Mechanical behaviour of PVC-CFRP confined concrete column with RC beam joint subjected to axial load Mechanical behaviour of PVC-CFRP confined concrete column with RC beam joint subjected to axial load

An experimental investigation on failure mode, ultimate strength, strain variation, and load-displacement curves of PVC-CFRP confined concrete column with reinforced concrete (RC) beam joint (PCRBJ) subjected to axial load was conducted in this study. Samples of a PVC confined concrete column with RC beam joint (PRBJ) and nine PCRBJs were designed using the principle of weak column and strong joint. A numerical analysis approach for convenient prediction of the load-displacement curve of specimen was proposed. It was established that the estimated values are in good agreement with test data.


Introduction
Fibre reinforced polymer (FRP) has been widely utilized in engineering repairs due to its good durability, fatigue resistance, convenient structure, and corrosion resistance. Good reinforcing effect of FRP has already been achieved in the repair of members, such as walls, columns, beams, and plates [1][2][3][4][5][6][7][8]. The members strengthened with FRP show good bearing capacity, ductility and seismic resistance. Recently, it has been suggested to use FRP in some new structural elements, such as concrete-filled square steel tubes with FRP-confined concrete [9], FRP-reinforced concrete beams [10], and FRP confined concrete columns [11]. Mirmiran [11] proposed FRP tube concrete columns, and investigated their behaviour using experimental approach. Results demonstrated that FRP tube had a constraining effect on the core concrete, which significantly improved the ultimate strength and ductility of FRP tube concrete columns. However, the high cost hindered the application of FRP tubes in engineering. Hence, Saafi [12] proposed a PVC-CFRP Confined Concrete Column (PFCC) that used cheaper PVC tube wound by CFRP strips at the grooved section. Although the grooved PVC-FRP tube remarkably enhanced the ultimate strength and ductility of concrete, early failure of PVC tube may appear at the grooved portion due to stress concentration. To overcome this shortcoming, Yu [13,14] proposed non-grooved PFCC. The ultimate strength and ductility of core concrete improved a lot compared to those of grooved PFCC. Jiang [15] and Ma [16] conducted a finite element analysis to study the axial performance of PFCCs. The results showed that the slenderness ratio and layers of CFRP strips exerted a great influence on the bearing capacity. A simplified formula for predicting the ultimate strength was proposed depending on the test data. Fakharifar [17] analysed the effect of the type and thickness of FRP tube, compressible foam, and the loading zone, on the behaviour of PFCC. The experiment for the seismic resistance of PFCC was performed by Fakharifar [18], and high ultimate strength and good ductility of PFCC were demonstrated. Jiang [19] studied the influence of the axial force ratio, the layer and type of FRP on the circular section reinforced concrete composite column with FRP-PVC tube under cyclic loading. Good seismic performance and high energy consumption of PFCC were established. Yu [20,21] examined the influences of various parameters such as CFRP strip spacing, shear span ratio, and axial force ratio, on the seismic behaviour of PFCCs. As described above, a number of publications focusing on PFCCs have been reported. However, the mechanical behaviour of PCRBJ is limited. The effect of b, h, ρ, ρ sv and s f ' on the performance of PCRBJ under axial load is investigated in this study.

Specimen preparation
Nine PCRBJ and one PRBJ were designed based on the principle of weak column and strong joint. The outer diameter (D), thickness (t), and height (H), of PVC tube were 200 mm, 7.8 mm, and 500 mm, respectively. Two layers of CFRP strips were wound around the PVC tube. The width and thickness of CFRP strips were 20 mm and 0.22 mm, respectively, see Figure1. Three layers of CFRP strips were wrapped at the junction of joint and column to avoid premature failure at the interface between the column and the RC beam joint. The diameters of stirrups and longitudinal reinforcement were 6 mm and 10 mm, respectively. The lengths of the encryption zone and non-encrypted zone were 150 mm and 350 mm, respectively. The reinforcement ratios of stirrups in the encryption zone and non-encrypted zone were 1.18 % and 0.59 %, respectively. The reinforcement ratio of longitudinal reinforcement was 2.0 %. Additional details are provided in Figure 2.   Mechanical behaviour of PVC-CFRP confined concrete column with RC beam joint subjected to axial load Different spacing of winding CFRP strips considered were 40mm and 60mm. Five different sections of ring beam, such as 75 mm×300 mm, 100 mm×300 mm, 125 mm×300 mm, 75 mm×180 mm, 75 mm×240 mm, were considered. The reinforcement ratios of ring beam were 1.45 %, 1.85 %, and 2.25 %, and the stirrups ratios of ring beam were 0.85 %, and 1.70 % respectively, as shown in Table 1. All members of each subassembly were cast at one time, as shown in Figure 3.

