Keywords

1 Introduction

In recent years, with the development of the economy, a large amount of infrastructure construction has consumed a huge amount of steel. The rapid development of steel smelting technology has laid the foundation for the research and promotion of high-strength steel bars. High strength steel bars can effectively reduce the use of steel, reduce costs, save resources, and maintain stable mechanical properties. Developed countries such as Europe and America have used over 95% of 400-600MPa steel bars, and countries such as Germany, Japan, and Australia have also achieved an adoption rate of 80–90% for steel bars above 400MPa [1, 2].

In 1996, Lloyd and other scholars conducted a study on the eccentric compression performance of 400MPa reinforced concrete specimens, focusing on the influence of factors such as longitudinal strength and stirrup strength on the stress performance of specimens. Based on the experimental results, a constitutive model of high-strength concrete and a calculation theory of high-strength steel reinforced concrete eccentric compression columns were established. The results indicate that the calculation theory is reasonable and the calculation results are relatively accurate [3].

In 2005, Tan and other scholars conducted axial and eccentric compression tests on 30 high-strength concrete column specimens, focusing on the influence of concrete strength and volume stirrup ratio on the mechanical performance of the specimens. The stirrup strength is divided into two types: 455MPa and 636MPa, and longitudinal bar strength is 595MPa. Based on the experimental results, researchers have proposed a reliable, simple, and fast calculation method for obtaining concrete stress [4].

From 2004 to 2009, Liu lixin and other scholars carried out a series of studies on HRB500 reinforced concrete members. The results show that the stress characteristics of HRB500 reinforced concrete members are similar to those of ordinary reinforced concrete members, and can improve the performance in terms of deflection and bearing capacity compared with ordinary reinforced concrete members [5,6,7,8,9]. Li hongyan carried out eccentric compression test on 500MPa high-strength reinforced concrete members to verify whether the domestic concrete code at that time was applicable to the calculation of concrete members in the test. The results show that the failure characteristics of 500MPa reinforced concrete members under eccentric compression are basically similar to those of ordinary concrete members, and the bearing capacity of the specimens calculated in accordance with design code for concrete structure (GB50010-2002) [10] is in good agreement with the measured bearing capacity, It is proved that the calculation method of ultimate bearing capacity of eccentrically loaded members specified in design code for concrete structure (GB50010-2002) [10] is suitable for 500MPa reinforced concrete members [11].

At present, the reinforcement above HRB600 level has not been included in design code for concrete structure (GB50010-2010) [12] in China, and the research on the specimens of high-strength reinforcement combined with high-strength concrete is relatively small. For the reinforcement with strength of 600MPa and above, Luo Shaohua conducted eccentric compression test research on 11 600MPa reinforced concrete columns, and proposed the design value of 600MPa reinforcement [13]; Zhang Jianwei and other scholars have studied the bending, axial compression and eccentric compression properties of HRB600 reinforced high-strength concrete specimens [14,15,16]; Rong Xian and other scholars carried out a series of tests on the axial compression performance, eccentric compression performance, bond anchorage, etc. of HRB600 and HRB600E reinforced high-strength concrete specimens [17,18,19,20]; Liu Chengtao studied the axial compression and eccentric compression performance of HRB600 reinforced concrete columns, focused on the applicability of crack calculation formulas in different national codes, and combined with finite element analysis, studied the influence of Longitudinal bar strength, reinforcement ratio and other factors. The results showed that the specimens with 600MPa high-strength reinforced concrete had better performance in terms of ultimate bearing capacity, deflection and so on, The failure characteristics are similar to those of ordinary reinforced concrete specimens [21]. Li Zhipeng studied the axial compression and eccentric compression properties of HRB635 reinforced high-strength concrete specimens [22]; Lin Wei and other scholars have studied the eccentric compression performance and bearing capacity of HRB635 grade hot-rolled ribbed high-strength reinforced concrete short columns, and combined with finite element analysis, put forward a simplified calculation formula for evaluating the eccentric compression ultimate bearing capacity of HRB635 grade hot-rolled ribbed high-strength reinforced concrete short columns [23].

