There were 9 rectangular RC columns in this test, the overall length of which was 800 mm. The two end corbels had a cross section of 120 mm×250 mm and were 200 mm long. The tested specimens were subjected to eccentric compression with 35 mm of load eccentricity, and the parameters are shown in Table 1. Each tested specimen had a cross section of 120 mm×150 mm in the test region. The longitudinal reinforcement consisted of four HRB400 steel bars, and the shear reinforcement consisted of 6.5-mm-diameter HPB300 stirrups spaced at 100 mm in the test region, as shown in Figure 1. For convenient application of the eccentric load, the two ends of the columns were designed as corbel shapes, at the steel bars on the tensile side were bent into the corbel shape and used as oblique compression reinforcement. A steel plate with a thickness of 10 mm was placed at the end of the column to prevent partial crushing, and 3 layers of 100-mm-wide carbon fiber cloth were attached at two end corbels.

Before the reinforcement, the surface of the test region of the RC column was chiseled within the height range of 400 mm. In order to prevent the occurrence of stress concentration in the column edges, a corner radius of 20 mm was then applied to the specimens. The whole reinforcing process of the specimen was as follows: First, clean and wet the surface of the column. Second, apply fine-grained concrete to the surface of the column, with a thickness of approximately 2 mm. Third, lay the textile horizontally along the test region of RC column with a lap length of 200 mm (the available anchorage length of the FRCM should exceed the minimum development length of 152 mm according to the ACI 549.4R-13 (18)). Fourth, after the first matrix layer is spread on the surface of the RC column, apply the fine-grained concrete to the surface of the textile. If multiple layers of textile are needed, repeat the above steps. Finally, cure the textile reinforced mortar for the standard curing age. The application of TRM is shown in Figure 3.

In this experiment, a 7,000 kN pressure tester was used for loading. The test setup is provided in Figure 1; displacement sensors were placed at 1/4 height, 1/2 height, and 3/4 height and the ends of the column to measure the lateral deflection due to the eccentric compression applied to the column. To measure the change law of the section strain during the test process, 3 concrete strain gauges were uniformly spaced in the middle part of the column, and 2 concrete strain gauges were placed in the middle part of the other two sides. In addition, the strain gauges were arranged on the surface of the longitudinal steel bar in the column to measure the development of the strain during the test process. The grid sizes of the steel strain gauges and the concrete strain gauges are 2 mm×1 mm and 100 mm×1 mm respectively, and the resistance values and sensitivity coefficients of the two types of gauges are the same: 119.7±0.1 Ω and 2.08%±1%, respectively.

In this test, the specimens were measured under static loading conditions and positioned according to geometric alignment. Preloading was designed and implemented before the start of the test to not only eliminate the influence of the bearing offset but also ensure normal operation of the measuring instruments and the test equipment. A multistage loading was adopted for the test, and the loading rate was 10 kN/min. When the load was 90% of the theoretical bearing capacity, the load of each stage was increased by less than 5% of the limit load. After the completion of each stage, the loading was maintained for 10 minutes. The relevant data cannot be recorded until the readings of the test instruments are stable.

A summary of test results is shown in Table 6. The characteristic failure modes of the specimens are shown in Figure 4, there are two types of failure modes. For column C0, which was not strengthened with TRM, there were no obvious changes on the surface of the specimen in the early stage. When approaching its ultimate load, there were a number of subtle longitudinal cracks near the side with the vertical load. After continuous loading of column C0, the cracks developed rapidly. Several transverse cracks appeared on the section far away from the vertical pressure. At the ultimate load, C0 failed suddenly by crushing the concrete near the compression side, with compression steel buckling to the outside, as shown in Figure 4. There was no obvious indication of potential failure before the column was destroyed due to brittle damage. For a reinforced column, the deformation was similar to that of C0 in the previous period. When the load approached 90% of the ultimate load, a small number of longitudinal cracks appeared on one side of the vertical load. As the load continued to increase, cracks developed quickly. When the failure load was reached, the stress concentration at the column corner ruptured the textile. The failure of the columns strengthened with one and two textile layers first appeared in the mid-height of the column due to the fracture of the fibres. Then, the separation of the TRM from the core concrete occurred in the middle of the column near the compression side of the axial force, and the inner concrete was crushed and bent outward, as shown in Figure 4. On the tensile side, obvious transverse cracks appeared on the surface of the TRM in the middle of the column, almost cutting through the cross section of the column; this was the first type of destruction. In addition, the TRM was destroyed at the upper part of column C3 and C4; this was the second type of destruction.

After reinforcement, the failure of the column was delayed, and the ductility was enhanced. When the column was strengthened with 3 layers, the damage of the TRM occurred in the upper part of the column, and the transverse cracks on the tension side moved upward. The reason for this phenomenon was that the increase in the number of reinforcement layer improves the ring hoop action of TRM during the compression process. Therefore, the unreinforced part of the corbel was relatively weak, and the deformation was too large, causing damage to the upper part of the column and crushing the internal concrete. However, the ratio of longitudinal reinforcement and PVA short-cut fiber volume fraction had little influence on the failure mode of TRM-confined columns.