Material properties
HPB300 for reinforcement and stirrup and C35 concrete were utilized in this study. Mechanical properties of steel were determined according to Chinese code "Metallic materials -Tensile testing -Part 1: Method of test at room temperature" (GB/ T228.1 -2010) [22], as shown in Table 2. The stress-strain curve of the PVC tube established from the axial compression experiment according to Chinese codes GB/T 8804. 1 -2003 [23] and GB/T 3354 -2014 [24] is shown in Figure 4, while buckling of PVC tube is shown in Figure 5. Tensile strengths of PVC and CFRP were 62 MPa and 3903 MPa, respectively. Concrete strength was estimated based on the test method specified in Chinese Code "Standard for test method of mechanical properties on ordinary concrete " (GB/T 50081-2002) [25]. The compressive strength and Young's modulus of concrete were 24 MPa and 2.4 ×10 4 MPa, respectively, as illustrated in Table 3.

Loading procedure and arrangement of instruments
The test was performed using the electron-hydraulic servo compressive machine Type YAW-5000F. The test started by preloading with 5 % of the estimated ultimate strength, which was to make sure that each instrument works properly. Force-controlled and displacement-controlled loading schemes were applied in the experiments. The experiments were initi- Compressive strength [MPa] Elastic modulus [10 4 MPa] Mechanical behaviour of PVC-CFRP confined concrete column with RC beam joint subjected to axial load ated with the load-controlled program at the rate of 50 kN / min. The load increment was 1/10 of the estimated ultimate strength of the specimen. Each load step kept constant for 2 minutes. After the axial compressive load attained approximately 90 % of the estimated ultimate strength, the displacement-controlled method with 0.5 mm/min was adopted. When the axial compressive load fell to 85 % of the ultimate strength, the test was terminated. Four strain gauges were glued in the circumferential direction of the CFRP strip and 4 strain gauges were placed in the longitudinal direction of PVC tube for getting the circumferential and longitudinal strain of the concrete column of PVC-CFRP tube, as depicted in Figure 6.  As load increased, PRBJ came into the crack developing stage. Subsequently, the volume of core concrete expanded rapidly and several small cracks occurred in the joint zone, which were then extended continuously. In addition, the development rate of PVC tube strain and the longitudinal reinforcement strain increased. When the load increased to approximately 80 % of the ultimate strength of specimen, the longitudinal reinforcement yielded. Finally, as depicted in Figure 8, the PVC tube was buckled.

PCRBJ specimen
The PCRBJ was damaged with PVC tube cracking and CFRP strips fracture. The failure process of the PCRBJ was approximately composed of three stages. In the elastic stage, the deformation of PCRBJ, similar to the PRBJ, was not obvious. The strains of concrete, CFRP strips and longitudinal reinforcement developed slowly, and PVC tube had little effect on the concrete. As the load increased, the PCRBJ entered the crack developing stage. Several small vertical cracks occurred in the joint zone, The lateral deformation of concrete increased, and cracks in the concrete extended continuously. The development rate of CFRP strip strain and PVC tube strain increased rapidly, the confining effect of PVC-CFRP tube on column was obvious. When the load increased to approximately 90 % of ul-timate strength, a loud sound demonstrating CFRP strips fracture could be heard. Eventually, as depicted in Figure 9, PVC tube cracked.

Ultimate strength
The influence of all studied parameters on ultimate strength is shown in Figure 10. Obviously, the influence of the s f ' on ultimate strength of specimen was significant, and the ultimate strength of specimen decreased as the s f ' increased. This may come from that the increase in the s f ' decreased the confinement effect of CFRP strips on specimen. For instance, the ultimate strength of the PCRBJ with the spacing of 40 mm was by 13.8 % higher than that of the specimen with the spacing of 60 mm. In contrast, the influence of the b, h, ρ, ρ sv ,on the ultimate strength of specimen was not obvious. Thus, the ultimate strength of the specimen increased by 4.1 % when the ρ increased from 1.45 % to 1.85 %.

Axial strain of PVC tube
The axial stress and strain curves (σ-e) are depicted in Figure  11. Obviously, with the increase of axial stress, axial strain strain of the PVC tube decreased as the s f ' or ρ sv increased. In contrast, the influence of the b, h, ρ on ultimate strain of the PVC tube was not significant. For instance, the ultimate strain of the PVC tube increased by 2.1 % when the ρ increased from 1.45 % to 2.25 %. Compared to the PCR-BJ, the PRBJ did not show the strengthening stage, and the PVC tube buckled at earlier stage, as shown in Figure 11.e. Therefore, the PCRBJ showed better performance than the PRBJ.

