Seismic Performance Evaluation of Prefabricated Shear Wall Structure with Rabbet-Unbonded Horizontal Connection

Sun, Chongfang; Zhao, Zhiqiang

doi:https://doi.org/10.1155/2022/8898079

Advances in Civil Engineering

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Abstract Introduction Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2022 | Article ID 8898079 | https://doi.org/10.1155/2022/8898079

Seismic Performance Evaluation of Prefabricated Shear Wall Structure with Rabbet-Unbonded Horizontal Connection

Chongfang Sun¹and Zhiqiang Zhao²

Academic Editor: Guojun Wu

Received17 Dec 2021

Revised06 Mar 2022

Accepted09 Mar 2022

Published25 Mar 2022

Abstract

This paper is concerned about seismic performance evaluation of precast shear wall structure with Rabbet-unbonded Horizontal Connection (RHC). RHC is composed of rabbets and unbonded rebar segments. The rabbets are used to improve the shear capacity and prevent slippage of connection, and the unbonded rebar segments are used to improve the ductility and energy dissipation. The constitutive relation of unbonded region is put forward and verified, which is applied in RHC shear wall structure model. The pushover analysis, capacity spectrum analysis and seismic performance evaluation of RHC shear wall structure are performed, which are compared with that of conventional connection shear wall structure and cast-in-place shear wall structure. The result shows that RHC shear wall structure reaches basic seismic fortification target of “no damage in small earthquake, repairable in moderate earthquake, no collapse in severe earthquake,” and basically reaches the seismic performance of cast-in-situ shear wall structure. Finally the effect of unbonded length and unbonded level on storey drift and interlayer drift angle are analyzed and the design proposal is put forward.

1. Introduction

The development of precast structure is an important path to realize the architecture industrialization [1]. In particular, the precast shear wall structure with large rigidity and great bearing capacity is the first choice [2, 3], however, the horizontal connection in the structure is the key to ensure structural integrity and seismic performance [4], and to date, the main connections that are used widely are unbonded posttensioned connection, bolted connection and grouting connection and so on [5–7]. In this paper, the authors invent a new horizontal connection-RHC [8], and the seismic performance of RHC shear wall component has been studied, however, the seismic performance of whole structure has not been studied.

To date, addressing the seismic performance evaluation of whole structure, many engineers or scholars has made contributions. For cast-in-situ shear wall structure, Özlem et al. [9] investigated the seismic behavior of a reinforced-concrete shear wall building that collapsed during the 2003 Bingöl earthquake by nonlinear static analysis and nonlinear dynamic analysis. Soleimani et al. [10] performed a new energy-based multi-mode pushover analysis to assess seismic demands of asymmetric-plan buildings. Kim et al. [11] proposed a new equivalent lateral force design method for low-rise reinforced concrete wall-frame mixed buildings and validated its feasibility by pushover analysis. Han et al. [12] performed the elastoplastic analysis on frame-supported shear wall structures under severe earthquake. The damage and performance of structural components were assessed, and the safety of the structure under rare earthquake was further analyzed by using the seismic performance evaluation method based on component deformation index.

For composite shear wall structure, Huang et al. [13] selected three types of infill walls with different load capacity to install in the bare self-centering prestressed concrete frame and conducted the seismic performance evaluation of the whole structures. Li et al. [14] proposed a new composite structural system with separate gravity and lateral load resisting system and evaluated its seismic performance. Qin et al. [15] proposed two types of performance quantification, namely story drift and damage index based on the improved Park-Ang two-parameter damage model to evaluate the seismic performance of high monolithic precast shear wall structure under earthquake action. Masoumeh et al. [16] performed pushover analyses on steel plate shear wall frames to study the effect of two lateral load distribution patterns (triangular loading and uniform distribution loading) on seismic performance. Krishnapriya et al. [17] put forward a type of hybrid coupled wall and carried out the time history analysis on the wall. Smail et al. [18] proposed a seismic design procedure for cold-formed steel sheathed shear wall frames and assessed the seismic performance. Ji et al. [19] put forward a novel type of hybrid coupled wall, which was used in an 11-story building located in a highly seismic area. Its seismic performance was assessed and compared with that of conventional reinforced concrete coupled walls. Keunyeong et al. [20] performed the seismic performance evaluation of coupled steel plate shear wall systems, and analyzed the influence of bay width and coupling beam length on structural performance. Wu et al. [21] performed the pseudostatic test and seismic performance evaluation of new precast shear wall spatial structure. Li et al. [22] evaluated the coupled wall system with novel replaceable steel truss coupling beams using nonlinear time history analysis and compared with the response of reinforced concrete coupled wall system with reinforced concrete coupling beams. Pan et al. [23] conducted the seismic performance evaluation of the newly proposed infilled rocking wall frame structure through quasistatic cyclic testing, designed and verified the critical joints, established and calibrated the numerical models to estimate the frame-shear forces.