At present, there is no research on the mechanical properties of 650MPa steel bars in China. Based on the eccentric compression performance test of HRB650E reinforced high-strength concrete columns, this paper uses ABAQUS to carry out finite element analysis, and compares the test results with the experimental results to study the variation of eccentric compression performance of specimens with the parameters such as steel bar strength, concrete strength, stirrup ratio and eccentricity.

2 Experimental Overview

2.1 Experimental Design

Five HRB650E reinforced high-strength concrete columns and two HRB400E reinforced high-strength concrete columns were designed, including two small eccentric compression specimens and five large eccentric compression specimens. The number and main parameters of the test piece is presented in Table 1, and the size and reinforcement arrangement of the specimens is presented in Fig. 1. The size of each specimen is the same, and the concrete grade, eccentricity, longitudinal bar strength, reinforcement ratio and eccentricity are the main variation parameters of the specimen.

Table 1. The main design parameters of eccentric compression specimens.
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Fig. 1.
figure 1

Specimen size and reinforcement layout.

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2.2 Test Setting and Loading Scheme

Figure 2 shows the layout rules for strain measuring points. The middle section of the test piece is segmented into three layers, denoted as A, B, and C, with a 250 mm spacing between them. For the longitudinal bar, four strain measuring points are positioned in a clockwise manner at the corners of each layer. Additionally, four strain measuring points are situated at the four sides of the outer stirrup, as well as at the midpoint of the two long sides of the inner stirrup, resulting in a total of eight strain measuring points for the stirrup. Regarding the longitudinal bar, Z-1 and Z-4 are situated on the compression side, while Z-2 and Z-3 are located on the tension side.

Symmetrically arranged at the middle height of the compression side and two sides of the concrete outer surface of the specimen, with a 125 mm spacing, are three strain measuring points. Furthermore, two strain measuring points are symmetrically arranged on the tension surface, with a 250 mm spacing. In total, there are 11 concrete strain measuring points.

Fig. 2.
figure 2

Number of strain gauges for longitudinal bars and stirrups of the specimens.

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For displacement measurement, five displacement meters are symmetrically arranged along the height direction at the tensile side of the central test piece, with a 200 mm spacing between them to measure the deflection of the test piece.

The test employs a 40000 kN multifunctional loading system for loading, with the vertical load value being directly read by the loading system. The loading scheme is formulated in accordance with the standard for test methods of concrete structures (GB50152-2012) [24]. Prior to the test, a steel base plate is placed at the lower support, and the test piece is lifted using a crane. After lifting, a steel base plate with the same size is placed on the upper part of the test piece. During the lifting and placing of the steel base plate, the eccentric position of the test piece and the center of the steel base plate are positioned on the connecting line between the center of the upper and lower supports. The laser broom is used to ensure that the connecting line is vertical.

Before the formal start of the test, preloading is carried out to clear the gap between the test piece and the loading part. After the formal loading commences, the large bias test piece is loaded to 500 kN, while the small bias test piece is loaded to 1000 kN. Subsequently, the load of each level is increased by 500 kN, with a load holding time of 60 s. After loading to approximately 50% of the ultimate bearing capacity, the load of each level of the large bias test piece is reduced to 300 kN, while the load of each level of the small bias test piece is reduced to 500 kN, and the load holding time is increased to 90 s. Upon reaching the peak value, the test switches to displacement control. The experiment is terminated when the bearing capacity drops to 85% of the peak value or when the component is severely damaged.

2.3 Mechanical Properties of Steel Bars and Concrete

The mechanical properties of reinforcement measured by the tensile test is presented in Table 2.Three grades of concrete (C50, C55, and C60) were used in the test. Simultaneously with making the test pieces, three samples of each grade were cast with the same concrete, resulting in a total of nine standard cube concrete test pieces, consistent with the curing conditions of the test pieces. The test is conducted in accordance with the standard for test methods for mechanical properties of ordinary concrete (GB50081-2002) [25], and the average compressive strength \({\text{f}}_{{{\text{cu}}}}^{{ 0}}\) of concrete is measured. Based on the formula (1) in Sect. 4.1 of the article description of design code for concrete structure (GB50010-2010) [12], the standard value of compressive strength \({\text{f}}_{{\text{cu,k}}}\), the standard value of axial compressive strength \({\text{f}}_{\text{ck}}\), and the standard value of axial compressive strength \({\text{f}}_{\text{c}}\) of cubic concrete are calculated. The mechanical properties of concrete materials is presented in Table 3. The actual measured concrete strength in the test is different from the expected, and the measured compressive strength of C55 and C60 is relatively small.

