#### Abstract

Reactive powder concrete (RPC) was confined by the circular steel tube to obtain the required ductility. The axial compression test results of 139 columns from different scholars were collated and compared to study the axial compression and bearing capacity of a reactive powder concrete-filled circular steel tube, of which the confining coefficient is 0.057–2.312 and the RPC strength is 76.6–178.2 MPa. Load-displacement curves have been categorized into four stages: (1) elastic; (2) elastic-plastic; (3) descending; and (4) strengthening. The failure mode can be divided into three types according to the different confining coefficients as (1) wall buckling; (2) diagonal shear; and (3) drum-shaped. The confining coefficient, core RPC strength, steel fiber volume, steel tube *D*/*t* ratio, and loading mode on the ultimate bearing capacity were analyzed. The results showed the confining coefficient to be the main factor affecting ultimate bearing capacity. The equation for determining ultimate bearing capacity was established based on the limit equilibrium theory, with the lateral confining coefficient of RPC (*k*) determined to be 2.86, less than that of normal concrete at 4.1. Based on the experimental analysis results and China’s “Design and Construction Code for Concrete-Filled Steel Tube Structure” (CECS 28-2012), the design proposal for an RPC-filled steel tube was recommended.

#### 1. Overview of Experiments

Reactive powder concrete (RPC) is the direction for further development of high-strength concrete (HSC) and ultrahigh performance concrete (UHPC), with a relatively new type of cement-based composite material successfully developed by Richard in 1993, which has ultrahigh strength, good volume stability, and excellent durability [1, 2]. The science behind the development of RPC is mature, and many studies have focused on its mechanical properties for further broad application in engineering [3–5]. However, RPC is very dense and uniform since it does not contain coarse aggregate; therefore, the pinning effect provided by coarse aggregates in normal concrete (NC) is weakened or even absent in RPC, and most RPCs are “explosive” and are destroyed by top-down longitudinal splitting after compression [5]. Measures to decrease brittleness and increase ductility of RPC are used for structures with ductile seismic performance requirements. RPC has been used in concrete-filled steel tubes (RPCFTs) [6]. The steel tube restrains transverse deformation of the core RPC to allow the superior compressive performance of RPC to be fully utilized and its ductility to meet the requirements of the column design. The successful application of steel tube RPC in the construction of the Sherbrooke Bridge, Quebec, Canada, demonstrated its superior mechanical properties and economic benefits [7]. Although both RPC and NC are cement-based composite materials, their water/binder ratios, composition of raw materials, and mechanical properties differ considerably [8]. Therefore, the theory and method for calculating the ultimate bearing capacity of CFT cannot be directly applied to RPCFT.

The present study aimed at analyzing the axial compressive mechanical behavior and ultimate bearing capacity of RPCFTs. Many studies have focused on the experimental determination of the axial compression performance and ultimate bearing capacity of RPCFTs. The present study collated the experimental results of past studies on the axial compression performance of 139 RPCFTs during 2003 to 2016, including Meng Shiqiang [8], Zhang Jing [9], Yang Wusheng [10], Wu Yanhai [11], Feng Jianwen [12], Yan Zhigang [13], Luo Hua [14], Yang Guojing [15], and Jian Wei [16]. Among the studies, tube diameter, wall thickness, and strength varying between 102 mm and 273 mm, 1 mm and 12 mm, and 210 MPa and 425 MPa, respectively, were considered to cause variation of the steel tube confining coefficient () in the range of 0.057–2.312. RPC strengths in the range of 76.6 MPa–178.2 MPa were affected by the RPC water/binder ratio (0.16–0.26), RPC steel fiber content (0%–2%), and curing methods (standard curing, 90°C steam curing, and curing in an autoclaved reactor with a maximum temperature and pressure of 200°C and 1.3 MPa, respectively). The main parameters are shown in Table 1.

