Cyclic behavior of prefabricated reinforced concrete frame with infill slit shear walls

Abstract

A composite structural system consisting of prefabricated reinforced concrete frame with infill slit shear walls (PRCFW), with good ductility, is a new type of earthquake resistant structure. Pseudo-static tests were performed to evaluate the seismic behavior of the PRCFW system. Two one-bay, two-story PRCFW specimens were both built at one-half scale. Additional computational research is also conducted to enhance the nonlinear analytical capabilities for this system. Combined with the concrete damaged plastic (CDP) model provided by finite element program ABAQUS and the constitutive model of concrete proposed by Chinese code, the damage process of the PRCFW structure under cyclic load is simulated. The simulated results show a good agreement with the test data, the dynamic behavior of the PRCFW system can be simulated sufficiently accurate and efficient to provide useful design information. The experimental and numerical study show that this system has the potential to offer good ductility and energy absorption capacity to dissipate input energy, and stiffness adequate for controlling drift for buildings located in earthquake-prone regions.

Keywords

slit shear wall / constitutive model / cyclic / seismic / damage

Introduction

Due to the large lateral stiffness, ordinary reinforced concrete (RC) shear wall has a poor deformation capacity. When suffering from severe earthquake, the structure tends to form concentrated crack zone at the bottom of the wall, and the width of the major crack is usually very large, which causes the final brittle failure in the form of shear failure or crush [ 1, 2], thus reducing the energy dissipation capacity of the structure. To overcome the above disadvantages, a particular RC shear wall, with good properties of seismic energy dissipation, called slit shear wall, was patented by Professor K. Muto [ 3] in Japan. Compared with the solid shear wall, the slit shear wall has a lower lateral stiffness, whose main deformation is bending deformation under the action of high intensity earthquakes, and the structure turns into a flexible one. Initial energy dissipation was achieved by the micro cracks distribution on a large surface in slit walls [ 3, 4]. Korean researchers have proposed another type of slit wall, used especially for reinforced concrete structures, in which strips are anchored in beams [ 5]. Compared with slit walls made of prefabricated strips, these walls have a better ductility, but inconvenient for construction. Taking account of the advantages of prefabricated RC structures, such as speedy erection, high project quality, energy conservation and environmental protection [ 6], and the advantages of the slit shear wall in good ductility, PRCFW system has a brilliant application prospect.

Compared with the cast-in situ structures, connections between the members of fabricated structures have a more essential influence on the overall performance and seismic behavior. For example, during the 1994 Northridge earthquake, some large-space precast concrete structures were severely destroyed, mainly for the reason that joint connections between the members failed fast during the earthquake to cause the whole collapse of the structures. This paper presents an experimental study of the cyclic behavior of the PRCFW system, overall structural performance and local performance of the designed connections such as beam-column joints, frame-infill wall shear connectors were inspected. To study this composite system thoroughly, additional computational research is also conducted to enhance the nonlinear analytical capabilities for this system. Based on the cyclic load test and corroborating analysis, the research reported herein elucidates many new aspects of the seismic behavior of the PRCFW system, including the strength, deformation capacity, stiffness deterioration, hysteretic behavior and damage evolution law, etc.

Experimental study

Experimental program

Specimen design

Two one-bay, two-story PRCFW test specimen were designed at one-half scale, labeled as PRCFW-1 and PRCFW-2 respectively. Figure 1 shows an elevation of the specimen with the loading system. Each story was 2.4 m wide and 1.4 m high. The frame consisted of prefabricated RC beams with 150 mm × 250 mm section and prefabricated RC columns with 300 mm × 300 mm section. The strong axes of all members were oriented in the plane of the infill shear wall. Beams and columns were spliced together by Cast-in situ joints using high-slump concrete. The tensile and compressive longitudinal reinforcement at the beam ends was 6Ф10 and 4Ф10 respectively, which extended through the Cast-in situ joints and intersected with 12Ф12+ 4Ф8 longitudinal bars extended from the prefabricated columns. Longitudinal bars extended from the columns were connected by the steel connecting sleeves and tied by Ф6@50 compound stirrups. The RC infill slit wall was designed based on the Technical specification for steel structure of tall buildings [ 7], The RC infill wall was 100 mm thick, and was divided into strips by seven slits with 500-mm high and 5-mm wide, the distance between slits was 250 mm. The RC infill wall was reinforced by two layers of steel reinforcing mat, the boundary strips were reinforced with 2Ф8 longitudinal bars in each side, the inside strips were reinforced with 1Ф8+ 1Ф6 longitudinal bars in each side. The distributed reinforcement was Ф6 bars at 75 mm spacing in both the horizontal and the vertical directions. The material properties of each member are reported in Table 1.

