Experimental analysis on the structural seismic behavior of steel frame-precast steel reinforced concrete (SRC) infill wall with lateral force resisting

2.1. Problem description and design principle

In this paper, the seismic model of eccentric structure of reinforced concrete frame beam-column structure is studied. Firstly, the finite element modeling of high-rise building is carried out. Before modeling, several principles of seismic model design are described. Under strong earthquake load, the seismic optimization of push over lateral eccentric structure of reinforced concrete frame beam-column structure should follow the following principles:

(1) In building seismic input, it can analyze the weak floors of the original building, and try not to transfer them. If they are transferred, new weak floors will be generated. When external factors occur, disasters cannot be prevented and controlled;

(2) In the optimization ratio of building seismic input and impact resistance, the needs of building use should be comprehensively considered, which should not only pursue the improvement of building performance, but also consider the cost control and impact resistance use of the building body;

(3) When the new support points are used for the seismic design of buildings, the seismic redistribution and stress of the system shall be considered.

Bracing is the first line of defense in the two lines of defense of lateral force resisting system, which bears most of the earthquake action compared with frame beams, frame columns and other components under the earthquake action. Under the horizontal earthquake action, the supporting members experience reciprocating axial tension and compression cycles, which dissipate a large amount of seismic energy input into the structure, so they can play the role of energy dissipation and vibration reduction in the structure, ensuring that the frame column and frame beam will not be damaged under the greater earthquake action. At the same time, under the action of strong earthquake, some lateral force resisting members of the structure will also be partially destroyed under strong earthquake, which makes the seismic action borne by the whole structure decrease with the decrease of the overall stiffness of the structure. Therefore, compared with bracing, the frame part composed of frame beam and frame column bears less residual seismic force, which avoids local serious damage or overall collapse of the structure under strong earthquake.

2.2. Finite element model of the structure of precast SRC wall with lateral force resisting

According to the above design principles, the shaking response seismic model design of reinforced concrete under strong earthquake load is carried out. The seismic material grades of reinforced concrete buildings are divided into four strength grades: C70, C60, C50 and C40. The coordinate system of the model is set as $XOY$, where the $X$ axis is 50 m and the $Y$ axis is 40 m. During the earthquake, the force transmitted by the building block is mainly borne by the horizontal tie bar on the upper surface of the bent cap/abutment cap. In the test, the sampling frequency of the data acquisition system is 1000 Hz, the MAXWELL seismic strong connection unit is used, and the coordinate system of the steel concrete structure model under the strong seismic load is set as $XOY$, where the $X$ axis is 50 m, the $Y$ axis is 40 m, and the seismic strength grade of the steel pipe and steel beam is Q345. In the design of high-rise buildings, the building structure studied in this paper is 60 floors, the height of ground floor is 5.4 m, and the 1~20 floors are the strength grade of the internal and external layers of the C60 wall structure, Floors 21~35 are C70 seismic strength grade. Based on the above description, the simulation analysis of the post-earthquake buckling relationship of steel reinforced concrete and the yield field effect of the specimen structure are analyzed, the mesh division of the concrete elastoplastic model and the boundary condition analysis are carried out, and the finite element model of the reinforced concrete eccentric structure under the strong earthquake load is obtained by using MAXWELL strong damping connection element and combining with the finite element analysis software, as shown in Fig. 1.

Fig. 1Finite element model of reinforced concrete eccentric structure under strong earthquake load

a) SED support steel frame

b) BRB steel frame

In Fig. 1, considering the influence of high temperature creep and transient thermal strain on the residual pushover lateral bearing capacity of reinforced concrete, the relationship between the mechanical properties of reinforced concrete, temperature and load during the post earthquake buckling relationship simulation of steel reinforced concrete is obtained.

However, under the horizontal reciprocating load of the earthquake, the internal force of the ordinary steel support changes repeatedly under the axial tension and axial compression, resulting in compression buckling. The whole structure loses the first line of defense against the earthquake after its buckling (the bearing capacity and stiffness of the support are significantly reduced). At the same time, the hysteretic curve shape of ordinary steel support under horizontal reciprocating load is not full, and its ability to consume seismic energy through supporting its own hysteretic is poor, so it cannot fully absorb the energy of ground motion after yielding under strong earthquake.

The influence of seismic sloshing response on the seismic performance index of SRCSSC-SB side node under strong earthquake is shown in Fig. 2.

Fig. 2Influence relationship of seismic performance indexes of SRCSSC-SB side joints

The same form of steel distribution is used to complete the segmentation of the three-dimensional nodes of the side columns in the middle layer of the special-shaped column frame. In the simplified positive overpressure pulse load part, the time history curve is simplified into two hypothetical triangular loads, and the load wave reduces to zero after a period of time (positive overpressure), thus generating positive overpressure pulse load and negative overpressure pulse load.

Through the above design, the shaking response finite element modeling of reinforced concrete eccentric structure under strong earthquake load is obtained, which lays the foundation for seismic model setting.