However, the seismic performance of RHC shear wall overall structure has not been studied before. Therefore, this paper aims to evaluate its seismic performance. Firstly, the innovative horizontal connection RHC is described briefly, and then pushover analysis and capacity spectrum analysis are performed, seismic performance of overall structure is evaluated. Finally, the effect of unbonded length and unbonded level on storey drift and interlayer drift angle are analyzed, and the design proposal is put forward.

2. Brief Description of RHC

RHC is an improvement and optimization connection on basis of grouting connection, see Figure 1. In the lower wall, a segment of rebar is left unbonded to increase the ductility and energy dissipation of the assembled structure. The rebar reserved in the lower wall is connected with that in the upper wall by a well-developed grouting connection technology. The two walls are integrated by filling high performance mortar into the space between a pair of trapezoidal rabbets, which plays a role in enhancing the shear capacity of the connection and preventing wall slipping.

3. The Evaluation Model

The evaluation model is selected from a high-rise residential building with 33 storeys [24], structural height of 93.04 m and construction area of 28036.9 m², as shown in Figure 2. In this building, the cast-in-situ shear walls are applied from the 1st floor to the 4th floor and precast shear walls with conventional connection (flat-interface connection shown in Figure 3) are applied from the 5th floor to the top floor.

This paper intends to substitute the conventional connection by RHC and evaluate the seismic performance of RHC shear wall structure, which is finally compared with that of conventional connection shear wall structure and cast-in-situ shear wall structure.

4. Pushover Analysis

4.1. Element Types

The finite element analysis software ABAQUS is applied. The high-rise residential building falls in the category of shear wall structure, its components include wall, floor and beam, which are simulated by different element types according to different component characteristics.

4.1.1. Shell Element

The walls and floors are simulated by S4R (four-node quadrilateral finite thin film strain with linear reduced integration) shell element, because the length and width of wall and floor are far larger than thickness. The rebars in walls and floors are simulated by “rebar layer” operation in INPUT file. As there are different boundary components in walls, the walls can be divided into several parts with different steel smeared parameters in the model.

4.1.2. Beam Element

The beam components are simulated by B31 (three-dimensional linear fiber beam) element, because their transverse size is far smaller than longitudinal size. The rebars in beam components are simulated with “rebar layer” operation in INPUT file.

4.2. Constitutive Relation of Materials

4.2.1. Concrete in Walls and Floors except Unbonded Region

In this part, concrete is simulated with the damage plasticity model available in the ABAQUS library, which can simulate the unidirectional and cyclic loading process considering the tensile and compressive properties of concrete [25]. The model curve is shown in Figure 4, and the corresponding parameters are shown in Table 1.

(a)

(b)

4.2.2. Steels in Walls and Floors except Unbonded Region

In this part, steels are simulated with dynamic hardening bilinear elastoplastic model, as shown in Figure 5. The yield strength, Elasticity modulus and Poisson’s ratio are 400 N/mm², 2 × 10⁵ N/mm² and 0.3, respectively.

4.2.3. Concrete and Steel in Beams

The beams are treated with uniaxial hysteresis constitutive relation set: PQfiber. The concrete in beams is treated with UConcrete01 constitutive relation in PQfiber (Table 2) and the steels in beams are treated with USteel01 constitutive relation in PQfiber. And the yield strength, Elasticity modulus and Poisson’s ratio of steel are 400 N/mm², 2 × 10⁵ N/mm² and 0.3, respectively.

