prefabricated TRC shell-confined columns. This can be explained by the fact that the ultimate load of the confined columns was mainly dependent on the confinement provided by the TRC shell, rather than the core concrete strength. Compared with the columns without confinement, the core concrete of the confined columns was limited by the TRC shell, which delayed the failure of the core concrete. Failure of the core concrete occurred when the TRC shell ruptured. Therefore, the ultimate load of the specimens with TRC shells was less affected by concrete strength. Note that if the confinement level of the TRC confined columns is low, the TRC shell does not completely limit the failure of the core concrete. Therefore, for these columns, the peak load may still depend on the core concrete strength.

3.3.2 Deformation

In this study, a displacement ductility factor µ, which was used to estimate the deformation capacity of the columns, was proposed. Tab.5 also shows the ultimate displacement and displacement ductility factors for all column specimens. As shown in the table, the ultimate displacement and factor µ of the columns increased after being confined by the TRC shell. For columns without TRC confinement (200-PVC-C30 and 160-PVC-C30), the values of the displacement ductility factor were 1.08 and 1.37, respectively. Meanwhile, for columns confined by prefabricated TRC shells, the value ranged from 1.87 to 3.41.

In addition, the effect of the number of textile layers on the displacement ductility factor was analyzed. It was found that for columns confined by TRC shells, the increase in textile layers led to a decrease in ductility. For 200 mm diameter columns with 0, 2, and 4 textile layers, the increase in the displacement ductility factor was 215.7%, 143.5%, and 79.6%, respectively, compared with the control specimens. The 160 mm diameter columns confined with 0, 2, and 4 textile layers exhibited increases of 43.1%, 40.9%, and 36.5% in the displacement ductility factor, respectively, and a similar result was obtained for TRC-shell-confined RC columns. This was attributed to the fact that increasing the number of textile layers enhanced the confinement effectiveness, which led to a higher axial load-bearing capacity of the columns. When the confinement of the TRC shell failed, failure of the confined concrete quickly occurred owing to the high load. In addition, as discussed above, the confinement effectiveness of the TRC shell was more pronounced in columns with smaller diameters, which led to a decreased ductility. Therefore, it is suggested that the column diameter should be considered to satisfy the ductility requirement.

Tab.5 also presents the deformation energy of the specimens to evaluate the ductility of the columns confined with TRC shells in different directions. The deformation energy is defined as the area under the load–displacement curves, as shown in Fig.8. It was found that the deformation energy of the specimens with TRC shells was significantly improved compared with those without TRC shells, and the deformation energy was increased by increasing the number of textile layers. The maximum improvement was up to six times when four textile layers were used. For the RC columns, the deformation energy also improved with a decrease in the stirrup space.

4 Theoretical model for confined concrete

4.1 Model overview

Using the load–displacement curves of the prefabricated TRC shell-confined concrete columns in this study, the stress–strain relationship of the columns could be obtained. The stress is equal to the ratio of the load carried by the concrete to the sectional area of the core concrete. For the PC columns, this load was equal to the test load, and for RC columns, this load was equal to the test load minus the load on the longitudinal bars. In addition, strain is the ratio of the displacement to the effective height of the columns. These values were determined by actual measurements.

Fig.9 shows typical stress–strain curves of both PC and RC columns with and without TRC shells. As shown in Fig.9, for these two types of columns, the stress–strain curve can be simplified into two stages. Before the peak point, a parabolic ascent stage occurs and a linear decrease stage is then seen until failure of the column. A simplified model of the curve was constructed to describe the stress–strain relation of the prefabricated TRC shell-confined concrete, as shown in Fig.10. It should be noted that the curve is decided by three key points: the peak point (P), the point corresponding to the peak stress dropping to 85% (U) and the residual stress point (F), i.e., the point when the peak stress drops to 30% [40]. The curve is expressed by Eq. (1):

(1)

where σ and ε denote the axial stress and axial strain of the core concrete, respectively; f_cc denotes the peak stress of the confined concrete (i.e., the compressive strength); ε_p is the peak strain, corresponding to the strain at the peak stress; ε_0.85 and ε_f are the strains at points U and F, respectively.

The calculation methods for these coefficients are presented below. The residual stress point can then be determined using Eq. (1).

4.2 Peak point

4.2.1 Peak stress

According to previous research [47], the peak stress of confined concrete is determined by the value for unconfined concrete and the lateral fluid pressure provided by the confinement. For the TRC-confined PC specimens, the lateral confinement on the core concrete is provided by the TRC shells, whereas in the case of the TRC-confined RC specimens, the lateral confinement is provided by the TRC shells and stirrups, as shown in Fig.11(a) and Fig.11(b). In addition, for TRC-confined RC columns, the compound action of the TRC and stirrups must be considered. Therefore, the peak stress f_cc is equal to the sum of the compressive strength of concrete without confinement, the confinement strength provided by the TRC shell and stirrups, and the interaction effect between the TRC shell and stirrups, as shown in Eq. (2):