#### 2. Test Results

##### 2.1. Load-Displacement Relationship

A review of the 139 RPCFT axially compressed experiments conducted in past studies found that the vertical stress and strain of the steel tube and core RPC gradually increased with increasing axial load due to pressure, and the core RPC was compressed in three directions because of constraints placed by the steel tube. The RPC peak strain under pressure varied from 0.0035 to 0.008 and increased by 3% to 32%, respectively. The ultimate bearing capacity of RPCFT increased between 2% and 58% over the sum of the bearing capacity of the steel tube and RPC, and brittle failure of the core RPC was not found with effective restraint, plastic deformability of the components was gradually reduced, and the integrity of samples with larger confining coefficients remained after sizeable deformations of 5%, thereby demonstrating excellent ductility. Figure 1 shows the load-displacement curve of the specimen. The mechanical characteristics of RPCFT could be divided into four stages: (1) elasticity; (2) elastic-plastic; (3) descending; and (4) strengthening.

###### 2.1.1. Elastic Stage (OA)

Vertical deformation of the steel tube and RPC increased proportionally with increased load, and no significant deformation of the steel tube surface was observed. The proportional ultimate load of RPCFT ranged from 85% to 95% of the ultimate bearing capacity, whereas the value of CFT was 70%, smaller than that of RPCFT, thereby explaining the disproportionately high strength of RPC in relation to NC. RPC had a uniform and denser internal structure, with mechanical properties closer to elastic material. RPC remained elastic at the ultimate load of 80–95% with no significant volume expansion and maintained Poisson’s ratio at 0.2–0.4. CFT at 40% of the ultimate load experienced rapid expansion of the cracks in the interface between aggregate and cementite, with sharp increases in deformation and significant expansion of volume, resulting in the appearance of the Lüder J slip line. Figure 2 compares the longitudinal and transverse strains between RPC and NC.

###### 2.1.2. Elastic-Plastic Stage (AB)

With the increasing axial load, yielding of the steel tube occurred due to compression and redistribution of internal force between RPC and steel tube. Thus, there were sharp increases in RPC compressive stress and internal microcracks emerged. In addition, there was continuous expansion of the widths and lengths of cracks, along with increases in transverse volume expansion deformation. The overall stiffness was degraded and the load-deformation curve showed a significant nonlinearity. Since RPC does not contain coarse aggregates, the fracture surface was relatively smooth, the steel fiber at the fracture surface was almost broken, and cracks were filled with powdery material. After the steel tube was extruded, the surface was partially convex, the rust began to peel off, and the Lüder J slip line appeared.

###### 2.1.3. Descending Stage (BC)

At the attainment of the ultimate load, a large amount of internal energy accumulated inside the core of RPC due to compression deformation being suddenly released. Internal cracks rapidly expanded to form a fracture surface. When the steel fiber was almost broken at the fracture surface, the strain energy was rapidly released and the sample broke into pieces. A sound of a sudden splitting failure could then be heard, indicating a load-deformation curve on the decline in the bearing capacity (BC). The sudden drop of bearing capacity involved a process where strain energy was rapidly released, which was dependent on the confining coefficient. RPCFT with a small confining coefficient experienced a small confining force provided by the steel tube. After reaching the ultimate load, the drop in longitudinal stress in the steel tube was higher than that of the restraining effect on the RPC strength provided by the steel tube. There was a marked drop in bearing capacity, and the slope ratio of the descending segment became almost equal to the RPC. An increasing confining coefficient resulted in a significant increase in the confinement effect of the steel tube on the core RPC, and the load-deformation curve showed that the load amplitude did not descend obviously or no obvious decrease after reaching the ultimate bearing capacity was evident. Taking specimens XG1-1 and G1 of Wu Yanhai [11] as examples, the confining coefficient of XG1-1 was small; thus, the steel tube had little restraining effect on RPC and the specimen emitted a bursting sound after reaching the ultimate load. The bearing capacity then drastically dropped and the remaining bearing capacity became only 65% of the ultimate load. The specimen showed significant brittle failure, whereas G1 had a large confining coefficient, the steel tube had a strong constraint on the RPC and the ultimate load bearing capacity descended slowly. The remaining bearing capacity reached as high as 95% of the ultimate load, the curve of the descending section was gentle, and the specimen underwent ductile failure.

