# Seismic Performance of Reinforced Concrete Coupled Walls with Segmental Coupling Beams

Authors: Xiaobin Hu; Qinwang Lu; Zihao Xu; Shen Zhang
Journal: Advances in Civil Engineering
 (2019)

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## Abstract

A novel reinforced concrete (RC) segmental coupling beam (SCB), which mainly comprises the energy dissipating (ED) segment and load bearing (LB) segment, is proposed in this paper. In order to examine its applicability in engineering practice, one scaled RC coupled wall specimen with the proposed SCBs was constructed and experimentally investigated under cyclic loading. The results show that both cracking and yielding occurred much earlier on the ED segments of the SCBs compared to the LB segments. In addition, a lot more cracks distributed densely on the ED segments were observed at the end of the test. It demonstrates that the ED segments play a main role in the energy dissipation, while the LB segments are always reliably capable of carrying the gravity load transferred from the floor beams. Finally, the finite element analysis model of the RC coupled wall is established and validated by comparing the analysis results with the experimental ones. Utilizing the proposed analysis model, parametric analyses are conducted to investigate the influence of a variety of design parameters, including the axial compressive ratio of the wall pier, concrete strength, and especially sectional height of the SCB, on seismic performance of the coupled wall. It shows that as the sectional height of the ED segment increases, the energy dissipating capacity of the coupled wall may improve while the ability of supporting the gravity load is lowered.


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## Body

## 1. Introduction

In the high-rise or super high-rise buildings, reinforced concrete (RC) shear walls are usually employed to enhance the overall structural lateral stiffness and strength especially in the high seismic intensity zone. Due to the existence of door or window openings, shear walls are often divided into smaller wall piers linked together by the coupling beams. During a major earthquake, the coupling beam is desired to yield first and dissipate excessive energy through plastic deformations, thus protecting the wall piers from severe damages.In recent decades, extensive studies have been carried out to investigate the nonlinear behavior of the coupling beam or its influence on the structural performance of the coupled wall. Either the coupling beams or the coupled walls are involved in these studies by experimental, theoretical, or analytical methodologies [1–13]. The research outcomes generally indicate that the coupling beam behaves more like a deep beam due to its small span/depth ratio. Different from the ordinary beam in the frame structure, significant local deformation occurs at the beam-wall joints and the coupling beam tends to fail in shear other than in flexure. To improve the ductility and energy absorption of the coupling beam, several novel approaches have been proposed and investigated thoroughly. For example, specially detailed diagonal reinforcement, developed by Paulay et al. [1], has shown to be an effective way to enhance the strength and ductility of the coupling beam. In addition to the conventional RC coupling beam, scholars have developed a variety of different types of coupling beams, such as steel coupling beam [14], composite coupling beam [15–23], double coupling beam [24], replaceable coupling beam [25, 26], and assembled coupling beam [27].To ensure the energy dissipating ability of the coupling beam and avoid the brittle shear failure, it is inadvisable to let the ordinary coupling beam (OCB) carry the gravity load transferred by the floor beam [28, 29]. As such, for the framed core tube structure, the floor beams connecting the peripheral frame and the interior tube are often arranged obliquely to shy away from the OCBs, as shown in Figure 1(a). It not only results in great difficulties in room division and equipment layout but also remarkably increases the construction cost. To address this issue, the authors of this paper proposed a novel RC segmental coupling beam (SCB) [30], which consists of the load bearing (LB) segment and energy dissipating (ED) segment. By means of numerical analysis, it is shown to reliably support the floor beam by the LB segment while maintaining the adequate energy dissipating ability through the ED segment. By replacing the OCBs with the SCBs, the structural plan shown in Figure 1(a) can be optimized as illustrated in Figure 1(b). It can be seen that the new layout has a lot of obvious advantages over the original one, such as the easiness of room arrangement and high constructional cost efficiency.Figure 1
Typical structural plan of the framed core wall structure. (a) Original plan using the OCBs. (b) Optimized plan using the proposed SCBs.
(a)
(b)To further verify the effectiveness of the proposed SCB in engineering practice, one scaled RC coupled wall specimen with the proposed SCB is constructed and tested under cyclic loading, respectively. Emphases are laid on studying their damage process, ductility, and energy dissipating performance. Afterwards, finite element (FE) analysis model of the RC coupled wall is established and validated by comparing the analysis results against the experimental ones. Finally, utilizing the proposed FE model, the influence of a variety of design parameters, including the axial compressive ratio of the wall pier, sectional height of the SCB, and concrete strength, on the seismic performance of the coupled walls is investigated comprehensively by way of parametric analysis.