The infill wall was connected to the frame using shear connectors made of Q345B killed steel. Figure 2 shows the details of the typical shear connectors M1~M3 used in the specimen. They consisted of steel plates with 10 mm thick and equal angle steels (L36 × 5). Optimum performance of the PRCFW system depends on the transfer of stresses between the frame members and infill walls [ 8]. The shear connectors were designed to transfer 100% of the design lateral shear force. For each shear connector, a 15% reduction in calculated shear strength (as per Ref. [ 8]) was assumed to account for cyclic loading. The column feet were embedded in the foundation beam with rebar splicing by grout-filled coupling sleeves.

Test procedure

The vertical loads were applied on the top of the column by using vertical hydraulic actuators with 10000-kN loading capacity (Fig. 1). The design axial compression ratios of frame columns of PRCFW-1 and PRCFW-2 specimens were 0.2 and 0.3, the applied vertical loads were 1000 and 1500 kN accordingly.

A loading beam consisting of two steel plates and six steel rods was attached tightly to the top beam of the specimen, cyclic loads were applied on the loading beam center by using hydraulic actuators. The cyclic loading history acting on PRCFW system was determined according to the Specification of testing methods for earthquake resistant building [ 9] through consideration of the deformation characteristics of the PRCFW system. The loading program was dominated by forces in elastic stage and by drifts in elastic-plastic stage. At the first stage, lateral load was controlled by the force loading pattern, with 50 kN increment for each loading step including one cycle until the specimen yield. At the second stage, lateral load was changed into the displacement loading pattern, with the yield displacement as increment for each loading step including three cycles until failure.

Experimental results

In contrast to the quick failure of the solid infill shear wall [ 8], the slit infill shear walls failed more gradually. Figure 3 shows the relationship of lateral load-total drift of the specimen (the total drift was measured between the top of the foundation beams and top girders). Compared to the solid shear wall, the slit shear wall had a lower lateral stiffness, whose main deformation was bending deformation so that during the damage propagation, the strength and lateral stiffness of the PRCFW system decrease slowly.

Figure 4 shows the final failure and damage patterns of PRCFW specimens. It is observed from the test that the PRCFW system exhibited three stages of performance during the loading before the final failure.

At the first stage, the specimen was in the range of elasticity, the lateral stiffness of the system was high, the slit shear wall acted like solid shear wall. Minor cracks were observed at the tips of the prefabricated silts when the lateral loading reached at about 600 kN.

As the horizontal load was further increased, vertical macro-cracks along the prefabricated silts formed, and at the same time, the width of horizontal cracks at the top and bottom of the wall strips and diagonal cracks in the wall were very small before the peak load, this was the second elastic-plastic stage. At this stage, the slit shear wall, which has small aspect ratio, can be considered as several ‘wall columns’ with large aspect ratio, whose main deformation is bending deformation, the bearing capacity of the system decreased slowly and the deformability was greatly improved. In this sense, the PRCFW system exhibits good ductility.

After the peak load, the specimen entered the last stage. At this stage, horizontal cracks at the top and bottom of the wall strips and diagonal cracks in the wall corner developed quickly to form the macro main shearing crack, which caused the PRCFW system turning into the equivalent frame-compression struts system. The girder ends suffered from large shear force and bending moment at the same time, the girders should be designed to have the capacity to resist the shear forces induced by the equivalent compression strut from brittle failure.

The damage propagation of the two PRCFW specimens was similar, the difference is that bending plastic hinge occurred at the bottom beam ends of PRCFW-1 specimen before failure, as shown in Fig. 5(a), while brittle shear failure occurred at the top beam ends of PRCFW-2 specimen at the last stage, as shown in Fig. 5(b).

To evaluate the ductility of the specimen, the following ductility index was used (see Fig. 6): μ=Δ_u/Δ_y, where Δ_u is defined as the drift at which the degraded post-peak strength reaches 85% of the maximum strength, and Δ_y corresponds to the displacement at which significant yielding of the structure occurs (i.e., a pseudo-yield point). The pseudo-yield point in this idealized bilinear approximation of the structural response can be determined by graphic method as shown in Fig. 6. The pseudo-yield displacement Δ_y of PRCFW-1 specimen is 0.6% and −0.61% respectively in the positive and negative direction; and the corresponding ultimate drift Δ_u is 2.44% and −2.28%. The ductility index μ of PRCFW-1 then can be deduced as 4.07 in the positive and 3.74 in the negative. The ductility index of PRCFW-2 specimen can be deduced in the same way, with the value of 3.02 in the positive and 3.16 in the negative. The PRCFW-1 specimen exhibits a better ductility than PRCFW-2 specimen for the reason that bending failure occurred in the girder ends of PRCFW-1 to form the plastic hinge instead of brittle shear failure occurred in the girder ends of PRCFW-2 at the final loading stage.