###### 2.1.4. Strengthening Stage (CD)

The steel tube entered the strengthening stage after the plastic flow stage under a sufficiently thick steel tube wall, and the strong restraint provided by the steel tube continued to slow down the decline in the core RPC bearing capacity. The entire test bearing capacity entered a rebound state when the increased bearing capacity of the steel tube was sufficient to offset the decline of the core RPC bearing capacity, with the amplitude of its rebound dependent on the confining coefficient of the specimen itself. The larger the confining coefficient, the greater the magnitude of the rebound. Yang Wusheng [10] obtained a similar conclusion when analyzing these test results, namely, under a confining coefficient < 0.4, the bearing capacity of the specimen did not rebound and the curve was flat or continued to decrease, whereas when the bearing capacity was >1.3, the curve enhancement segment could experience sustainable growth.

##### 2.2. Failure Mode

It was found that the failure modes of the 139 RPCFTs could be categorized into three types, as showed in Figure 3.

**(a)**

**(b)**

###### 2.2.1. Steel Tube Buckling Failure

The CFT research results showed that under a large steel tube diameter-thickness ratio (*D/t*), the straight steel tube underwent a “bowstring effect” under the axial pressure, and the specimen formed a “string” buckling instability by brittleness failure when the ultimate bearing capacity was reached. The CFT design specification of every country provides the *D/t* limit, and China’s “Technical Specification for CFT” (GB50936-2014) stipulates *D/t* to be: . However, Zhang Jing [9] studied A1-1 specimens with a diameter of 125 mm and a wall thickness of 1 mm, and Yang Wusheng [10] studied specimens of a diameter of 104 mm and a wall thickness of 1 mm, with *D/t* of 125 and 104, respectively, thereby meeting the requirements of the technical specifications for CFT. However, “string” buckling instability remained, mainly because deformation of NC increased rapidly reaching 40% of the ultimate load, and the volume of the core concrete expanded significantly, thereby playing a certain role in supporting the steel tube wall. The transverse strain and volume expansion of RPCFT did not markedly change before reaching the ultimate load. The core concrete cannot support or restrain the tube wall. Therefore, it is recommended that the *D/t* ratio of RPCFT be determined in accordance with the “Code for Design and Construction of CFT” (CECS 28 : 90) as .

###### 2.2.2. Oblique Shear Failure

The internal energy accumulated in the core RPC was suddenly released to form a fracture surface after the RPC reached the ultimate strength. The fracture surface generated a misalignment and formed two wedge blocks above and below, which were able to slide along the shear surface, resulting in local convexity of the steel tube. However, the increase in the confining coefficient resulted in a strengthening of the restraining effect of the steel tube, an increased restriction of sliding, a slowing down of the development speed of the internal shear crack, and a decrease in the bearing capacity of the steel tube RPC. Yang Wusheng [10] observed a significant shear slip plane after cutting the specimen with shear failure. An inclination angle of 25°–31° was evident; the steel fiber at the shear failure surface was removed, and powdery particles were observed at the RPC contact surface.

###### 2.2.3. Drum-Shaped Failure

Under a large confining coefficient, although the upper and lower wedge blocks of core RPC were able to slide to form a shear slip plane, slide was prevented because the wedge block was placed under a large lateral constraint. The core RPC formed a second shear plane in the opposite direction, thereby increasing the transverse deformation of the specimen to form a partially roughened portion, eventually forming a multifold shear failure, i.e., drum bending in the position of the top and bottom roofs of the bearing capacity. The RPC was severely crushed and could be peeled off by hand. For NC, Zhang Sumei [17] found that CFT with a confining coefficient of approximately 0.8 would suffer from drum-type damage. The characteristics of RPC material and the results of 139 RPCFT showed that the critical confining coefficient is suggested to occur in oblique shear failure and waist drum failure.