4.2.4. Concrete and Steel in Unbonded Region

There are 33 storeys in overall structure, if the constitutive relation of concrete and steels in unbonded region are set one by one, that will be complicated and difficult to converge, therefore, the authors propose a new constitutive relation for the unbonded region.

(1) Constitutive Relation of Unbonded Region. Compared with the bonded region, there is no cohesive force between concrete and steel in unbonded region, so the constitutive relation of unbonded region should not use the conventional constitutive relation. Therefore, here, we regard the unbonded region as a new material merging the concrete and steel. The constitutive relation generally consists of two types: compressive relation and tensile relation. For compressive relation, compressive strength of steel is not considered, because the steel’s compressive strength is far smaller than tensile strength. Consequently, the compressive relation adopts the conventional concrete compressive constitutive relation. For tensile relation, it is obtained by considering the stress-strain rule of unbonded rebars and concrete during tension process according to continuum damage theory [26]. The selected specimen is cuboid, wherein there is no bonding between steel and concrete. The tensile process can be divided into three stages as follows:(a)Before cracking of specimen

In this stage, the effect of steel should be neglected, because there is no bonding between steel and concrete, so the tensile force acting on specimen is mainly tolerated by concrete. The specimen experiences the following process in this stage: elastic, partial plasticity, microcrack propagation, which also is the damage continuous development process inside concrete. The strain of specimen also is the concrete strain, the stress-strain relationship is shown in (1).where σ is the specimen stress, ε is the specimen strain, E_c is Elasticity modulus of concrete.(b)Cracking instant of specimen

The load acting on the specimen starts to transfer from concrete to steels. As the damage and stress transfer in this process is complex, the process is assumed to be finished in an instant. According to Mazars damage model under one-dimensional load, concrete strain is shown in (2).where s_c is the concrete stress, which is denoted as σ_c = F/[(1-ρ)A₀], where F is the applied load, ρ is the rebar ratio, A₀ is the total area of cross-section. D is the damage parameter, which is denoted in literature [27].

Therefore, from (2), the concrete strain equation can be rewritten, as shown in (3).

As the specimen stress can be expressed as σ = F/A₀, the constitutive equation of specimen is shown in (4).(c)After cracking of specimen

As there is no bonding between concrete and steel, tensile steel-effect and slip strain of steel are not considered. The steels continue to be elongated and crack width continues to increase with the increase of applied load. The specimen stress is the sum of steel stress and concrete stress, which is shown in (5).where E_s is Elasticity modulus of steel, σ_con is the stress of decline stage in concrete tensile constitutive relation, k is the slope of hardening stage, ε_y is the yield strain of steel.

From above stress-strain relations of three stages, we can obtain the tensile constitutive relation of unbonded region as shown in Figure 6.

Verification of unbonded region’s constitutive relation: the RHC shear wall specimen was constructed and tested under quasi-static cycle loading with axial compression ratio of 0.2 [28]. It was composed of a wall and a base as shown in Figure 7. The wall had a height, width and thickness of 3.4 m, 1.7 m and 0.2 m. The base had a length, width and height of 2.3 m, 0.69 m and 0.82 m. The horizontal connection was located between wall and base. Considering the longitudinal rebar intensity of constraint boundary element and configuration of metal bellows, seven rabbets were set up symmetrically at connection. High performance mortar was grouted in metal bellows and connection. The grouting region was located at the low part of the wall. The unbonded segments at the longitudinal rebars were located in the base. Based on the FE simulation results of specimens before test, take the unbonded length as 300 mm.

The test specimen is simulated using the proposed unbonded region’s constitutive relation, and finally obtain the simulated skeleton curve of specimen, which is compared with test skeleton curve, as shown in Figure 8.

Figure 8 reveals a good agreement between test curve and simulated curve, which states that the proposed unbonded region’s constitutive relation is feasible in simulating RHC shear wall structure.

