Finite element analysis on the seismic behavior of side joint of Prefabricated Cage System in prefabricated concrete frame

Abstract

The Prefabricated Cage System (PCS) has the advantages of high bearing capacity and good ductility. Meanwhile, it is convenient for factory production and it is beneficial to the cost savings, construction period shortening. Side joint is the weak region of PCS concrete frame and has great influence on seismic behavior of the whole structure. Thus systematically study on the seismic behavior of PCS concrete side joint is necessary. This paper presents a finite element study on behavior of the side joint under seismic loading. In the finite element model, PCS concrete and the reinforced concrete (RC) is modeled by the solid element and fiber-beam element, respectively. The numerical results is compared with the experimental results and it is found that the results of model based on fiber-beam element is in better agreement with the experimental results than solid element model. In addition, the overall seismic behavior of the side joints in PCS concrete is better than that of the RC with the same strength.

Keywords

PCS concrete side joint / numerical simulation / fiber-beam element joint model / solid element joint model / seismic behavior

Introduction

Prefabricated Cage System (PCS) concrete structure is a new type of steel-concrete composite structure, it is formed by opening hole on steel tube and steel plates in longitudinal and transverse directions instead of the longitudinal rebars and stirrups. It can be prefabricated in the factory, and has the advantages of good ductility, high bearing capacity, fast construction, and convenience for industrial production. Prefabricated concrete frame structure is a concrete frame structure formed by connecting concrete precast members. The concrete members are prefabricated at the construction site or processing plant after curing to hoisting strength through mechanical lifting and certain connection means. Compared with the cast-in-place concrete frame, the prefabricated concrete frame needs less wet operation and shorter construction period and is able to achieve higher comprehensive benefit and better member quality. Therefore, this technique is conducive to the environment and social sustainable development.

PCS is a new structure under the background of industrial production which combines the prefabricated structure and PCS concrete structure and have the advantages of the these two structural forms. The side joint is a weak link in the earthquake resistance of reinforced concrete (RC) frame structure. This problem is more prominent in the prefabricated frame structure, and it is the focal point of the seismic research of the prefabricated structure [¹]. In this paper, the finite element method is used to study the seismic behavior of the side joints of PCS in prefabricated concrete frame. The research results will promote the application of PCS concrete structure in the prefabricated structure, and help to promote the development of residential industrialization.

Research status of PCS concrete

Research status of steel cage concrete in foreign countries

Sezen and Shamsai tested 16 small size PCS concrete columns and RC columns under ordinary concrete strength and analyzed the experimental data to conclude that PCS concrete columns are better in ductility and integrity than RC columns with equivalent strength [²].

Fisher researched the mechanical behavior of 6 beam column joints under low cyclic loading [³]. According to the different design of joints, it was divided into three groups. The bending strength of group C column was greater than that of beam, and the bending strength of group E is approximately equal. The bending strength of group B was greater than that of column bending strength, and the equivalent yield strength of each group of PCS was the same as that of RC. The corresponding cracking failure forms, hysteresis characteristics, skeleton curves, stiffness degradation, ductility performance, energy dissipation capacity, reinforcement strain, concrete strain, and other seismic properties were obtained.

Research status of steel cage concrete in China

Zeng et al. designed and conducted axial compression experiments of four PCS short concrete columns and one RC short concrete column [⁴]. The influence of different stirrup rates on the axial compression performance of PCS concrete short columns were compared and analyzed. The comparison results showed that the axial compression failure of the PCS concrete column was basically the same as that of the RC column, and the ductility of the PCS concrete column was better than that of the RC column.

Liang designed eight PCS concrete simple supported beams and two RC simple supported beams [⁵]. The main factors affecting the bending stiffness of the simple supported beam of the PCS concrete were compared and analyzed, including the different longitudinal reinforcement rates at the bottom and the connection spacings of different transverse steel plates. Under the same conditions of steel rate, the bending performances of PCS concret simple supported beam and RC simple supported beam were compared. The conclusion was that the elastic modulus, deformability, and ultimate bearing capacity of the simple supported beam of the PCS concrete beam were proportional to the steel rate of the bottom steel plate, the failure form of the simple supported beam of the PCS concrete was ductile failure.