## 2. Experimental Program

### 2.1. Specimen Design

The prototype structure involved in this test is a three-storey coupled wall with the SCBs, which originates from a real super high-rise building located in Wuhan, China. According to the geometry dimensions of the prototype structure as well as the test conditions, the length similitude ratio is taken as 1/4. The other main similitude ratios are determined based on the similarity relations and listed in Table1.Table 1
Main similitude ratios involved this study.
Parameter
Length
Area
Concentrated force
Area load
Similitude ratio
1/4
1/16
1/16
1The test specimen mainly consists of six parts: wall pier, SCB, floor beam, slab, loading beam, and foundation, as shown in Figure2. The SCB can be divided into two segments: the load bearing (LB) segment and the energy dissipating (ED) one. The former with a larger sectional height is designed to support the gravity transferred by the floor beam, while the latter with a smaller sectional height is responsible for energy dissipation.Figure 2
Overall illustration of the specimen.The dimensions and reinforcement details of the specimen are shown in Figure3. It can be seen that each wall pier can be divided into the wall web in the middle and the two boundary elements at the edges. Note that the diameters of rebars are strictly determined according to the similarity requirement unless the scaled rebars are not available in the market. Under this circumstance, the diameters or spacing of the rebars are adjusted provided that the corresponding reinforcement ratio remains nearly same.Figure 3
Dimensions and reinforcement details of the specimen (length unit: mm).


### 2.2. Materials

According to the similarity requirement, the reinforcement rebars involved in the test and their measured mechanical properties are summarily listed in Table2. The cementitious grout, instead of the normal concrete, is used to pour the specimens due to the extremely small spacing between the rebars. A total of nine prism specimens with the size of 150 mm × 150 mm × 300 mm were casted to measure its mechanical properties. The measured average strength and elastic modulus are 58.45 MPa and 37.1 GPa, respectively.Table 2
Mechanical properties of the reinforcement rebars.
No.
Diameter (mm)
Yield strength (MPa)
Ultimate strength (MPa)
Elastic modulus (GPa)
9#
3.658
305.25
403.12
206.25
11#
2.946
174.21
212.35
206.41
14#
2.032
239.36
343.44
207.39
C6
6
428.96
645.36
204.35
C8
8
423.56
638.74
205.26


### 2.3. Test Setup and Procedure

The test setup is specially designed as shown in Figure4. In order to apply the gravity load on the floor beam, a total of three steel channels, with each fixed transversely at the cantilever end of each floor beam, are laid to carry a steel gravity beam through steel rods. In addition, two jacks are laid on the top of the two wall piers to apply the axial force with the help of the vertical reaction fixture. In order to apply the lateral load, a horizontal fixture is mounted to connect the hydraulic actuator to the loading beam. Besides, to prevent the likely out-of-plane instability, two steel bracing channels are installed at each storey and connected to the reaction wall. Figure 5 shows the photo of the specimen equipped with all the loading devices.Figure 4
Illustration of the test setup. (a) Front elevation. (b) Back elevation.
(a)
(b)Figure 5
Test photo.According to the analysis results of the prototype structure and the similitude relations given in Table1, the gravity load acting on the specimen is obtained as listed in Table 3. For convenience, the moment and shear force at the fix end of each floor beam are equivalent as a concentrated force at the cantilever end, which are applied by the weight of the steel gravity beam as aforementioned. Additionally, the area load on the slab is applied on the wall pier directly through the jack, since the slabs are symmetrical about the wall piers.Table 3
Gravity load acting on the specimen.
Location
Load
Values for the prototype structure
Values for the specimen
Fix end of each floor beam
M (kN·m)
425.85
6.654
V (kN)
203.10
12.69
Top of left wall
N (kN)
10096.35
631.02
Top of right wall
N (kN)
10940.35
683.77
Slab
q (kN/m2)
3.75
3.75The gravity load is applied first, and the cyclic lateral load is exerted subsequently up to the failure of the specimen [31], as shown in Figure 6, where Δ represents the increment of the displacement amplitude. For each level of the displacement amplitude, three cycles are repeated to observe strength degradation of the specimen.Figure 6
Loading scheme of the cyclic test.


### 2.4. Measurements

A total of eight displacement sensors are arranged as shown in Figure7. Among them, five are configured along the height of the specimen to measure the in-plane displacements, while another three are located at each storey to monitor the possible out-of-plane displacements. In addition, a total of 72 strain gauges are deployed on the longitudinal rebars as shown in Figure 7. They are mainly located at both ends of the bottom of the wall piers at each storey, as well as both ends of the LB segment and ED segment of the SCB at each storey. Moreover, another 18 strain gauges are mounted on the concrete surface where the stress, which is obtained from the preliminary FE analysis, is relatively large.Figure 7
Overall measurements of each specimen.