$$ \left\{ {\begin{array}{*{20}c} {f_{{\text{cu,k}}} = f_{{{\text{cu}}}}^{{0}} { - 1}{\text{.645}}\sigma } \\ {f_{{{\text{ck}}}} = {0}{\text{.88}}\alpha_{{{\text{c1}}}} \alpha_{{{\text{c2}}}} f_{{\text{cu,k}}} } \\ {f_{{\text{c}}} = f_{{{\text{ck}}}} {/1}{\text{.4}}} \\ \end{array} } \right. $$
(1)
Table 2. Mechanical properties of reinforced bars.
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Table 3. Mechanical properties of concrete.
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3 Establishment of Finite Element Model

3.1 Constitutive Relation

Constitutive Relation of Reinforcement.

The constitutive relation of reinforcement adopts the bilinear model. The two straight lines are used to represent the elastic section and yield strengthening section of the reinforcement.

Constitutive Relation of Concrete.

The CDP model is used in this simulation test, and the parameters in the CDP model are determined by using the concrete constitutive relationship provided in code for design of concrete structures (GB50010-2010) [12]. The stress-strain curve of the model can be determined according to the following formula:

$$ \begin{array}{*{20}c} {\sigma = (1 - d_{{\text{t}}} )E_{{\text{c}}} \varepsilon } \\ {d_{{\text{t}}} = \left\{ {\begin{array}{*{20}c} {1 - \rho_{{\text{t}}} [1.2 - 0.2x^{5} ]} & {x \le 1} \\ {1 - \frac{{\rho_{{\text{t}}} }}{{\alpha_{{\text{t}}} (x - 1)^{1.7} + x}}} & {x > 1} \\ \end{array} } \right.} \\ {x = \frac{\varepsilon }{{\varepsilon_{{\text{t,r}}} }}} \\ {\rho_{{\text{t}}} { = }\frac{{f_{{{\text{t}},{\text{r}}}} }}{{E_{{\text{c}}} \varepsilon_{{\text{t,r}}} }}} \\ \end{array} $$
(2)

\({\text{d}}_{\text{t}}\) is the uniaxial damage evolution parameter of concrete, \(\upalpha _{{\text{t}}}\) is the parameter value of the descending section of the concrete uniaxial tensile stress-strain curve, \({\text{f}}_{\text{t,r}}\) is the representative value of uniaxial tensile strength of concrete, \(\upvarepsilon _{{\text{t,r}}}\) is the peak tensile strain of concrete corresponding to the representative value \({\text{f}}_{\text{t,r}}\) of uniaxial tensile strength.

$$ \begin{array}{*{20}c} {\sigma = (1 - d_{{\text{c}}} )E_{{\text{c}}} \varepsilon } \\ {d_{{\text{t}}} = \left\{ {\begin{array}{*{20}c} {1 - \frac{{\rho_{{\text{c}}} n}}{{n - 1 + x^{n} }}} & {x \le 1} \\ {1 - \frac{{\rho_{{\text{c}}} }}{{\alpha_{{\text{c}}} (x - 1)^{{2}} + x}}} & {x > 1} \\ \end{array} } \right.} \\ {\rho_{{\text{c}}} { = }\frac{{f_{{{\text{c}},{\text{r}}}} }}{{E_{{\text{c}}} \varepsilon_{{\text{c,r}}} }}} \\ {n = \frac{{E_{{\text{c}}} \varepsilon_{{\text{c,r}}} }}{{E_{{\text{c}}} \varepsilon_{{\text{c,r}}} - f_{{{\text{c}},{\text{r}}}} }}} \\ {x = \frac{\varepsilon }{{\varepsilon_{{\text{c,r}}} }}} \\ \end{array} $$
(3)

\({\text{d}}_{{\text{c}}}\) is the damage evolution parameter of concrete under uniaxial compression, \(\upalpha _{{\text{c}}}\) is the parameter value of the descending section of the stress-strain curve of concrete under uniaxial compression, \({\text{f}}_{{\text{c,r}}}\) is the representative value of uniaxial compressive strength of concrete, \(\upvarepsilon _{{\text{c,r}}}\) is the peak compression strain of concrete corresponding to the representative value \({\text{f}}_{{\text{c,r}}}\) of uniaxial compression strength.