Circumferential strain of CFRP strip
The relationships between the σ-e of CFRP strips is depicted in Figure 12. The stress-strain curves included three stages: elastic stage, crack developing stage, and strengthening stage. In the elastic stage, the strain of the CFRP strips increased linearly with an increase in stress. With the further increase of load, the strain of CFRP strips deviated linearly, and the PCRBJ came to the stage of fracture development. Subsequently, the longitudinal rein- Mechanical behaviour of PVC-CFRP confined concrete column with RC beam joint subjected to axial load forcement yielded. The PCRBJ entered the strengthening stage, and the strain of CFRP strips significantly increased. Finally, PCR-BJ reached ultimate strength and the PVC tube cracked. Obviously, the effects of all studied parameters on the strain of CFRP strips were similar to those of the PVC-CFRP tube, as shown in Figure 12. The increase in the s f ' or ρ sv decreased the ultimate strain of CFRP strips. The influence of the b, h, and ρ on CFRP strips strain was not obvious.

Strain of concrete in joint zone
The influence of the b, h, ρ and ρ sv, on longitudinal and transverse strain of concrete is depicted in Figure 13. Initially, the concrete strain in the joint zone increased linearly, and the PCRBJ was in the elastic stage. The concrete in the joint zone was always in a tension state in transverse direction. With an increase of b and decrease of h of the ring beam, the growth rate of the transverse and longitudinal strains of the concrete in joint zone decreased, and the longitudinal strain of the concrete in the joint zone gradually changed from compression to tension, as shown in Figure13.a and Figure13.b. This can be explained by the fact that the concrete around the joint zone received extrusion by the increased deformation of longitudinal concrete. The increase in b increased the confinement effect of concrete in the joint zone, and decreased the transverse deformation of concrete in the joint zone. However, the increase in h had adverse effect on the transverse and longitudinal strains of concrete in the joint zone. The growth rate of transverse strain of concrete in the joint zone decreased with an increase of ρ, while the effect of ρ on longitudinal strain was not obvious, as shown in Figure 13.c. This may come from the fact that an increase in ρ increased the confining effect of concrete on the joint core, and decreased the transverse deformation of concrete in the joint zone, which effectively confined the development of vertical cracks in the side of the joint zone. As the ρ sv increased, the growth rate of longitudinal strain of concrete in joint zone decreased, as shown in Figure 13.d. This was mainly because the confining effect of the concrete on the joint core increased, and longitudinal deformation of concrete in the joint zone decreased as the ρ sv increased, which significantly confined development of lateral cracks in the joint zone. The influence of the ρ sv on transverse strain in the joint zone was not obvious. Figure 14 shows the relationship between load and displacement of specimens. Obviously, consistent with the above description, the load-displacement curves consist of three stages (i.e., the elastic stage, the crack developing stage and the strengthening stage). Initially, the load-displacement curves of the PCRBJs were approximately linear showing an elastic behaviour of specimen. As the load increased, the load-displacement curves started to deviate from linearity, and the specimens entered the crack developing stage. As the load increased further, the confinement effect of PVC-CFRP on specimens increased significantly, and specimens entered the strengthening stage. Finally, the specimens reached the ultimate strength and the PVC tube cracked. As shown in Figure 14, the displacement of specimens decreased as the b, h or s f ' increased. This was mainly due to the fact that the confinement effect of ring beam on concrete core increased as the b and h increased. Additionally, the increase in

Modelling of PFCC
As recommended by Yu [12], the model for predicting the axial stress of PFCC is depicted in the following formulas, as shown in Figure 15.
0 ≤ e cz ≤ e t (1) Where, σ cz , e cz are the axial stress and axial strain of PVC-CFRP confined concrete column, respectively; E c is the Young's modulus of concrete; E 2 is the slope of the strengthened section; f R0 is the intercept of the straight line of PFCC; e t is the intersection of the parabola and the enhanced section line; e ccR is the axial ultimate strain of PFCC.