## 2.1. Specimen Design

The prototype structure involved in this test is a three-storey coupled wall with the SCBs, which originates from a real super high-rise building located in Wuhan, China. According to the geometry dimensions of the prototype structure as well as the test conditions, the length similitude ratio is taken as 1/4. The other main similitude ratios are determined based on the similarity relations and listed in Table1.Table 1
Main similitude ratios involved this study.
Parameter
Length
Area
Concentrated force
Area load
Similitude ratio
1/4
1/16
1/16
1The test specimen mainly consists of six parts: wall pier, SCB, floor beam, slab, loading beam, and foundation, as shown in Figure2. The SCB can be divided into two segments: the load bearing (LB) segment and the energy dissipating (ED) one. The former with a larger sectional height is designed to support the gravity transferred by the floor beam, while the latter with a smaller sectional height is responsible for energy dissipation.Figure 2
Overall illustration of the specimen.The dimensions and reinforcement details of the specimen are shown in Figure3. It can be seen that each wall pier can be divided into the wall web in the middle and the two boundary elements at the edges. Note that the diameters of rebars are strictly determined according to the similarity requirement unless the scaled rebars are not available in the market. Under this circumstance, the diameters or spacing of the rebars are adjusted provided that the corresponding reinforcement ratio remains nearly same.Figure 3
Dimensions and reinforcement details of the specimen (length unit: mm).


## 2.2. Materials

According to the similarity requirement, the reinforcement rebars involved in the test and their measured mechanical properties are summarily listed in Table2. The cementitious grout, instead of the normal concrete, is used to pour the specimens due to the extremely small spacing between the rebars. A total of nine prism specimens with the size of 150 mm × 150 mm × 300 mm were casted to measure its mechanical properties. The measured average strength and elastic modulus are 58.45 MPa and 37.1 GPa, respectively.Table 2
Mechanical properties of the reinforcement rebars.
No.
Diameter (mm)
Yield strength (MPa)
Ultimate strength (MPa)
Elastic modulus (GPa)
9#
3.658
305.25
403.12
206.25
11#
2.946
174.21
212.35
206.41
14#
2.032
239.36
343.44
207.39
C6
6
428.96
645.36
204.35
C8
8
423.56
638.74
205.26


## 2.3. Test Setup and Procedure

The test setup is specially designed as shown in Figure4. In order to apply the gravity load on the floor beam, a total of three steel channels, with each fixed transversely at the cantilever end of each floor beam, are laid to carry a steel gravity beam through steel rods. In addition, two jacks are laid on the top of the two wall piers to apply the axial force with the help of the vertical reaction fixture. In order to apply the lateral load, a horizontal fixture is mounted to connect the hydraulic actuator to the loading beam. Besides, to prevent the likely out-of-plane instability, two steel bracing channels are installed at each storey and connected to the reaction wall. Figure 5 shows the photo of the specimen equipped with all the loading devices.Figure 4
Illustration of the test setup. (a) Front elevation. (b) Back elevation.
(a)
(b)Figure 5
Test photo.According to the analysis results of the prototype structure and the similitude relations given in Table1, the gravity load acting on the specimen is obtained as listed in Table 3. For convenience, the moment and shear force at the fix end of each floor beam are equivalent as a concentrated force at the cantilever end, which are applied by the weight of the steel gravity beam as aforementioned. Additionally, the area load on the slab is applied on the wall pier directly through the jack, since the slabs are symmetrical about the wall piers.Table 3
Gravity load acting on the specimen.
Location
Load
Values for the prototype structure
Values for the specimen
Fix end of each floor beam
M (kN·m)
425.85
6.654
V (kN)
203.10
12.69
Top of left wall
N (kN)
10096.35
631.02
Top of right wall
N (kN)
10940.35
683.77
Slab
q (kN/m2)
3.75
3.75The gravity load is applied first, and the cyclic lateral load is exerted subsequently up to the failure of the specimen [31], as shown in Figure 6, where Δ represents the increment of the displacement amplitude. For each level of the displacement amplitude, three cycles are repeated to observe strength degradation of the specimen.Figure 6
Loading scheme of the cyclic test.


## 2.4. Measurements

A total of eight displacement sensors are arranged as shown in Figure7. Among them, five are configured along the height of the specimen to measure the in-plane displacements, while another three are located at each storey to monitor the possible out-of-plane displacements. In addition, a total of 72 strain gauges are deployed on the longitudinal rebars as shown in Figure 7. They are mainly located at both ends of the bottom of the wall piers at each storey, as well as both ends of the LB segment and ED segment of the SCB at each storey. Moreover, another 18 strain gauges are mounted on the concrete surface where the stress, which is obtained from the preliminary FE analysis, is relatively large.Figure 7
Overall measurements of each specimen.