2.3. Mechanical analysis of concrete strength structure under strong earthquake load

On the basis of the above model framework, the mechanical analysis of concrete strength structure under strong earthquake load is carried out, and the solid phase extraction method is used to analyze the solid phase adsorption layer of structural members under the splitting load. The adsorption splitting load makes the response and failure of the building structure present certain probability characteristics. In order to accurately analyze the overpressure load model of steel beam building structure under the splitting load, the definitions of the following parameters are given: arrival time of seismic wave front $T_a$, peak to peak value of positive overpressure pulse load $P_r$, and the elastic modulus of transverse reinforcement of concrete mixture is expressed as:

where, $c_1$ and $c_2$ represent the static and residual tensile strength of the residual tensile strength of steel reinforced concrete after the earthquake, respectively, and $\mu$, $\nu$, ${\lambda }_1$ and ${\lambda }_2$ represent the weight coefficient proportion of each energy item in the process of concrete cracking, longitudinal reinforcement yielding, and concrete protection, all of which are constants greater than 0. The measured damage state of concrete eccentric structure under strong earthquake is linked with the engineering limit state, and the expressions of the reinforcement section area and the concrete section area are obtained as follows:

where, $w_i$ refers to the proportion of the bearing capacity of the building beam in the whole tensile strength force field analysis of concrete, and ${\sigma }_i$ refers to the overall sectional area of the eccentric structure under strong earthquake load. According to the above structural mechanics analysis relationship, the general software PKPM is used for structural design. The constraint function relationship of load control reinforcement between different seismic strengths $v_i$ and $v_j$ of high-rise frame buildings is as follows:

where, $EFT(v_{cp,i},p_q)$ represents the displacement increment of reinforced concrete section steel after yielding, $p_q$ represents the ultimate bearing capacity, and $v_i$ represents the horizontal loading load. Based on the measured hysteresis curve, the distribution relationship of the internal force of the reinforced concrete specimen section under the ultimate load in the seismic load is obtained as follows:

According to the Euler-Bernoulli beam theory, the distribution model for the longitudinal residual stress of the impact resistance of the reinforced concrete under the ultimate load is obtained, and the structural mechanics analysis of the reinforced concrete of the steel structure building under the strong seismic load is realized, based on which the seismic model is analyzed. The horizontal lateral force in the steel frame structure is mainly borne by the steel brace. The vertical bearing capacity of the main structure will not be reduced due to the yielding of the brace. Generally, the brace is more sensitive to the lateral deformation than the frame column, frame beam and other components under the horizontal seismic action. Therefore, the brace, as the main energy dissipation component in the structure, will yield first than the beam and column components under the seismic action. If appropriate supports can be adopted, so that more energy can be consumed by the supports under a given structure, more energy can be absorbed by the secondary structure, so as to reduce the damage of the main structure and protect the main structure under the earthquake. Finally, the energy based seismic design method can be embodied from the construction level.

3.1. Specimen structure and loading method

According to the above theoretical analysis, the anti-seismic model test design of reinforced concrete under strong earthquake load is carried out. The test specimen structure is selected as the steel distribution form of column section, the reinforced concrete structure form of horizontal load and column section, and the distance between column bending points is 1600 mm. In order to accurately simulate the load and tensile strength of nodes under actual earthquake, the anti-seismic layer section of strong concrete under earthquake action is H300 mm×150 mm×6 mm×10 mm, the thickness of concrete cover is 20 mm, the loading strength of concrete column ends distributed transversely is 45 N/mm², and the middle reinforcement of concrete is ϕ6@200. In order to accurately simulate the stress performance under earthquake, the loading profile of reinforced concrete specimen under strong earthquake load is shown in Fig. 3. The test specimen of the sacrificial section adopts Q345 square steel pipe with a thickness of 25 mm in the form of outer three side enclosure to ensure that the mechanical properties of the sacrificial section are consistent under tension and compression. The square steel pipe and the fixed end of the sacrificial section are connected by means of bolt connection (bolted connection plate in Fig. 3(a)). Shear failure of the connecting bolts in the bolted connection plate is the main means to control the sacrifice of the sacrificial section. In order to meet the requirement that the tensile bearing capacity of the sacrificial section of the square steel pipe is far greater than the shear bearing capacity of the bolt, the test uses two bolts to form a bolted connection plate, and its shear bearing capacity is calibrated through the test. The energy consuming section shall meet the requirements of continuous and efficient energy consumption after the sacrificial section is out of service. Therefore, the energy consuming section adopts LY225 steel as its core plate material, which is a buckling resistant support with excellent energy dissipation performance. In the subsequent study, the strength of sacrificial section and energy dissipation section can be achieved by modifying their corresponding section parameters and material strength.

Fig. 3Loading profile of reinforced concrete specimen under strong earthquake load

a) Reinforced concrete specimen loading frame diagram

b) Sacrificial energy-dissipation support specimen loading device

The mathematical model of initial damage and free degradation of concrete material after earthquake is established, and the elastic modulus of concrete mixture is obtained. The numerical analysis results of the residual tensile strength of the steel reinforced concrete buckling relationship after earthquake are obtained from the perspective of test analysis. In the load control stage, a statistical model of the splitting load is obtained by taking 5 kN as the load step. Based on this model, 77 groups of data measured from the splitting test are combined to form a splitting load database, and the average value, standard deviation and variation coefficient of each parameter of the splitting load at different proportional distances $Z$ are obtained.