ABAQUS numerical simulation analysis of side joint

Solid element simulation

Solid element simulation joint test

In this paper, the finite element model of two side joints (C-2-RC and C-2-PCS) of group C in Ref. [³] is modeled in ABAQUS. Among them, C-2-PCS is the concrete side joint member of PCS. C-2-RC is the RC side joint member, which is used as the contrast member of PCS concrete side joint C-2-PCS. The specimen is designed according to the design guide lines of ACI-318-05 [⁶], and considering the requirements of strong column and weak beam. Meanwhile, 1/3 scale model is adopted. The concrete size and reinforcement of the two side joint members are shown in Table 1. The compressive strength of concrete cylinder is about 22.88 MPa, which is similar to the C27 grade concrete in China. The property parameters are derived from the test results and shown in Table 2.

The constitutive model of concrete is based on the plastic damage model of ABAQUS. According to the measured strength of concrete in Ref. [³], the constitutive relation of concrete and the corresponding damage factors are calculated, as shown in Table 3.

According to the calculation, the expansion angle of the plastic damage model of concrete is 30°, the displacement of flow potential is 0.1, the ultimate strength ratio of biaxial compression to uniaxial compression is 1.16, the stress ratio of invariant is 0.667, and the viscosity coefficient is 0.005. The reinforcement constitutive model USteel02 in PQ-fiber is selected, the longitudinal and stirrups constitutive model in jointed beams and columns are shown in Table 4.

PCS is processed by laser cutting on the steel tube, and the opening size is obtained by the strength conversion of PCS, and the specific size is shown in Fig. 1. Among them, t = 6.35 mm, h= 4.98 mm, c= 13.21 mm, w= 37.08 mm, m= 26.42 mm.

According to the experimental conditions used in the side joints of group C in Ref. [³], the hinge joints are used at the upper and lower ends of the column. Meanwhile, axial force is applied at the end of the column and reciprocating load is applied at the end of the beam. In the CAE modeling process, the upper end and the lower end of the column are respectively coupled to the corresponding reference points. Then, the translational freedom of the reference point at the upper end of the column in X and Z directions and the rotational freedom in Y and Z directions are restrained, while the translational freedom of the reference point at the lower end of the column in X, Y, and Z directions and the rotational freedom in Y and Z directions are restrained (as shown in Fig. 2). The loading system of the specimen is controlled jointly by force and displacement, and the load is controlled as 0.1, 0.25, 0.5, 0.75, and 1 times of the yield load at each stage. After the member is yielded, Displacement is controlled by loading at the end of beam, loading at 2, 3, 4, 6, and 8 times, respectively. The loading cycle is carried out three times until the component is failed.

According to the joint size in Ref. [³], the finite element models of PCS concrete and RC side joints are established by ABAQUS software. Among them, the concrete is selected as a solid element, and the type is an eight-node reduced integral element C3D8R. Three-dimensional truss element T3D2 is used for all reinforcements and shell element is used for PCS. The reinforcement is usually discretized via a discrete, embedded or smeared model [⁷]. The element type is four-node reduced integral element S4R. The steel plate adopts the following hardening model of ABAQUS, and the PCS and the reinforced cage skeleton are embedded in the concrete by Embed method.

In ABAQUS, the division of the mesh has a great influence on the accuracy of the simulation results. Therefore, the reasonable size of mesh cannot only ensure the accuracy of the calculation results, but also reduce unnecessary calculation costs. The mesh seed size of concrete element is 50 mm, and the size of reinforcement is 25 mm. Since the shape of PCS is extremely irregular, the PCS finite element model should be divided first and then meshed. According to the actual size of the above members, the finite element model of the RC side joint and the concrete side joint of PCS is established respectively, as shown in Figs. 3(a) and 3(b).