## 3. Test Results

### 3.1. Experimental Observations

No obvious phenomenon was observed after the gravity load was applied. Later, the cyclic loading shown in Figure6 was exerted following the preliminary loading. According to the preliminary FE analysis results, Δ is set to 8 mm. For clarity purpose, it is supposed that the load and displacement are positive for the specimen loaded to the left; otherwise they are negative.When the top lateral displacement amplitude reached about 8 mm, inclined cracks occurred at the bottom of the ED segment of the SCB at the second storey. As the displacement amplitude reversed to around −8 mm, inclined cracks were found at the top of the ED segment of the SCB at the second storey. In the following, two cycles with the same displacement amplitude were repeated. The existing cracks spread diagonally while no visible cracks were found on the wall piers. Later, as the displacement amplitude increased to about 16 mm, inclined cracks were found at the bottom of the ED segments of the SCBs at all the three storeys. In addition, cracks were found at the top of the LB segment of the SCB at the second storey, as well as the edge of the right wall pier at the first storey. Subsequently, when the displacement amplitude turned to around −16 mm, crossing inclined cracks appeared on the ED segments of the SCBs at all the three storeys. Meanwhile, small cracks were found at the edge of the left wall pier at the first storey.When the lateral displacement amplitude went to about 24 mm, the cracks on the ED segments of the SCBs grew wider and new cracks emerged at the top of the LB segments of the SCBs. At the same time, inclined cracks were found at the edge of the right wall piers at all the three storeys. Subsequently, as the lateral displacement amplitude reversed to around −24 mm, inclined cracks were seen at the edge of the left wall pier at all the three storeys. Later, as the displacement amplitude increased to about 32 mm, more cracks were found at the ED segments of the SCBs and the edge of the wall piers. In addition, concrete was spalled at the bottom of the ED segments of the SCBs, while crossing inclined cracks were seen at the wall piers. In the following, as the cyclic loading continued, the existing cracks kept developing and new cracks emerged continually.When the displacement amplitude proceeded to around 60 mm, the concrete at the ED segments of the SCBs was spalled with the rebars exposed outside. Meanwhile, the concrete at the edge of the wall pier at the first storey was crushed. At this time, the specimen was damaged seriously and the test was finished.Figure8 shows the failure of the SCBs at the end of the test, and Figure 9 plots the cracks collectively on the specimen. It can be seen that much more and denser cracks emerged on the ED segments of the SCBs compared to the LB segments. This demonstrates that the ED segments play a primary role in energy dissipation during the loading. In contrast, the LB segments are damaged slightly at the end of the test, showing that they are always reliably capable of bearing the gravity load transferred from the floor beam.Figure 8
Failure of the SCBs at the end of the test. (a) The ED segment of the SCB at the third storey. (b) The LB segment of the SCB at the third storey. (c) The ED segment of the SCB at the second storey. (d) The LB segment of the SCB at the second storey. (e) The ED segment of the SCB at the first storey. (f) The LB segment of the SCB at the first storey.
(a)
(b)
(c)
(d)
(e)
(f)Figure 9
Distribution of the cracks (numbers represent crack order).


### 3.2. Yielding Mechanism

According to the measured elastic modulus and yield strength of the longitudinal rebar, the yield strain can be obtained. It is supposed that when the measured tensile strain of the longitudinal rebar exceeds the yield strain, the region where the rebar is located is considered to yield. Thereby, the yielding process of the specimen can be approximately explored by examining the yield sequence of the longitudinal rebars.Figure10 shows the yield process of the longitudinal rebars. It can be seen that the ED segment of the SCB at the second storey yielded first. In the following, the ED segments of the SCBs at the first and third floor yielded consecutively. Later, the boundary elements of the wall piers at the first and second storeys yielded in succession. Finally, the LB segments of the SCBs at all the three storeys yielded.Figure 10
Yielding process (numbers represent yield order).From the above yielding process, it can be concluded that for the coupled wall with the SCBs subjected to lateral loading, the ED segments of the SCBs yield first and work as the first defense. The LB segments of the SCBs yield much later, thus being always reliably capable of carrying the gravity load transferred from the floor beam.