Inspection after the test revealed that the rigid shear connectors performed well during the test, without obvious plastic deformation or anchorage failure. Crack and damage mainly occurred in the girders and infills, columns with different design axial compression ratios were largely intact, only a few bending cracks occurred at the column foot of PRCFW-1 specimen, as shown in Fig. 5(c). Cast-in situ joints also remained basically intact, only a few micro cracks appeared on the middle beam-column joint of PRCFW-2, as shown in Fig. 5(d). It meets the “weak beam-strong column” principle and the design prospective of dissipating earthquake energy by the damage of infills.

Numerical analysis

There is a necessity to possess a tool for use in conducting parametric studies of PRCFW system response to earthquake hazards. On this account, a finite element (FE) method based on ABAQUS program was proposed to simulate the damage process of the PRCFW structure under cyclic load.

Figure 7 shows the FE model of PRCFW system, using the modeling method of discrete reinforced concrete model. Concrete was modeled by solid element C3D8R, steel reinforcement and steel shear connector were modeled by truss element T3D2 and shell element S4R respectively. The steel elements can be directly embedded into the concrete elements in ABAQUS so that different types of elements do not have to use the same nodes for connection.

Constitutive model

The concrete damaged plastic (CDP) model was used to simulate the cyclic constitutive response of concrete, based on the past research by Lee and Fenves [ 10]. It uses concepts of isotropic damaged elasticity in combination with isotropic tensile and compressive plasticity to represent the inelastic behavior of concrete. The model makes use of the modified Lubliner yield surface, the yield function takes the form as follows:

(1) F={\displaystyle \frac{\mathrm{1}}{\mathrm{1}-a}}\left(\sqrt{\mathrm{3}{\bar{J}}_{\mathrm{2}}}+\alpha {\bar{I}}_{\mathrm{1}}+\beta ({\epsilon }^{pl})⟨{\bar{\sigma }}_{\max }⟩-\gamma ⟨-{\bar{\sigma }}_{\max }⟩\right)-{\bar{\sigma }}_c({\epsilon }_c^{pl})=\mathrm{0},

where, {\bar{\sigma }}_c is the effective compressive cohesion stress, the effective stress considering strength reduction caused by damage can be calculated by the Eq. (2); {\bar{\sigma }}_{\max } is the maximum principal effective stress; {\bar{I}}_{\mathrm{1}} and {\bar{J}}_{\mathrm{2}} are the first invariant effective stress tensor and the second invariant effective stress deviator respectively. Other parameters are given by Eq. (3).

(2) {\bar{\sigma }}_c={\sigma }_c/(\mathrm{1}-d_c),\hspace{1em}{\bar{\sigma }}_t={\sigma }_t/(\mathrm{1}-d_t),

(3) \alpha ={\displaystyle \frac{{\sigma }_{b\mathrm{0}}/{\sigma }_{c\mathrm{0}}-\mathrm{1}}{\mathrm{2}{\sigma }_{bo}/{\sigma }_{c\mathrm{0}}-\mathrm{1}}}, \beta ={\displaystyle \frac{{\overline{\sigma }}_c({\epsilon }_c^{pl})}{{\overline{\sigma }}_t({\epsilon }_t^{pl})}}(\mathrm{1}-\alpha )-(\mathrm{1}+\alpha ), \gamma ={\displaystyle \frac{\mathrm{3}(\mathrm{1}-K_c)}{\mathrm{2}{K}_c-\mathrm{1}}},

where {\bar{\sigma }}_t is the effective tensile cohesion stress; d_c and d_t are damage variables for compression and tension; {\sigma }_{b\mathrm{0}} and {\sigma }_{c\mathrm{0}} are the biaxial and uniaxial compressive strength respectively, ABAQUS program allows user to calibrate the shape of yield surface in the plane of plane stress by the parameter {\sigma }_{b\mathrm{0}}/{\sigma }_{c\mathrm{0}} ; K_c is a parameter which controls the shape of yield surface in the π plane, as shown in Fig. 8, when K_c = 1, the projection of yield surface in the deviatoric plane is circular, similar as the classic Drucker-Prager criterion, K_c = 2/3 is proposed for the reinforced concrete with normal steel ratio.