4.3. Storey Assembly

As there are lots of beam elements and shell elements in overall structure model, it is time-consuming and difficult to converge to assemble them by contact elements. Therefore, this paper adopts a equivalent simulation method to implement all storeys assembly. In this method, as the shear wall in overall structure is high shear wall, the effect of rabbets on connection’s shear capacity is small, therefore, the connection’s interface can approximately be set to be flat. Furthermore, in every storey, the constitutive relation of the connection is approximately set to be grouting constitutive relation. In addition, the unbonded region is given the constitutive relation proposed in Section 4.2.4.

After the constitutive relation of each storey is set, the overall structure can be assembled rapidly. The principle of the rapid assembly method is that through the floor node coordinates match, replace the repeat nodes in floor interface so as to realize the node share in interface of up and down floor. For more information about the rapid assembly procedure, the readers are advised to refer to the literature [24]. Through the procedure, the assembly model of RHC shear wall structure is shown in Figure 9.

4.4. Pushover Analysis Results

The basic principle of pushover analysis is that apply the vertical load on the structure and keep it constant, and then apply the specific lateral load distribution pattern on the structure and enlarge it step by step until to structure plastic deformation. Based on it, determine whether the deformation and force of structure and components meet the specification requirements, and analyze the plastic hinge position and possible failure mechanism of the structure. Finally, evaluate the structure seismic performance according to seismic demand in different performance level.

4.4.1. Basic Assumptions

The basic assumptions of pushover analysis are as follows:(1)Earthquake response of structure is only controlled by the first vibration modal.(2)The structure deformation along the structure height is expressed by shape vector. In the whole process of earthquake action, the shape vector remains constant regardless of the structure deformation.(3)Floor stiffness in plane is infinite and the stiffness out-of-plane is not considered.

4.4.2. Calculation Steps

The calculation steps of pushover analysis are as follows:(1)Build the structure pushover model and apply vertical load on the model.(2)Select appropriate lateral load distribution pattern. The commonly used lateral load distribution patterns include uniform distribution, inverted triangle distribution, multi-mode combination distribution, equivalent height distribution and adaptive distribution.(3)Select appropriate lateral load increment. The lateral load increment should make the weaker components yield firstly and constantly modify its stiffness in order to make structure continue to tolerate the horizontal load.(4)Based on steps (2) and (3), calculate accumulated structure internal force and deformation until the structure roof displacement reaches the target displacement or the structure becomes institution.

4.4.3. Analysis Results

According to above calculation steps, the pushover curve of RHC shear wall structure is obtained, which is compared with that of conventional connection shear wall structure and cast-in-place shear wall structure.

It is noteworthy that for conventional connection shear wall structure model, the connection interface is flat, and the connected steels are subjected to tensile-shear or compressed-shear force, therefore, the conventional constitutive relation cannot be applied in connected steels. According to the fourth strength theory of Mechanics of Materials [26], the connected steels strength is reduced. The constitutive relations of connected steels before and after reduction are shown in Figure 10.

However, for RHC shear wall structure, as the rabbets in connection are subjected to the connection’s shear force, the connected steels in RHC can be regarded as only tolerating tensile force or compressed force which adopts the conventional steel constitutive relation.

The pushover curves of three structures in x and y direction are demonstrated in Figure 11.

(a)

(b)

Figure 11 reveals that the trend of three pushover curves in two directions is similar with curve overlapping in elastic stage and curve separation in elastic-plastic and plastic stages. In elastic-plastic and plastic stages, the stiffness of RHC shear wall structure is smaller than that of other structures because of the unbonded segment. What’s more, the stiffness of conventional connection shear wall structure is little smaller than that of cast-in-place shear wall structure because of the connection. In conclusion, the difference of three curves is small.

It also can be seen that the structure stiffness in x direction is smaller than that in y direction because of shear wall configuration (Figure 12), the most shear walls in x direction are short which can be regarded as the flanges of shear walls in y direction. They are connected by frame beams, therefore, the whole structure in x direction falls in the category of frame-shear wall structure. However, there are many long shear walls in y direction, which are connected by linking beams, so the whole structure in y direction falls in the category of shear wall structure. Consequently, the structure stiffness in y direction is larger than that in x direction.