The damage figure of bolt connecting plate obtained by the test is shown in Fig. 4. The test hysteresis curve is positive under pressure and negative under tension. Before the specimen reaches the peak bearing capacity, the sacrificial section and the energy dissipation section work together. When the specimen is compressed, the peak bearing capacity is 789 kN, and the displacement of the specimen is 2.45 mm; When the specimen is in tension, the peak bearing capacity is 865 kN, and the displacement of the specimen is 2.45 mm. After reaching the peak bearing capacity, the hysteresis curve enters the descending section, that is, the upper bolt and the lower bolt have shear failure successively in the first circle of 3 mm and the second circle of 3 mm, the bolt falls down and exits the work (as shown in Fig. 4(a) and 4(b)), and the sacrificial section exits from the stress.

Fig. 4Damage diagram of bolt connecting plate

a) Damage of upper bolt

b) Damage of lower bolts

According to curve fitting, the parameters of pushover lateral bearing strength of reinforced concrete eccentric structure under strong earthquake load are shown in Table 1.

Combined with the parameter settings given in Table 1, in the seismic model design and test, the load-displacement dual control loading system is adopted. The horizontal loading under strong earthquake is divided into two stages: load control and displacement control. The incremental decomposition of displacement and cyclic loading simulation are carried out. The mathematical analysis of the index parameters of seismic performance is carried out by using the column end loading method, until the load drops to 85 % of the limit value. The sloshing response coefficient in earthquake is calculated, and the seismic wave loads along different directions of beams in three directions are obtained through test acquisition, so as to realize the linear behavior simulation of sloshing response of reinforced concrete under seismic load. At this time, only BRB in the member as the energy dissipation section continues to work, and then the compression bearing capacity of the test piece decreases to 402 kN, and the tensile bearing capacity decreases to 384 kN, so the average strength of the energy dissipation section is 393 kN, the average strength of the sacrificial section is 434k N, and the strength ratio of the sacrificial section and the energy dissipation section is 5.3:4.7. When the load reaches 22 kN/m², the core area of the energy consuming section is obviously deformed and the load is stopped. The descending section of the hysteresis curve is obvious. In the later stage, only the energy consuming section is in full shape. The energy consuming section using BRB has good ductility and strong deformation capacity, so the energy dissipation effect of the sacrificial energy dissipation brace is good. In the later research, by adjusting the shear strength of the shear bolt of the bolted connection plate, as well as the parameters such as the material and section of the energy dissipation section, the peak load of the sacrificial section after it exits the work and the strength of the energy dissipation section after it exits the work can be controlled, which is used to study the optimal proportion of the sacrificial section and the energy dissipation section of the sacrificial energy dissipation support in the steel frame support structure.

3.2. Seismic strength analysis test

Under the above test device and test component loading mode, the seismic strength analysis test of reinforced concrete shaking response failure mode under strong earthquake load is carried out. This paper analyzes the eccentric structure model under strong earthquake action of reinforced concrete, arranges 4 longitudinal bars with diameter of 16 mm, stirrup spacing of 150 mm, and conducts simulated earthquake impact test. Through the simulated earthquake impact test, the finite element simulation of shaking response is realized. The damage process of test group members under strong earthquake load is shown in Fig. 5.

Fig. 5Concrete damage process under strong earthquake load

It can be seen from Fig. 5 that under strong earthquake load, concrete fragments are splashed around the column, generating eccentric process and shaking response, and sudden crushing brittle failure occurs. According to the Code for Seismic Design of Building Structures (GB50011-2010), a yield mechanism of strong column and weak beam is built, and pushover analysis and elastic-plastic time history analysis are carried out for concrete structures under strong earthquake load. According to the 10 storey frame beam-column element model structure, the stiffness method is used to simulate the yield surface constitutive relationship under sloshing response at the section level, and the axial force expression of the structural pushover section is obtained as follows:

The constitutive relationship of yield surface under sloshing response is simulated, and the axial force expression of structural pushover section is obtained as follows:

where, $N\left(x\right)$ represents the incremental constitutive deformation of the concrete bending yield surface under strong earthquake load, and $M\left(x\right)$ represents the spatial strength of the internal force of the section hierarchy. The assessment coefficient of integral yield mechanism for the structure of steel frame-precast SRC infill wall with lateral force resisting under strong earthquake load is obtained:

where, $V_{t1}$ represents the lateral bearing capacity of the nappe, and $V_{u1}$ represents the peak displacement of the characteristic period of the sloshing response. Under the strong earthquake load, the eccentricity of the concrete is calculated, and the maximum interlayer displacement $D_s$ is:

where, $D_r$ is the number of integral sections. Through the above analysis, considering the seismic input of SSI effect, the seismic analysis model of shaking response of reinforced concrete eccentric structures with integral yield mechanism under strong earthquakes is obtained.