The symbols and parameter values provided in the specifications align with their intended meaning. The measured values are substituted into the formula to determine the constitutive relationship, which is subsequently input into ABAQUS for analysis.

3.2 Modeling

The numerical simulation of the quasi-static test was conducted using ABAQUS with a finite element analysis model, and the results were compared with the experimental test results. The finite element model of the reinforced high-strength concrete column was established, as depicted in Fig. 3. The concrete column was represented using solid elements, while the reinforcement cage was modeled using truss elements. Additionally, a steel pad was included at the top area of the concrete column to match the actual test setup. The boundary condition at the bottom surface of the column constrained the displacement in XYZ directions. Vertical displacement was applied at a specific location on the top surface to simulate the loading conditions.

Fig. 3.
figure 3

The model of concrete columns and steel reinforcement cage.

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4 Numeric Simulation Results and Analysis

4.1 Comparison Between Simulation Results and Test Results

The load-displacement curve obtained from ABAQUS numerical simulation is illustrated in Fig. 4. Using the test piece DP3 as a case study, a comparison between the finite element simulation results and the observed failure behavior is depicted in Fig. 5. It can be observed that the Mises stress in the upper section of the mid-span is notably high. This high Mises stress is near the compressive strength of the concrete when it is crushed, aligning with the observed behavior in the actual tests. Upon reaching the peak load, a significant concrete collapse initially occurs in the upper section of the mid-span, subsequently spreading to both sides of the lower section. A comparison between the peak load simulation result, \({\text{N}}_{\text{m}}\), and the actual peak load result, \({\text{N}}_{\text{u}}\), is illustrated in Table 4. \({\text{N}}_{{\text{m}}}\) is calculated using the measured data. The average ratio of \({\text{N}}_{\text{u}}\)/\({\text{N}}_{\text{m}}\) is 1.001, with a variance of 0.085. This suggests a strong agreement between the simulation and the actual results.

Fig. 4.
figure 4

Load-displacement curve.

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Fig. 5.
figure 5

Comparison between simulation results and experimental results of specimen failure phenomenon using DP3 as an example.

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Table 4. Comparison between the actual value of peak load \({\text{N}}_{\text{u}}\) and the simulated value of peak load \({\text{N}}_{\text{m}}\)
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4.2 The Influence of Concrete Strength

In addition, ABAQUS was utilized to simulate the conditions outlined in Table 5, which involved concrete grades C70 and C80, represented as test pieces KZ1 and KZ2. The concrete strength, derived from the standard value of concrete compressive strength specified in the Code for Design of Concrete Structures (GB50010-2010) [12], was integrated into the CDP model for calculation purposes, resulting in the determination of the concrete constitutive relationship. The load-displacement curve obtained from ABAQUS is illustrated in Fig. 6. A comparison between the actual and simulated peak load values for test pieces KZ1, KZ2, and DP2 to DP4 is provided in Table 5. It is important to note that the differences in concrete strength among DP2, DP3, and DP4 are not significant. However, upon the inclusion of KZ1 and KZ2, the data presented in Table 6 unequivocally demonstrates that increasing the concrete strength enhances the load-bearing capacity of the concrete columns.

Fig. 6.
figure 6

Load-displacement curve of KZ1 and KZ2.

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Table 5. Design parameters of specimens with concrete of C70 and C80.
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Table 6. Comparison of peak loads of KZ1 and KZ2 with DP2-4
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5 Conclusion

The simulation results for the bearing capacity of HRB650E reinforced high-strength concrete columns closely align with experimental findings, demonstrating a strong fitting effect.

The finite element analysis model of HRB650E reinforced high strength concrete column is established by using ABAQUS. Numerical simulation analysis was conducted using test data, and the results were compared with experimental findings. The analysis revealed that increasing concrete strength extends the working condition and significantly enhances the bearing capacity of HRB650E reinforced high-strength concrete columns, as evidenced by the comparison of experimental and simulated data.