(2)f_{\text{cc}}=f_{\text{c}0}+k_{\text{ef}}{f}_{\text{lu,f}}+k_{\text{es}}{f}_{\text{lu,s}}+\gamma \frac{f_{\text{lu,f}}\cdot f_{\text{lu,s}}}{f_{\text{c0}}},

where f_c0 represents the peak stress for concrete without confinement; f_lu,f and f_lu,s denote the confinement stress provided by the TRC confinement and stirrups, respectively; k_ef denotes the coefficient of TRC confinement; and \gamma denotes the compound action coefficient of the TRC and stirrup. Hereafter, we introduce these coefficients. The coefficient k_es is the coefficient of stirrup confinement, determined by referring to the confinement model established by Mander et al. [47], and can be calculated as follows:

(3)k_{\text{es}}=\frac{f_{\text{c0}}}{f_{\text{lu,s}}}\left(-2.254+2.254\sqrt{1+\frac{7.94f_{\text{lu,s}}}{f_{\text{c0}}}}-2\frac{f_{\text{lu,s}}}{f_{\text{c0}}}\right).

The lateral stress f_lu,f and f_lu,s can be expressed by Eqs. (4) and (5), based on force analysis (Fig.11(c)). In the figure, σ_c is the total lateral stress, which is equal to the sum of f_lu,f and f_lu,s. It can be inferred from the figure that for columns confined only by prefabricated TRC shells, the value of f_lu,s is 0, and in the case of columns confined only by stirrups, the value of f_lu,f is 0.

(4)f_{\text{lu,f}}=\frac{2n{A}_{\text{f}}{f}_{\text{f}}}{d_{\text{cor}}s},

(5)f_{\text{lu,s}}=\frac{2k_{\text{e}}{A}_{\text{sv}}{f}_{\text{yv}}}{d_{\text{cor}}{s}^{\prime }},

where f_f and f_yv are the tensile strength of the carbon fiber yarn and stirrup, respectively (refer to Section 2); A_f denotes the bundle area of the fiber textile; A_sv denotes the sectional area of the stirrup; d_cor denotes the diameter of the concrete core; n is the number of textile layers, which is an integer and less than or equal to 4 in this study; s denotes the spacing between the adjacent carbon yarns, which is 10 mm in this study; s' denotes the stirrup spacing of the columns; and k_e denotes the confinement effectiveness coefficient. In this study, k_e is applied according to Mander et al. [47].

As discussed above, the values of coefficients k_ef and \gamma need to be determined. In the case of prefabricated TRC shell-confined PC columns, the values of k_ef can be obtained from the test data. In addition, to increase the applicability and accuracy of this TRC-confined concrete model, 20 TRC-confined circular concrete columns with similar characteristics were tested by Chen et al. [48], di Ludovico et al. [36], and Ombres [49] and compiled to form a database in this study, as shown in Tab.6. This test data was also evaluated in this study. It can be observed that the value of k_ef is affected by column size and concrete strength, as shown in Fig.12. Subsequently, an optimum analysis of the test results from both the current study and the database was performed. The parameter k_ef can be obtained using Eq. (6):

(6)k_{\text{ef}}=\left(k_0{f}_{\text{c0}}^{\text{2}}+k_1{f}_{\text{c0}}\right) k_2{\lambda }_{\mathrm{v}}+k_3,

where k₀, k₁, k₂, and k₃ are the coefficients of the concrete strength and column size, respectively. Optimum analysis based on these data was performed to determine the following values: k₀ = 0.0097, k₁ = −0.757, k₂ = 0.892, and k₃ = 13.51. The volume coefficient of the columns is λ_v, which reflects the column size, and is defined as follows:

(7){\lambda }_{\mathrm{v}}=\frac{\left(h/d\right)A_{\text{c}}}{\left(h^{\prime }/d^{\prime }\right)A_{\mathrm{c}}^{\prime }},

where h and d are the height and diameter of the columns; A_c donates the sectional area of the columns; h^{\prime }, d^{\prime }, and A_{\mathrm{c}}^{\prime } are the height, diameter, and sectional area of the standard specimens, respectively. In this study, a standard column specimen was defined as a column with a diameter of 200 mm. It should be noted that the equations in this study were mainly developed for columns that do not exceed 600 mm in diameter. Further research needs to be conducted for columns larger than 600 mm in diameter.

For RC columns confined by TRC shells in Tab.1, the value of \gamma can be obtained in accordance with Eq. (2). According to the test results, \gamma was significantly influenced by the reinforcing ratio of both the textiles and stirrups. Regression analysis was then performed, and the compound action coefficient \gamma was calculated as follows:

(8)\gamma =-\left(k_{\text{r1}}{\rho }_{\mathrm{f}}+k_{\text{r2}}\right) {\rho }_{\mathrm{s}\mathrm{v}}-k_{\text{r3}},

where k_r1, k_r2, and k_r3 are coefficients considering the textile reinforcement ratio and stirrup ratio, equal to −1227.1, 95.5, and 17.4, respectively, according to the fitting analysis; ρ_f is the reinforcing ratio of the textiles, which is obtained as follows:

(9){\rho }_{\text{f}} =\frac{2n{A}_{\text{f}}}{ds}\times 100\mathrm{\%}.