Results and comparative analysis of solid element simulation joints

Based on the ABAQUS platform, the solid element model was used to simulate the concrete side joints of the RC and PCS concrete, and the hysteresis curves of C-2-RC and C-2-PCS were obtained, as shown in Fig. 4. Figure 5 shows the results of the hysteresis curve of C-2-RC and C-2-PCS. The final deformation stress nephograms of C-2-RC and C-2-PCS numerical simulation are shown in Figs. 6 and 7, respectively. Figure 8 shows the failure of the test for C-2-RC and C-2-PCS. Figures 9 and 10 show the comparison between the simulated values of C-2-RC and C-2-PCS and the experimental values of the skeleton line.

Figures 6 and 7 shows the final deformation stress cloud at end of the loading stage. Considering that failure of concrete is not modeled in the finite element model, peeling is believed to occur at region with large surface deformation. From the comparison of in Figs. 6 and 7 and the experimental failure diagram in Fig. 8(a), it is clear that the failure modes of the joints are roughly consistent. Reinforced concrete structures often undergo extensive cracking before failure, particle methods are very attractive for tracking dense failure patterns in Refs. [⁸,⁹].

From comparison of Figs. 4(a) and 9, the finite element hysteresis curve of RC side joint is basically consistent with the experimental curve and fits the skeleton line of hysteresis curve better. The skeleton line of the numerical simulation and the experimental results are inverted S type, which is clearly divided into three stages: elastic, elastic-plastic, and plastic. The ultimate bearing capacity is slightly lower than the experimental value, the stiffness degradation curves of numerical simulation results and the experimental results are approximately the same, and they decrease with the increase of displacement series. The numerical simulation also obtains a better descending section. When the beam end displacement is loaded into 6 times yield displacement, the cycle is loaded into the second time, the hysteresis curve begins to decrease and that is basically consistent with the experimental result. By comparing and analyzing the finite element values and experimental values of PCS concrete side joint in Fig. 4(b) and the skeleton line in Fig. 10, the similar conclusions can be obtained.

In summary, based on the results of finite element analysis of C-2-RC and C-2-PCS, it can be seen that the finite element hysteresis loop of the PCS concrete joint is more full and the skeleton line is higher and the seismic performance is better than that of the RC joint.

Fiber element joint simulation

Simulation of C-2-RC RC exterior joints

In this section, the joint based on the fiber-beam element model simulation is the RC side joint C-2-RC in Ref. [³]. The element size, reinforcement and material parameters are presented in section 3.1.1. For arrangement of rebars in joint members, the rebar keyword is added in ABAQUS INP file to insert the rebar in the beam element. An enhanced cross-section with different material composition is formed, which essentially increases the number of integral points on the cross-section of the beam element. In this paper, the constraint effect of stirrups on core concrete is taken into account by increasing the strength of core concrete.

Kent-Scott-Park constrained concrete constitutive model is used for fiber-beam element concrete constitutive model beyond the core area of joints [¹⁰]. For C-2-RC RC side joint member, the concrete strength grade corresponds to the concrete grade of C27 strength grade in China [¹¹]. According to Chinese concrete structure design code-GB50010-2010 [¹²], the corresponding concrete axial compressive strength standard value is obtained as the unconstrained concrete axial compressive strength in Kent-Scott-Park constrained concrete constitutive. The calculation results are shown in Table 5, the parameters of the constrained concrete are shown in Table 6.

In the core region of the joint, bearing capacity of the diagonal bar is calculated by softened tension and compression model of the deformation element, and then the corresponding stress is obtained by dividing the effective area. In Ref. [¹³], it is considered that the stirrup and longitudinal reinforcement of the core area of the nodule have a strong constraint on the diagonal bar, so the peak intensity and strain of the diagonal bar have been greatly improved. Therefore, Mander-constrained concrete constitutive [¹⁴] can be used to describe the stress-strain relationship of diagonal bars. At the same time, the compressive strength of the concrete in the core area will decreases with the occurrence of cracks in the direction of the parallel diagonal bar. Therefore, the compressive strength of the concrete needs to be reduced. In this paper, the stress of the baroclinic bar is calculated by the softened tension and compression bar should correspond to the compressive strength of the concrete in Ref. [¹³]. It is necessary to calculate the compressive strength of the uncompressed concrete in the diagonal bar to the corresponding peak strain of the Mander-constrained concrete. The corresponding constitutive results of the diagonal bar are obtained in Table 7.