The CDP model uses nonassociated multi-hardening plasticity, ABAQUS program allows user to define the hardening criterion by the uniaxial compressive stress-inelastic strain curve and tensile stress-cracking strain curve. In this paper, the uniaxial skeleton curve proposed by the Code for design of concrete structures [ 11] was adopted, which offers a good balance between simplicity and accuracy. The uniaxial tensile envelope curve is described by the Eq. (4), in which d_te is the tensile damage variable given by the Eq. (5).

(4) \sigma =(\mathrm{1}-d_{\mathrm{te}})E_c\epsilon ,

(5) d_{\mathrm{t}\mathrm{e}}=\{\begin{array}{ll}\mathrm{1}-{\displaystyle \frac{f_{t,r}}{E_c{\epsilon }_{t,r}}}\left[\mathrm{1.2}-\mathrm{0.2}{\left({\displaystyle \frac{\epsilon }{{\epsilon }_{t,r}}}\right)}^{\mathrm{5}}\right]\hfill & {\displaystyle \frac{\epsilon }{{\epsilon }_{t,r}}}\le \mathrm{1}\hfill \\ \mathrm{1}-{\displaystyle \frac{f_{t,r}/E_c{\epsilon }_{t,r}}{{\alpha }_t{\left({\displaystyle \frac{\epsilon }{{\epsilon }_{t,r}}}-\mathrm{1}\right)}^{\mathrm{1.7}}+x}}\hfill & {\displaystyle \frac{\epsilon }{{\epsilon }_{t,r}}}>\mathrm{1}\hfill \end{array},

where f_t,r is the representative value of concrete tensile strength. ε_t,r is the tensile strain of concrete corresponding to the peak tensile strength f_t,r. α_t is a parameter which contributes to the tensile strain softening zone with a value range from 0.31 to 5.0 depending on the value of f_t,r.

The uniaxial compressive envelope curve follows the Eq. (6), in which d_ce is the compressive damage variable given by the Eq. (7) − (8).

(6) \sigma =(\mathrm{1}-d_{\mathrm{ce}})E_c\epsilon ,

(7) d_{\mathrm{ce}}=\{\begin{array}{ll}\mathrm{1}-{\displaystyle \frac{f_{c,r}n/E_c{\epsilon }_{c,r}}{n-\mathrm{1}+{\left({\displaystyle \frac{\epsilon }{{\epsilon }_{c,r}}}\right)}^n}}\hfill & {\displaystyle \frac{\epsilon }{{\epsilon }_{c,r}}}\le \mathrm{1}\hfill \\ \mathrm{1}-{\displaystyle \frac{f_{c,r}/E_c{\epsilon }_{c,r}}{{\alpha }_c{\left({\displaystyle \frac{\epsilon }{{\epsilon }_{c,r}}}-\mathrm{1}\right)}^{\mathrm{2}}+{\displaystyle \frac{\epsilon }{{\epsilon }_{c,r}}}}}\hfill & {\displaystyle \frac{\epsilon }{{\epsilon }_{c,r}}}>\mathrm{1}\hfill \end{array},

(8) n={\displaystyle \frac{E_c{\epsilon }_{c,r}}{E_c{\epsilon }_{c,r}-f_{c,r}}}.

where f_c,r is the representative value of concrete compressive strength. ε_c,r is the compressive strain of concrete corresponding to the peak compressive strength f_c,r. α_c is a parameter which contributes to the compressive strain softening zone with a value range from 0.74 to 3.99 depending on the value of f_c,r.

The cyclic unloading and reloading behavior of CDP model in the uniaxial condition can be represented by a set of straight lines, Fig. 9 shows that hysteretic behavior occurs under, both, tensile and compressive stress. Two damage variables, d_t and d_c, one for tensile damage and the other for compressive damage, are introduced to simulate the elastic stiffness degradation caused by the damage during unloading and reloading. When d = 0, means no damage, unloading stiffness is equal to the initial elastic stiffness. When d = 1, means complete damage, unloading stiffness is equal to zero. The two damage variables should not be given too large value, otherwise may cause severe computational disconvergence.

Stiffness recovery, caused by crack closing during reverse reloading, can also be simulated by using CDP model with two stiffness recovery factors w_c and w_t, as shown in Fig. 9. When w = 0, means no stiffness recovery during reloading. When w = 1, means complete stiffness recovery, reloading stiffness is equal to the last unloading stiffness.