The load-strain curves of the representative specimens C0, C2 and C5 are shown in Figure 5. In general, most of the cross section of a concrete column was in a state of compression, while a small part was in a state of tension. Most likely, at the 130 mm section, the strain was zero. After reinforcement with TRM, the strain of the cross section linearly increased with the load and basically conformed to the plane section assumption. According to Figure 5, the longitudinal strain of column C2 was smaller than that of the column without strengthening measures under the same load. This shows that the TRM can better restrain the deformation of the eccentric column and improve its bearing capacity. From a comparison with the load-strain curves of C2, it can be found that the longitudinal strain of C5 with a high reinforcement ratio is smaller under the same load, indicating that the ultimate bearing capacity of C5 was improved.

The limitation of compressed elements’ transverse strains is achieved by FRP and TRM wrapping, so the basic principle for both systems was similar (19). On the basis of the model of concrete confined with carbon fiber sheet, which has been studied and proven to be effective (20), the constraint model of the TRM is obtained analogously. Referring to the restraining action of rectangular columns strengthened with FRCM (18), the regional confinement of TRM is shown in Figure 7. Because of the influence of the section size on the textile layer in TRM, the constraint on the rectangular section in the compression process is uneven, and an effectively confined region and a weakly confined region form.

Considering the weakening of the textile layer due to the section shape and column corner and referring to the simplified method in reference (18), an equivalent circle is derived in order to conveniently calculate the formula. That is, the diagonal length of the rectangular section is the diameter of the equivalent circle. Additionally, the formula considers the weakening caused by longitudinal and lateral non-uniform constraints, and the reduction coefficient k_f of the tensile strength of the textile layers is introduced by the stress concentration at the column corner. The lateral confining strength (21) can be converted into [1]

where f_l is the equivalent lateral confining strength of the textile layer;

k_e is the sectional influence coefficient;

k_s is the weakening coefficient considering longitudinal non-uniform constraint;

k_f is the reduction coefficient of the tensile strength of the textile layers due to the stress concentration at the column corner;

k_f is the ultimate tensile strength of the textile layer;

k_f is the thickness of the textile layer (t_f=0.17mm in this test);

h is the height of the rectangular section;

b is the width of the rectangular section.

(1) sectional influence coefficient k_e

According to references (18, 21), the modified coefficient of the section shape is the ratio of the area of the effectively confined region to the entire area constrained by the fiber, that is [2],

where r_c is the corner radius of the rectangular section;

A_g is the gross cross-sectional area of the rectangular section;

r_g is the reinforcement ratio.

(2) weakening coefficient k_s

The presence of the fiber bundles spacing will result in uneven longitudinal restraint. Compared with the continuous wrapping of the fiber sheet, the lateral confining strength is reduced to some extent, that is [3],

where s is the spacing of the weft fiber bundles.

(3) reduction coefficient k_f of the tensile strength of textile layers due to the stress concentration at the column corner.

It is noted in the literature (22) that the stress concentration at the corner section of the column leads to the weakening of the tensile strength of the textile layer, which is related to the corner radius and height of the rectangular section, that is [4],

It is noted that the confinement of the textile layer around the concrete is similar to the hoop action of stirrups. Referring to the results of a concrete cylinder under three-directional pressure, a rectangular column is still subjected to the compressive stress around it. The compressive strength of the confined concrete f_c is calculated by equation [5].

where f_c0 is the compressive strength of the unconfined concrete.

The calculating diagram for the column strengthened with TRM is shown in Figure 8. According to the equilibrium condition of force and moment, it can be obtained that

where x is the compression zone height of concrete, and when x > h, x = h;

A_s is the area of tension steel, Asˊ is the area of compression steel;

α₁ is the ratio of the stress value to the f_c in the equivalent rectangular stress block in the compression zone and is 1.0 (23);

β₁ is the ratio of the height of the compression zone in the equivalent rectangular stress block to the height of neutral axis assumed by the plane section assumption, and the value is 0.8 (23);

N_u is the load-bearing ultimate capacity of the concrete column under a small eccentrically load;

f_y is the design value of the tensile strength of tension steel, fyˊ is the design value of compressive strength of compression steel;

σ_s is the stress of the steel bar on the tensile side far from the vertical load;

ξ is the relative height of the compression zone, that is, ξ=x / h₀, and ξ_b is relative-boundary compressive region’s height;

h₀ is the sectional effective height, h₀ = h – a_s;

e is the distance from the vertical load point to the resultant force point of the tensile reinforcement, e_i is the initial eccentricity;

a_s is the distance from the resultant force point of the tensile reinforcement to the edge of the tensile area; and asˊ is the distance from the resultant force point of the compression reinforcement to the edge of the compression area.

Combined with the above formula, the theoretical bearing capacity value of the column can be calculated by the following steps:

In this chapter, the effect of PVA fiber on the loading capacity of TRM-strengthened columns is very small, so its influence is not considered. According to the derived calculation formula, Table 7 gives the calculation values of the bearing capacity. The proposed model was also used to verify the experimental results (24) for FRCM confined concrete columns. It can be seen that the error becomes larger as the number of reinforcement layers increases, which is due to the failure to make full use of the tensile strength of the fibers. Besides, column C6, with a 14-mm-diameter longitudinal reinforcement, did not completely yield during the test. In the calculation, the strength of the longitudinal reinforcement of the compression side is taken as the yield strength, so the calculated value is larger. The relative error is within 10% for the remaining reinforced specimens, showing the accuracy of the model for designing TRM-strengthened concrete columns.