### 3.3. Seismic Performance

#### 3.3.1. Load vs. Displacement Curves

Figure11 plots the lateral load vs. top displacement curves of the specimen. It can be seen that the hysteresis curve is plump with a typical shuttle shape initially and turns gradually to an inversed “S” shape. This is consistent with the serious damage observed on the specimen, as shown in Figure 8. Moreover, the positive strength is obviously higher than the negative one, which may arise from the asymmetry of geometry dimensions and reinforcement details of the coupled wall specimen.Figure 11
Lateral load vs. top displacement curve.


#### 3.3.2. Ductility and Deformation

From the load vs. displacement curve, the ductility of the specimen can be calculated by(1)μ=ΔuΔy,where Δy is the yield displacement, which can be approximately obtained by means of the plotting method [32] and Δu is the ultimate displacement, which is taken as the displacement at the end of the test. Note that the skeleton curve corresponding to the hysteresis curve shown in Figure 11 is used to determine the ductility.The ductility under the positive and negative loading is computed, respectively, and listed in Table4. Moreover, the maximum top drifts are also presented in Table 4. It can be seen that the average maximum roof drift reaches about 1/40, which is far beyond 1/120, the limit value of elasto-plastic storey drift of the shear wall structure specified in the Chinese Code [28]. This demonstrates that the coupled wall specimen with the SCBs has a rather good deformation capacity.Table 4
Ductility and roof drift.
Positive
Negative
Average
Ductility
2.296
2.542
2.419
Top drift
1/35
1/44
1/40


#### 3.3.3. Stiffness and Strength Degradation

(1) Stiffness Degradation. The effective stiffness pertaining to the i-th loading cycle is defined as follows [31]:(2)K=Fi++Fi−Δi++Δi−,where Fi+ and Fi− represent the maximum forces corresponding to the i-th positive loading and negative loading, respectively and Δi+ and Δi− denote the displacements pertaining to Fi+ and Fi−, respectively.Figure12 plots the effective stiffness vs. displacement amplitude curve of the specimen, where the effective stiffness is computed only using the third cycle for each loading level. It can be seen that the stiffness degrades quickly at the early loading phase, and as the loading continues, the stiffness degradation gets slower.Figure 12
Effective stiffness vs. displacement amplitude curve.(2) Strength Degradation. As the number of cyclic loading with the same displacement amplitude increases, strength of the RC structure usually decreases due to the plastic damage accumulation of concrete material. To describe this phenomenon quantitatively, the strength degradation ratio is defined as follows [31]:(3)λji=PjiPji−1,where Pji denotes the peak load of the i-th cycle for the j-th loading level and Pji−1 represents the peak load of the (i−1)-th cycle for the j-th loading level.The strength degradation ratios of the specimen under positive and negative loading are computed, respectively. The resultant strength degradation ratio vs. displacement amplitude curves are plotted in Figure13, where the strength degradations of the second and third circles relative to the first cycle at each loading level are both considered. It can be seen that the strength degradation ratios range between 0.9 and 1.0, showing that the specimen has only minor strength degradation on the whole. It may be explained by that, compared to the normal concrete, the cementitious grout has a relatively denser interior structure due to the absence of coarse aggregate and thus exhibits less damage under repeated loading.Figure 13
Strength degradation vs. displacement amplitude curve. (a) Negative loading. (b) Positive loading.
(a)
(b)


#### 3.3.4. Energy Dissipation

The energy dissipating capacity of structures or members can be quantified by the energy dissipation or equivalent viscous damping ratio. The energy dissipation is defined as the enclosed area of each hysteresis loop, as shown in Figure14, and the equivalent viscous damping ratio can be thus computed by [31](4)he=12π⋅SABD+BCDSAOF+COE,where SABD+BCD is the energy dissipation for the hysteresis loop and SAOF+COE represents the strain energy.Figure 14
Energy dissipation and equivalent viscous damping ratio.Figures15 and 16 present the energy dissipation vs. displacement amplitude curve and the equivalent viscous damping ratio vs. displacement amplitude curve of the specimen. It can be seen that the energy dissipation increases linearly with the increase of displacement, while the equivalent viscous damping ratio ascends first and then descends. This is in accordance with the shape transition of the hysteresis curve as seen in Figure 11.Figure 15
Energy dissipation vs. displacement amplitude curve.Figure 16
Equivalent viscous damping ratio vs. displacement amplitude curve.