The cyclic constitutive response of the steel reinforcement and steel plate was modeled by means of the simple linear kinematic hardening model.

Calculated results

The cyclic behavior of the PRCFW system under vertical and horizontal loading is simulated. The vertical loads are applied as dead loads on the loading plates tied on the top of the columns, and the horizontal loads are applied at the center of the loading beam tied on the two ends of the top girder in the model, the loading histories acting on the models coincide with the test. The calculated resilience curves of PRCFW-1 specimen are shown in Fig. 10. The numerical skeleton curve shows a good agreement with the experimental results (see Fig.10(b)), including the strength degradation in the soften zone after the peak load. characteristic points such as the calculated yield load, peak load and ultimate drift all agree well with the test data within the error range of 4%. There are some differences between calculated and experimental hysteretic curves (see Fig.10(a)), the analytical model overestimate the energy dissipating capacity of the specimen, though the stiffness degradation has been considered in the CDP material model, the calculated cycles are still plumper, which mainly accounts for the reason that the bond-slip behavior in the interfaces of both steel-concrete and reinforcement-concrete is ignored in the analytical model, CDP model cannot accurately describe the crack opening and closing behavior of concrete material under cyclic loadings. More sophisticated model with interface springs instead of simplified bond constraint may improve the shape of the numerical cycles and reflect the “pinching” phenomenon, Ref. [ 12] adopted a solid element based model on ANSYS program to analyze the nonlinear structural behavior of steel frame with reinforced concrete infill shear walls. Lots of normal and tangential linear spring elements were set on the interfaces of frame and infill walls, and also lots of linear spring elements on the interfaces of concrete and steel material to simulate the interface contact-slip behavior. Simulated results showed that the shape of the calculated cyclic cycles was improved, and can reflect some “pinching” phenomenon, but meanwhile the modeling and computational efficiency were greatly reduced.

Figure 11 shows the damage process of the PRCFW system under the cyclic loading in three typical stages: inelastic stage, peak stage and softening stage. When the total drift arrived at 0.43%, damage mainly concentrated at the infill slit wall as shown in Fig. 11 (a) – (b), the behavior of the specimen became inelastic. When the total drift arrived at 1.71%, the infill wall and bottom beam were severely damaged, and plastic hinges began to form at the ends of the top girder, as shown in Fig. 11 (c) – (d), meanwhile the specimen arrived at its ultimate strength. After then, when the total drift arrived at 2.14%, damage began to propagate and plastic hinges formed at the column foot, as shown in Fig.11 (e) – (f), the specimen failed eventually. During the simulation process, the infill wall divided into several wall stripes by slits acted like several columns with large aspect ratio after the specimen yielding, as illustrated in Fig. 11, whose main deformation is bending deformation. The simulated structural response and damage evolution of the specimen both agree with the observed performance and damage patterns during the test.

The numerical results showed that the infill shear wall carried the highest percentage of the lateral force (90%) at the first elastic stage. When the PRCFW specimen stepped into inelastic work stage (0.43% total drift), the lateral force carried by infill slit wall dropped to 81% accounting for the damage propagation and bending deformation. The proportion reached 85% as the specimen achieved its peak strength, the recovery of the shear capacity may be caused by the diagonal compression struts arising in the infills. During the softening stage, the proportion decreased gradually with increasing of lateral forces, the minimum percentage reached 79% at last (2.14 total drift).

Conclusions

Based on the experimental and numerical analysis, some conclusions are drawn as follows:

1) In this system, the prefabricated RC beams and columns are spliced by cast-in-site joints, thus enabling speedy erection. Cast-in-site joints and the presented rigid shear connectors performed well during the cyclic loading, which ensure the optimum performance of the PRCFW system.

2) Damage mainly occurred in the infills and ends of the beams before failure, which meets the design principle and prospective. But it is important to note that the frame beam should be designed to have the capacity to resist the shear forces induced by the equivalent compression strut at the ultimate strength load level.

3) The PRCFW system exhibits good ductility, its strength and lateral stiffness decrease slowly, offers a good energy dissipating capacity, thus is applicable for buildings in earthquake-prone regions.

4) The presented nonlinear FE model based on the ABAQUS program can well calculate the cyclic behavior of the PRCFW structure. It is sufficiently accurate and efficient to provide useful design information and a tool for use in further parametric studies of structural response to environmental hazards.

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