#### 3. Analysis of Factors Affecting RPCFT Axial Compression Bearing Capacity

##### 3.1. Confining Coefficient

The confining coefficient () is a comprehensive index that reflects the extent to which the core RPC is constrained by the steel tube and is the key factor affecting the ultimate bearing capacity and failure mode of the RPCFT. The fitting curve between and by the test results of 87 RPCFT without steel fibers in Table 1 is shown in Figure 4.

Figure 4 shows that is proportional to , and the proportional factor is 1.394; however, the factors for HSC and NC were 1.8 and 2, respectively. The factor decreased with increasing strength due to the weakened confining coefficients of HSC and RPC. This was mainly because when NC was loaded to 40% of the ultimate load, expansion of microcracks in the transition zone between cement stone and coarse aggregate caused discontinuity of the displacement field, resulting in a rapid increase of the transverse deformation coefficient of the concrete. The large sum exceededs Poisson’s ratio of the steel tube, and a large confining force was formed after the steel tube was extruded. The water-binder ratio was smaller, and the internal structure was denser for HSC or RPC. RPC was in particular close to an elastic material. Poisson’s ratio of RPC did not change much before the RPC was loaded 80%–90% of the ultimate load. The transversal strain and vertical strain ratio developed proportionally. The lateral deformation coefficient of RPC struggled to exceed Poisson’s ratio of the steel tube, and the confining force of the steel tube was difficult to initiate:

##### 3.2. Diameter to Thickness Ratio of Steel Tube

When applying a fixed steel tube outer diameter (D), the confining coefficient increased with increasing steel tube thickness (t) and the ultimate bearing capacity continued to increase. Figures 5 and 6 show the fit of the relationship between *D/t* and from the results of Yang Guojing [15] and Wu Yanhai [11], respectively. From the figures, it is evident that, under a relatively small *D/t*, the change in *D/t* had a greater influence on the ultimate bearing capacity, whereas under a larger *D/t*, variation of *D/t* had little effect on the ultimate bearing capacity, and the critical *D/t* ratio was 25–30.

##### 3.3. Core RPC Strength

Figure 7 shows the fitting relationship between and by Yang Guojing [15] using the results of 20 RPCFT with an RPC strength of 96.6 MPa. Figure 8 shows the above relationship from the study of Zhang Jing [9] and Wu Yanhai [11] with RPC strengths of 167.1 MPa and 172.1 MPa, respectively. Evident from Figures 7 and 8 is that the scale factor between and under a strength of 96.6 MPa is 1.43 and under the strengths of 167.1 MPa and 172.2 MPa is 1.37. Therefore, with an increase of RPC strength, the effect of the steel tube on RPC restraint was further weakened, and its proportional coefficient was reduced from 1.43 to 1.37. However, the change was merely 4.2%, which can be neglected for practical applications.

##### 3.4. Steel Fiber Content in RPC

Table 2 shows the effect of steel fiber content on the ultimate bearing capacity of RPCFT. It is evident from Table 2 that, for a steel fiber content of 1.2%, RPC axial compressive strength increased by 15%, and the total axial compressive strength of RPC and steel tube should be increased by approximately 10%, whereas the actual ultimate load of the test samples were increased by an almost negligible amount of 0.7% to 3.8%. The axial compressive strength of RPC increased by 25% under a steel fiber content of 2%. Considering the contribution of RPC to strength, the theoretical ultimate capacity of RPCFT resulting from an increase of the axial compressive strength of RPC increased by approximately 14%, whereas the ultimate load bearing capacity of the actual test increased by merely from 2.4% to 3.8%. Almost no effect on the ultimate bearing capacity could be expected. Therefore, although the steel fiber content could increase the axial compressive strength of RPC, the contribution to the ultimate bearing capacity of RPCFT was negligible, consistent with the conclusion of Dallaier [18], mainly because of differences in the action mechanism between steel fibers and steel tubes in RPC. The main role of steel fiber was to withstand some of the tensile stress placed on the RPC principal stress section, thereby increasing the strength of RPC. However, the core RPC confined by the steel tube was compressed in three directions, and the principal compressive stress failure was found when the ultimate load reached. Therefore, the addition of steel fiber to steel tube RPC did not contribute considerably to the bearing capacity. To reduce costs, the addition of steel fiber to RPCFT is not recommended.