## 3.1. Experimental Observations

No obvious phenomenon was observed after the gravity load was applied. Later, the cyclic loading shown in Figure6 was exerted following the preliminary loading. According to the preliminary FE analysis results, Δ is set to 8 mm. For clarity purpose, it is supposed that the load and displacement are positive for the specimen loaded to the left; otherwise they are negative.When the top lateral displacement amplitude reached about 8 mm, inclined cracks occurred at the bottom of the ED segment of the SCB at the second storey. As the displacement amplitude reversed to around −8 mm, inclined cracks were found at the top of the ED segment of the SCB at the second storey. In the following, two cycles with the same displacement amplitude were repeated. The existing cracks spread diagonally while no visible cracks were found on the wall piers. Later, as the displacement amplitude increased to about 16 mm, inclined cracks were found at the bottom of the ED segments of the SCBs at all the three storeys. In addition, cracks were found at the top of the LB segment of the SCB at the second storey, as well as the edge of the right wall pier at the first storey. Subsequently, when the displacement amplitude turned to around −16 mm, crossing inclined cracks appeared on the ED segments of the SCBs at all the three storeys. Meanwhile, small cracks were found at the edge of the left wall pier at the first storey.When the lateral displacement amplitude went to about 24 mm, the cracks on the ED segments of the SCBs grew wider and new cracks emerged at the top of the LB segments of the SCBs. At the same time, inclined cracks were found at the edge of the right wall piers at all the three storeys. Subsequently, as the lateral displacement amplitude reversed to around −24 mm, inclined cracks were seen at the edge of the left wall pier at all the three storeys. Later, as the displacement amplitude increased to about 32 mm, more cracks were found at the ED segments of the SCBs and the edge of the wall piers. In addition, concrete was spalled at the bottom of the ED segments of the SCBs, while crossing inclined cracks were seen at the wall piers. In the following, as the cyclic loading continued, the existing cracks kept developing and new cracks emerged continually.When the displacement amplitude proceeded to around 60 mm, the concrete at the ED segments of the SCBs was spalled with the rebars exposed outside. Meanwhile, the concrete at the edge of the wall pier at the first storey was crushed. At this time, the specimen was damaged seriously and the test was finished.Figure8 shows the failure of the SCBs at the end of the test, and Figure 9 plots the cracks collectively on the specimen. It can be seen that much more and denser cracks emerged on the ED segments of the SCBs compared to the LB segments. This demonstrates that the ED segments play a primary role in energy dissipation during the loading. In contrast, the LB segments are damaged slightly at the end of the test, showing that they are always reliably capable of bearing the gravity load transferred from the floor beam.Figure 8
Failure of the SCBs at the end of the test. (a) The ED segment of the SCB at the third storey. (b) The LB segment of the SCB at the third storey. (c) The ED segment of the SCB at the second storey. (d) The LB segment of the SCB at the second storey. (e) The ED segment of the SCB at the first storey. (f) The LB segment of the SCB at the first storey.
(a)
(b)
(c)
(d)
(e)
(f)Figure 9
Distribution of the cracks (numbers represent crack order).


## 3.2. Yielding Mechanism

According to the measured elastic modulus and yield strength of the longitudinal rebar, the yield strain can be obtained. It is supposed that when the measured tensile strain of the longitudinal rebar exceeds the yield strain, the region where the rebar is located is considered to yield. Thereby, the yielding process of the specimen can be approximately explored by examining the yield sequence of the longitudinal rebars.Figure10 shows the yield process of the longitudinal rebars. It can be seen that the ED segment of the SCB at the second storey yielded first. In the following, the ED segments of the SCBs at the first and third floor yielded consecutively. Later, the boundary elements of the wall piers at the first and second storeys yielded in succession. Finally, the LB segments of the SCBs at all the three storeys yielded.Figure 10
Yielding process (numbers represent yield order).From the above yielding process, it can be concluded that for the coupled wall with the SCBs subjected to lateral loading, the ED segments of the SCBs yield first and work as the first defense. The LB segments of the SCBs yield much later, thus being always reliably capable of carrying the gravity load transferred from the floor beam.


## 3.3. Seismic Performance

### 3.3.1. Load vs. Displacement Curves

Figure11 plots the lateral load vs. top displacement curves of the specimen. It can be seen that the hysteresis curve is plump with a typical shuttle shape initially and turns gradually to an inversed “S” shape. This is consistent with the serious damage observed on the specimen, as shown in Figure 8. Moreover, the positive strength is obviously higher than the negative one, which may arise from the asymmetry of geometry dimensions and reinforcement details of the coupled wall specimen.Figure 11
Lateral load vs. top displacement curve.