5. Capacity Spectrum Analysis

5.1. Calculation Steps

The basic principle of capacity spectrum analysis is that convert the pushover curve and the earthquake influence coefficient curve into capacity spectrum curve and demand spectrum curve, respectively. Evaluate the structure seismic performance based on the intersection of capacity spectrum curve and demand spectrum curve. The specific calculation steps are as follows:(1)Build equivalent single freedom degree system and convert the base shear versus top displacement curve obtained by pushover analysis into capacity spectrum curve.(2)Convert the earthquake influence coefficient curve into demand spectrum curve.(3)Calculate the intersections of capacity spectrum curve and demand spectrum curve firstly, which are called “performance points.” Then, analyze the structure internal force and deformation at the performance point, and finally complete the seismic performance evaluation.

5.2. Performance Point

Through capacity spectrum analysis, the pushover curve is converted into the capacity spectrum curve. In addition, the earthquake influence coefficient curve under frequent, moderate and severe earthquake in Specification [29] is converted into the corresponding demand spectrum curves. The intersections of two curves are shown in Figure 13.

(a)

(b)

Figure 13 reveals that there exists intersections between capacity spectrum curves and demand spectrum curves of frequent, moderate and severe earthquake, respectively. Furthermore, there are abundant surplus after severe earthquake performance point in the capacity spectrum curve. All above indicate that RHC shear wall structure has better anticollapse ability.

6. Seismic Performance Evaluation

“Seismic performance level” means the maximum expected damage extent for a building in a specific fortification level. According to the division of earthquake damage extent and building performance level in Specification [29], “seismic performance level” is divided into four levels: basic intact, slightly damage, moderate damage, serious damage, which are called “state points” in base shear versus top displacement curve (Figure 14). The “performance point” includes frequent earthquake, moderate earthquake and severe earthquake in base shear versus top displacement curve according to Section 5.2. Here, “performance points” and “state points” are regarded as the evaluation index to evaluate the seismic performance, which are marked in pushover curves of three structures in Figure 14.

(a)

(b)

It can be seen from Figure 14 that performance points and state points of three structures are overlapping basically in elastic stage and separated in elastic-plastic and plastic stages because of different structure characteristics. Under the same base shear, the top displacement of cast-in-place shear wall structure is smaller than that of conventional connection shear wall structure because of connected steels’ strength reduction, and the top displacement of conventional connection shear wall structure is smaller than that of RHC shear wall structure, which indicates that unbonded segment’s effect on top displacement is larger than that connected steels strength reduction’s effect on top displacement. In general, the location distance of performance points and state points in three structures is little, which states that RHC shear wall structure and conventional connection shear wall structure basically reach the seismic performance of cast-in-place shear wall structure.

It also can be seen from Figure 14 that in both x and y direction, for three structures, frequent earthquake performance point is located before basic intact point, which states that three structures reach the fortification target of “no damage in small earthquake”. Moderate earthquake performance point is located between slightly damage and moderate damage, which states that three structures reach the fortification target of “repairable in moderate earthquake”. Severe earthquake performance point is located between moderate damage and serious damage, which states that three structures reach the fortification target of “no collapse in severe earthquake”. In conclusion, three structures reach basic seismic precautionary target. Furthermore, there are large deformation capacity and strength reserve after severe earthquake in RHC shear wall structure curves, which indicates that RHC shear wall structure has better ductility and anticollapse ability.

7. The Effect of Unbonded Length and Unbonded Level on Seismic Performance of Overall Structure

7.1. Unbonded Length

RHC shear wall structure is subjected to inverted triangular load to simulate the earthquake action, and the performance points of the structure with different unbonded lengths are obtained under frequent and rare earthquakes. Finally, the effect of unbonded length on storey drift and interlayer drift angle in X and Y direction are obtained, as shownin Figures 15-16.

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

It can be seen that effect of unbonded length on storey drift and interlayer drift angle is smaller in frequent earthquake and larger in severe earthquake. The reason is that in frequent earthquake, the unbonded steel is in elastic stage, which has smaller deformation and smaller effect on structure. However, in severe earthquake, the unbonded steel is in plastic stage, which has larger deformation and larger effect on structure.