Finally, the peak stress of concrete confined by a prefabricated TRC shell was calculated. Fig.13 compares the calculated and measured values of the peak stress. It can be observed that the calculation results correspond well to the measured values.

4.2.2 Peak strain

According to a review [47], for confined concrete, peak strain ε_p is positively correlated with the ratio of f_cc to f_c0. In other words, the values of ε_p/ε_c0 and f_cc/f_c0 maintain a linear relationship. The peak strain ε_p can be obtained using the following equation:

(10)\frac{{\epsilon }_{\text{p}}}{{\epsilon }_{\text{c0}}}=1+ k_{\text{p}} \left(\frac{f_{\text{cc}}}{f_{\text{c0}}}-1\right),

where k_p denotes the improvement coefficient, considering the improvement ratio of the peak stress. In this study, regression analysis was performed to determine the value of k_p, as shown in Fig.14. From the test data in Section 3 and the database, it was determined that k_p = 1.9.

Fig.15 shows a comparison between the measured and calculated values of peak strain. It can be seen that the calculations correspond well with the corresponding measured data. This implies that Eq. (9) is accurate.

4.3 Point at which the stress drops to 85% peak stress

To determine the simplified curve of the confined concrete, point U(ε_0.85, 0.85f_cc) (the point at which the peak stress drops to 85%) must be determined. The parameter f_cc was introduced in Subsection 4.1, and the value of ε_0.85 can be obtained by regression analysis of the test data. Fig.16 shows the relationship between ε_0.85 and ε_p for all specimens in Tab.1. It can be observed from Fig.16 that ε_0.85 has an approximately linear relationship with peak strain ε_p. Therefore, the following equation is obtained:

(11){\epsilon }_{0.85} =k_4{\epsilon }_{\text{p}}+k_5,

where k₄ and k₅ are coefficients that describe the relationship between ε_0.85 and ε_p, respectively, which can be obtained using a regression analysis. The values of k₄ and k₅ are 1.1441 and 0.0017, respectively. It should be noted that for some of the stress–strain curves in the database, point U was not recorded. Therefore, these specimens were not considered in the fitting analysis.

Fig.17 presents a comparison of the calculated results for ε_0.85. It can be observed that the calculations agree well with the respective test data.

4.4 Model verification

As discussed above, the feature points of the simplified curve model can be obtained when typical points are determined. Fig.18 presents a comparison between some of the calculated and measured curves. The calculated curves are in good agreement with the measured curves; therefore, the proposed curve model can precisely describe the stress–strain relation of specimens with prefabricated TRC shells.

Moreover, according to the literature review, few theoretical models are applicable for establishing a complete stress–strain curve of circular concrete columns wrapped with a TRC shell. In addition, FRP materials and TRCs have similar confinement mechanisms when used for strengthening concrete columns to a certain extent, and the two FRP-confined circular concrete column models provided by Turgay et al. [50] and Wu et al. [51] were compared with the TRC-confined concrete model in this study, as shown in Fig.18. Evidently, the stress–strain curves calculated by the FRP-confined models do not agree well with the measured stress–strain curves. This indicates that existing FRP-confined concrete models are not applicable to TRC-confined concrete. For FRP materials, the bond between the confining and column surfaces relies on the epoxy resin. For the TRC, the bond between the column surface and confining layer is dependent on cementation. Therefore, FRP and TRC materials provide different confinement behaviors when used for strengthening concrete columns.

5 Conclusions

An experimental investigation focusing on the compression behaviors of concrete columns confined by prefabricated TRC shell with different parameters was carried out through axial compressive tests in this paper. Based on the experimental results, the effects of the number of textile layers, steel reinforcement, concrete strength, and column size on the axial compressive behavior were revealed and discussed. Accordingly, the following conclusions were drawn.

1) The columns confined with prefabricated TRC shells exhibited higher compressive behavior than the columns without confinement. The confined columns exhibited little spalling of the concrete, and cracks developed slowly under an axial compressive load. In addition, the mechanical properties of the columns improved with an increase in the strengthening ratio of the fiber textiles. In comparison to the control specimens, the maximum improvements in the peak load for the TRC-confined PC and RC columns were 56.3% and 60.2%, respectively, when four textile layers were applied.

2) In general, the 200 mm diameter columns had a higher load-bearing capacity than the 160 mm diameter columns, whereas the smaller columns had a relatively higher confinement effect. Indeed, for columns with small diameters, the confinement effect was significantly improved, which led to a higher axial load on the columns. Simultaneously, the columns lost their bearing capacity more rapidly upon reaching the peak load.

3) Calculation methods for the peak stress, peak strain, 85% peak stress, and corresponding strain of prefabricated TRC shell-confined concrete columns were proposed while considering the reinforcing ratio of carbon textiles, stirrups, concrete strain, and column size. A model for predicting the axial stress–strain relationship of columns was proposed based on these calculation methods. The predicted curves were in good agreement with the experimental curves, showing that the calculation method could accurately calculate the stress–strain curves of prefabricated TRC shell-confined concrete.

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