### 3.3.2. Ductility and Deformation

From the load vs. displacement curve, the ductility of the specimen can be calculated by(1)μ=ΔuΔy,where Δy is the yield displacement, which can be approximately obtained by means of the plotting method [32] and Δu is the ultimate displacement, which is taken as the displacement at the end of the test. Note that the skeleton curve corresponding to the hysteresis curve shown in Figure 11 is used to determine the ductility.The ductility under the positive and negative loading is computed, respectively, and listed in Table4. Moreover, the maximum top drifts are also presented in Table 4. It can be seen that the average maximum roof drift reaches about 1/40, which is far beyond 1/120, the limit value of elasto-plastic storey drift of the shear wall structure specified in the Chinese Code [28]. This demonstrates that the coupled wall specimen with the SCBs has a rather good deformation capacity.Table 4
Ductility and roof drift.
Positive
Negative
Average
Ductility
2.296
2.542
2.419
Top drift
1/35
1/44
1/40


### 3.3.3. Stiffness and Strength Degradation

(1) Stiffness Degradation. The effective stiffness pertaining to the i-th loading cycle is defined as follows [31]:(2)K=Fi++Fi−Δi++Δi−,where Fi+ and Fi− represent the maximum forces corresponding to the i-th positive loading and negative loading, respectively and Δi+ and Δi− denote the displacements pertaining to Fi+ and Fi−, respectively.Figure12 plots the effective stiffness vs. displacement amplitude curve of the specimen, where the effective stiffness is computed only using the third cycle for each loading level. It can be seen that the stiffness degrades quickly at the early loading phase, and as the loading continues, the stiffness degradation gets slower.Figure 12
Effective stiffness vs. displacement amplitude curve.(2) Strength Degradation. As the number of cyclic loading with the same displacement amplitude increases, strength of the RC structure usually decreases due to the plastic damage accumulation of concrete material. To describe this phenomenon quantitatively, the strength degradation ratio is defined as follows [31]:(3)λji=PjiPji−1,where Pji denotes the peak load of the i-th cycle for the j-th loading level and Pji−1 represents the peak load of the (i−1)-th cycle for the j-th loading level.The strength degradation ratios of the specimen under positive and negative loading are computed, respectively. The resultant strength degradation ratio vs. displacement amplitude curves are plotted in Figure13, where the strength degradations of the second and third circles relative to the first cycle at each loading level are both considered. It can be seen that the strength degradation ratios range between 0.9 and 1.0, showing that the specimen has only minor strength degradation on the whole. It may be explained by that, compared to the normal concrete, the cementitious grout has a relatively denser interior structure due to the absence of coarse aggregate and thus exhibits less damage under repeated loading.Figure 13
Strength degradation vs. displacement amplitude curve. (a) Negative loading. (b) Positive loading.
(a)
(b)


### 3.3.4. Energy Dissipation

The energy dissipating capacity of structures or members can be quantified by the energy dissipation or equivalent viscous damping ratio. The energy dissipation is defined as the enclosed area of each hysteresis loop, as shown in Figure14, and the equivalent viscous damping ratio can be thus computed by [31](4)he=12π⋅SABD+BCDSAOF+COE,where SABD+BCD is the energy dissipation for the hysteresis loop and SAOF+COE represents the strain energy.Figure 14
Energy dissipation and equivalent viscous damping ratio.Figures15 and 16 present the energy dissipation vs. displacement amplitude curve and the equivalent viscous damping ratio vs. displacement amplitude curve of the specimen. It can be seen that the energy dissipation increases linearly with the increase of displacement, while the equivalent viscous damping ratio ascends first and then descends. This is in accordance with the shape transition of the hysteresis curve as seen in Figure 11.Figure 15
Energy dissipation vs. displacement amplitude curve.Figure 16
Equivalent viscous damping ratio vs. displacement amplitude curve.


## 3.3.1. Load vs. Displacement Curves

Figure11 plots the lateral load vs. top displacement curves of the specimen. It can be seen that the hysteresis curve is plump with a typical shuttle shape initially and turns gradually to an inversed “S” shape. This is consistent with the serious damage observed on the specimen, as shown in Figure 8. Moreover, the positive strength is obviously higher than the negative one, which may arise from the asymmetry of geometry dimensions and reinforcement details of the coupled wall specimen.Figure 11
Lateral load vs. top displacement curve.