Modelling of the joint
A modified model for predicting the stress-strain relationships of joint was developed on the basis of the Mander's model and Yu's model [26][27], as shown in Eq. (3), and Figure 16.
Where, σ cj and e cj are the axial stress and axial strain of the joint zone, respectively; and e cc are the axial peak stress and strain of the joint zone, in which e co is the axial peak strain of unconfined concrete; h is the corrected parameter of peak strain; d is the internal diameter of PVC tube; r is the parameter that controlls the shape of the stress-strain curve; b h is the effect coefficient of height for the joint; b c is the effect coefficient of concrete; b 1 is the improvement factor for local compressive concrete; a is the reduction coefficient of indirect steel bar on concrete; f c stands for compressive strength of unconfined concrete; f c,i represents compressive strength of concrete after constraint by the i th annular reinforcement; l t,i is the characteristic value of stirrups. Mechanical behaviour of PVC-CFRP confined concrete column with RC beam joint subjected to axial load

Equilibrium equation
According to equilibrium equation and geometrical conditions, the following formulas can be established in this study. where whereby D z and D j are given Eq. (14) and (15): D j = e cj h (15) where, N is the of specimen, N z represents the ultimate strength of PFCC, and N j denotes the of the joint. D is the axial displacement of the specimen, D z stands for the axial displacement of PFCC, D j represents the axial displacement of the joint. l is the length of the column, h is the height of the ring beam, A c is the segmental area of concrete in PVC tube.

Calculation process
In order to estimate the load-displacement curve of the PCRBJ, the numerical analysis approach was proposed using MATLAB.
The following calculation steps were adopted: 1. input the initial equivalent strain value e cj,i (e cj,i = 0,01) of the joint zone and the estimated of the specimen, N e , which is given in reference [28]; 2. Determine the equivalent axial stress value σ cj,i according to Eq. (3) and Eq.(4); 3. Determine the value of N j,i according to Eq. (12) ; 4. Eestimate the of specimen N i = N j,i , and calculate the value of σ cz,i based on Eq. (10) and Eq. (11); 5. Estimate the value of e cz,i according to Eq. (1) and Eq. (2); 6. Predict the value of D z,i and D i based on Eq. (14) and Eq. (15) ; 7. Calculate the displacement of the specimen D i , using Eq. (13).
If the equilibrium condition N e -N i ≥ 0,1, is satisfied, output the load N i and displacement D i , then repeat the steps (2-7) ; otherwise terminate the computation.
8. Ooutput the load-displacement curves of the specimens.
More details can be found in the flow chart shown in Figure 17.
The load-displacement curves of specimens predicted by the numerical analysis approach and the measured experimental results are plotted and compared in Figure 18. The results show that the estimated values agree well with test results, which demonstrates that the numerical analysis approach is highly accurate.

Parametric studies
Parametric studies using the proposed numerical analysis approach were carried out to investigate the influences of different parameters on specimen behaviour, including the concrete strength grade of specimen, height of the column (H), width, height, the reinforcement ratio of ring beam, and CFRP strip spacing. Specimen A1 was employed as comparative reference. The load-displacement curves of the specimens with different parameters are shown in Figure 19. Compared to experimental results, the effects of b, h, ρ, and CFRP strip spacing of PCRBJ estimated by the parametric studies were similar, which further demonstrates accuracy of the numerical analysis approach. Figure 19 (a) illustrates the effects of the concrete strength grade of specimen, where the specimen with a higher concrete strength grade had a higher ultimate strength. This is mainly due to the fact that the compressive strength of the PCRBJ is mostly provided by concrete. Apparently, the increase in the height of column decreases the ultimate strength of specimen, as shown in Figure 19.b.

Conclusion
In this study, axial compression experiments were carried out for one PRBJ and nine PCRBJ, and numerical analysis was conducted in order to predict load-displacement curves of specimens. The following main conclusions were reached: -PRBJ is distinguished by the PVC tube buckling, and the PCRBJ is characterized by PVC tube cracking and CFRP strips fracture. -The ultimate strength of PCRBJ decreases with an increase in CFRP strip spacing. The height, width, stirrups ratio and reinforcement ratio, have a little effect on ultimate strength of specimens.
-The circumferential strain of CFRP strip, and axial strain of PVC tube, gradually increase with an increase in CFRP strip spacing. Other studied parameters have a small effect on the CFRP strip circumferential strain and PVC tube axial strain.
-The development rate of transverse and longitudinal strains of concrete in the joint zone decreases with an increase in width and decrease in height. The development rate of the transverse strain of concrete in joint zone decreases with an increase in reinforcement ratio. The development rate of longitudinal strain of concrete in joint zone decreases with an increase in stirrup ratio.
-The numerical analysis approach for predicting the loaddisplacement relationship of PCRBJ is proposed based on Mander's and Yu's models. The numerical method results are in good agreement with test data. Additionally, further parametric studies are to be carried out using this approach to numerical analysis.