##### 3.5. Loading Method

The most commonly used loading methods for CFT as shown in Figure 9 include full-section load and core-loaded concrete. Table 3 compares the ultimate bearing capacity from the study of Yang Guojing [15] under different loading methods. The differences in bearing capacities under both loading modes were within 5%. It can be considered that the loading method was applied to the mechanical properties of the axially compressed short columns of steel tube RPC. The impact could be regarded as negligible.

**(a)**

**(b)**

#### 4. Analysis of RPCFT-Bearing Capacity Based on Limit Equilibrium Theory

Methods of determining the ultimate bearing capacity of CFT can be divided into two categories: (1) numerical analysis methods and (2) limit analysis methods [19]. A numerical analysis method analyzes the material stress-strain relationship to simulate the load history and process, thereby determining the force and deformation characteristics of the entire process from elasticity to failure. The limit analysis method is based on the force balance relationship evident when components are in a limit bearing capacity state. This method can calculate the ultimate bearing capacity and is independent of the loading history and the deformation process. At present, research on the stress-strain relation of RPC remains inadequate, and no constitutive relationship is available to form a widely accepted constraint for RPC. Thus, this method does not meet the conditions for numerical analysis. Therefore, the limit analysis method was used to explore the ultimate bearing capacity of steel RPCFT axially compressed short columns.

The parameters are shown in Figure 10 so that the RPC core area and steel tube area are

According to the internal force balance, the relationship between annular tension and confining force of the steel tube is

Synthesis (equations (2)–(4)) can be obtained:

The steel tube conforms to the von Mises yield criterion, which is

Equation (6) can be solved as follows:

The study of confined concrete showed that there is a linear relationship between confined concrete strength and confining force:

Therefore,

When *N* reached the ultimate bearing capacity:

That is, under equation (10), when the ultimate bearing capacity was reached, the confining force was:

Substituting confining force into equation (9):replaced in (12),

#### 5. Calculation of Bearing Capacity of RPCFT

By referring to the “Technical Specifications for Concrete-Filled Steel Tubular Structures” (GB50936-2014) and the analysis results presented in Figure 4 and Equation (13), it is recommended that the value of RPC should be 1.394. The equation for calculating the bearing capacity of RPCFT is

#### 6. Conclusion

Circular steel tube-confined RPC is an effective method to increase ductility, and the following conclusions could be drawn from the results obtained for the analyzes:(1)Results for a total of 139 RPCFT axial compression columns showed that the load-displacement curves can be divided into four stages: (1) elastic; (2) elastic-plastic; (3) descending; and (4) strengthening. Moreover, the elastic limit could reach the ultimate limit of 90%. The failure modes could be divided into three categories: (1) wall buckling instability failure; (2) oblique shear failure; and (3) waist drum damage. It was suggested that the *D/t* ratio of RPCFT should be kept below to avoid buckling and brittle failure of the tube wall. Oblique shear failure and drum-type damage could both result in ductile failure, and it was recommended that the critical confining coefficient be set to 1.(2)The larger the confining coefficient, the greater the increase in bearing capacity of RPCFT. The core RPC strength, loading method, and steel fiber content of RPC had little effect on the RPC bearing capacity of the steel tube. To reduce cost, it was recommended that no steel fiber be added to the steel tube RPC.(3)Steel tube has less of a constraining effect on RPC than NC and HSC. The increase in the coefficient of steel tube-constrained RPC was 1.394. The equation for the ultimate bearing capacity of the steel tube RPC was proposed in reference to the “Technical Specifications for Concrete-Filled Steel Tube Structure” (GB50936-2014).

#### Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

#### Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

#### Acknowledgments

The author also would like to acknowledge the support provided by the National Natural Science Foundation of China (no. 51678190) for partially funding this research. All staff and laboratory technicians are thanked for their kind assistance during the research.