The storey drift and interlayer drift angle increase with the increase of unbonded length. In severe earthquake, when the unbonded length is 500 mm, the interlayer drift angle in X direction is about 1/133, which is slightly smaller than limit value 1/120 in specification [30]. In order to maintain a certain safe reserve, it is recommended that unbonded length should not be more than 500 mm.

7.2. Unbonded Level

The unbonded region is divided into three parts: two confined end-zones and one middle zone, see Figure 17(a). As the effect of confined end-zone on seismic performance is larger than middle zone, only the longitudinal reinforcements in confined end-zone are set unbonded segments. The constitutive relation of middle zone adopts that in the specification [29], and the constitutive relation of confined end-zone adopts that in Section 4.2.4 proposed.

When unbonded level varies, reinforcement ratio varies, and the corresponding relation between unbonded level and reinforcement ratio is shown in Figure 17(b). The reinforcement ratio is zero, which indicates that all longitudinal reinforcements are bonded, the corresponding structure is cast-in-situ shear wall structure, constitutive model of confined end-zone adopts that in specification [29].

RHC shear wall structure is subjected to inverted triangular load to simulate the earthquake action, and the performance points of the structure with different unbonded levels are obtained under frequent and rare earthquakes. Finally, the effect of unbonded level on storey drift and interlayer drift angle in X and Y direction are obtained, as shown in Figures 18‐19.

(a)

(b)

(c)

(d)

(a)

(b)

(c)

(d)

It can be seen that effect of unbonded level on storey drift and interlayer drift angle is smaller in frequent earthquake and larger in severe earthquake. The reason is the same as unbonded length.

The storey drift and interlayer drift angle increase with the increase of unbonded level. In severe earthquake, when the unbonded level is 0.73, the interlayer drift angle in X direction is about 1/132, which is slightly smaller than limit value 1/120 in specification [30]. In order to maintain a certain safe reserve, it is recommended that unbonded level should not be more than 0.73, that is to say, mostly, longitudinal reinforcements in confined end-zones are set unbonded segments.

7.3. Design Proposal

According to above analysis results, for this model structure, the proposal is put forward: unbonded length should not be more than 500 mm, unbonded level should not be more than 0.73, that is to say, mostly, longitudinal reinforcements in confined end-zones are set unbonded segments.

In actual engineering, when plane layout, floor height, wall width and thickness, confined end-zone length, steel diameter and quantity of connection vary, unbonded length and unbonded level vary. Therefore, specific analysis should be carried out for the specific connection form, and finally determine the appropriate unbonded length and unbonded level.

8. Conclusions

In this paper, the seismic performance of RHC shear wall structure is evaluated, which is compared with that of conventional connection shear wall structure and cast-in-place shear wall structure, and finally the design proposal is put forward. The following conclusions can be drawn:(1)The constitutive relation of unbonded region is put forward and verified through the test results. With that, build the overall structure model by rapid assembly method of standard storeys.(2)Pushover analysis of RHC shear wall structure is performed. The results reveal that the trend of RHC shear wall structure, conventional connection shear wall structure and cast-in-place shear wall structure is similar with curve overlapping in elastic stage and separation in elastic-plastic and plastic stages. In elastic-plastic and plastic stages, the stiffness of RHC shear wall structure is smaller than that of other structures because of the unbonded segment. In conclusion, the difference of three curves is small.(3)Capacity spectrum analysis of RHC shear wall structure is performed. The results reveal that RHC shear wall structure has better anticollapse ability.(4)The seismic performance evaluation of RHC precast shear wall structure is performed. The result shows that RHC precast shear wall structure reaches basic seismic fortification target of “no damage in small earthquake, repairable in moderate earthquake, no collapse in severe earthquake”, basically reaches the seismic performance of cast-in-situ shear wall structure.(5)The effect of unbonded length and unbonded level on storey drift and interlayer drift angle are analyzed, and the design proposal is put forward: unbonded length should not be more than 500 mm, unbonded level should not be more than 0.73.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that there is no conflict of interest regarding the publication of this paper.

Acknowledgments

The research was financially supported by the National Natural Science Foundation for Young Scientists of China (Grant no. 51908336).

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Copyright © 2022 Chongfang Sun and Zhiqiang Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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