The setting of boundary conditions can refer to Section 3.1.1 of this chapter.

Simulation of C-2-PCS steel cage concrete side joints

In this section, the joint based on the fiber-beam element model simulation is PCS concrete side joint C-2-PCS in Ref. [³]. And the hysteresis curve, skeleton line and stiffness degradation curve are compared with the experimental results. The element size and material parameters are presented in Section 3.1.1. The finite element model of C-2-PCS is established by referring to the above-mentioned RC fiber element. It can be seen from the foregoing, the constitutive relationship of constraint concrete are different between the fiber beam element model of PCS concrete joint and the RC. In this paper, based on the constrained concrete constitutive relationship of the RC side joint member C-2-RC, the peak strength of the PCS confined concrete is obtained by multiplying the amplification factor K_pcs, and then the corresponding peak strain is obtained by substituting the peak strength into the confined concrete constitutive.

Kent-Scott-Park constrained concrete constitutive model is used for fiber-beam element concrete constitutive model beyond the core region of joints of PCS concrete [¹⁰], Mander confined concrete constitutive model is used for diagonal bar constitutive of core region [¹⁴]. Based on the concrete constitutive model of RC joint C-2-RC, which is calculated in Section 3.2.1 of this chapter, the constrained concrete constitutive of PCS concrete joint C-2-PCS can be obtained by multiplying the enhancement factor Kpcs. The application of load and boundary conditions of fiber-beam element model of PCS concrete is similar to that of the RC joint member C-2-RC, the specific procedures refer to Section 3.1.1 of this chapter.

Based on the ABAQUS platform, the C-2-PCS fiber-beam element joint model of PCS concrete is tested, and the K_pcs = 1.25. The concrete constitutive of fiber element in outside core region of the PCS joint is shown in Table 8 and the constitutive of the diagonal bar is shown in Table 9. The fiber model of the side joint is shown in Fig. 11.

Fiber element simulation joints results and comparative analysis

The hysteresis curves of the fiber-beam element joint of the RC C-2-RC and PCS concrete C-2-PCS is shown in Figs. 12 and 13. The comparison of numerical simulation skeleton line and stiffness degradation curve of side joint are shown in Figs. 14 and 15.

It can be seen from Figs. 12 and 13 that the finite element results obtained from the joint model based on the fiber-beam element are approximately consistent with the experimental results. The simulation results have higher overall agreement, which can satisfy the engineering requirements and verify the effectiveness of the numerical simulation method for the fiber-beam joint model of PCS concrete. From Fig. 14, the skeleton lines of the two joints are basically coincident. Subsequently, the C-2-RC nonlinear strengthen stage obviously becomes much slower and shorter, and reaches the peak load quickly. The C-2-PCS skeleton line is obviously higher than C-2-RC, which indicates that the bearing capacity and ductility of side joint of PCS concrete are better. From Fig. 15, the stiffness degradation of both joints is faster at the initial stage of loading, and the stiffness degradation is slower and exhibits a certain nonlinearity in the middle and late loading stages. During the whole loading process, the stiffness degradation of C-2-PCS is relatively slow, which indicates the side joint of PCS concrete has better seismic performance.

In summary, compared with the simulated values of the hysteresis curves of the RC side joint C-2-RC and PCS concrete side joint C-2-PCS calculated by the solid element model, the numerical results calculated by the fiber-beam joint model are related to experimental results in terms of initial stiffness and have a better improvement in height of the skeleton line and stiffness degeneration law.

Conclusions

In this paper, finite element analysis on PCS concrete side joint was carried out by solid element model and fiber-beam element model respectively and the numerical results are compared with the experimental results. The numerical results of the joints under seismic loading obtained from the fiber-beam element model are basically consistent with the experimental results. And better agreement is achieved between results from fiber-beam element model and experimental results than the numerical simulation results based on the solid element model. From the research, the effectiveness of fiber-beam element joint model in simulating PCS concrete joints is verified, including the rationality of element selection and material constitutive relationship. It’s also proved that the overall seismic behavior of PCS concrete exterior joint is better than that of the RC side joint obtained by equivalent strength conversion.

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