## 3.3.2. Ductility and Deformation

From the load vs. displacement curve, the ductility of the specimen can be calculated by(1)μ=ΔuΔy,where Δy is the yield displacement, which can be approximately obtained by means of the plotting method [32] and Δu is the ultimate displacement, which is taken as the displacement at the end of the test. Note that the skeleton curve corresponding to the hysteresis curve shown in Figure 11 is used to determine the ductility.The ductility under the positive and negative loading is computed, respectively, and listed in Table4. Moreover, the maximum top drifts are also presented in Table 4. It can be seen that the average maximum roof drift reaches about 1/40, which is far beyond 1/120, the limit value of elasto-plastic storey drift of the shear wall structure specified in the Chinese Code [28]. This demonstrates that the coupled wall specimen with the SCBs has a rather good deformation capacity.Table 4
Ductility and roof drift.
Positive
Negative
Average
Ductility
2.296
2.542
2.419
Top drift
1/35
1/44
1/40


## 3.3.3. Stiffness and Strength Degradation

(1) Stiffness Degradation. The effective stiffness pertaining to the i-th loading cycle is defined as follows [31]:(2)K=Fi++Fi−Δi++Δi−,where Fi+ and Fi− represent the maximum forces corresponding to the i-th positive loading and negative loading, respectively and Δi+ and Δi− denote the displacements pertaining to Fi+ and Fi−, respectively.Figure12 plots the effective stiffness vs. displacement amplitude curve of the specimen, where the effective stiffness is computed only using the third cycle for each loading level. It can be seen that the stiffness degrades quickly at the early loading phase, and as the loading continues, the stiffness degradation gets slower.Figure 12
Effective stiffness vs. displacement amplitude curve.(2) Strength Degradation. As the number of cyclic loading with the same displacement amplitude increases, strength of the RC structure usually decreases due to the plastic damage accumulation of concrete material. To describe this phenomenon quantitatively, the strength degradation ratio is defined as follows [31]:(3)λji=PjiPji−1,where Pji denotes the peak load of the i-th cycle for the j-th loading level and Pji−1 represents the peak load of the (i−1)-th cycle for the j-th loading level.The strength degradation ratios of the specimen under positive and negative loading are computed, respectively. The resultant strength degradation ratio vs. displacement amplitude curves are plotted in Figure13, where the strength degradations of the second and third circles relative to the first cycle at each loading level are both considered. It can be seen that the strength degradation ratios range between 0.9 and 1.0, showing that the specimen has only minor strength degradation on the whole. It may be explained by that, compared to the normal concrete, the cementitious grout has a relatively denser interior structure due to the absence of coarse aggregate and thus exhibits less damage under repeated loading.Figure 13
Strength degradation vs. displacement amplitude curve. (a) Negative loading. (b) Positive loading.
(a)
(b)


## 3.3.4. Energy Dissipation

The energy dissipating capacity of structures or members can be quantified by the energy dissipation or equivalent viscous damping ratio. The energy dissipation is defined as the enclosed area of each hysteresis loop, as shown in Figure14, and the equivalent viscous damping ratio can be thus computed by [31](4)he=12π⋅SABD+BCDSAOF+COE,where SABD+BCD is the energy dissipation for the hysteresis loop and SAOF+COE represents the strain energy.Figure 14
Energy dissipation and equivalent viscous damping ratio.Figures15 and 16 present the energy dissipation vs. displacement amplitude curve and the equivalent viscous damping ratio vs. displacement amplitude curve of the specimen. It can be seen that the energy dissipation increases linearly with the increase of displacement, while the equivalent viscous damping ratio ascends first and then descends. This is in accordance with the shape transition of the hysteresis curve as seen in Figure 11.Figure 15
Energy dissipation vs. displacement amplitude curve.Figure 16
Equivalent viscous damping ratio vs. displacement amplitude curve.


## 4. Numerical Analysis Model

### 4.1. FE Modeling of the Coupled Wall with the SCBs

#### 4.1.1. Overall FE Model

The software ABAQUS [33] is used to establish the FE model of the coupled wall with the SCBs. As shown in Figure 17(a), the wall web, the SCB, and the floor beam are all simulated by the layered shell element S4R, and the rebars are added using the rebar layer. In addition, the loading beam and the boundary element of the wall pier are both modeled by the beam element B31, and the rebars are inputted by editing the keyword ∗rebar. The above elements are simply tied together to construct the overall FE model, as shown in Figure 17(b).Figure 17
Overall FE model of the coupled wall with the SCBs. (a) Element selection. (b) ABAQUS model.
(a)
(b)


#### 4.1.2. Materials

(1) Materials Concerning the Layered Shell Element. The layered shell element involves two types of materials, i.e., rebar and concrete. For the rebar, the bilinear kinematic hardening model is used. For the concrete, the concrete damaged plastic (CDP) model embedded in ABAQUS [34] is adopted.As shown in Figure18, the following uniaxial compressive and tensile stress vs. strain relations [35] are used respectively for the CDP model:(5)σ=Ecε,ε≤ε0,nε/εcn−1+ε/εcnfc,ε0≤ε≤εc,ε/εcαcε/εc−12+ε/εcfc,ε>εc,σ=E0ε,ε≤εt,ε/εtαtε/εt−11.7+ε/εtft,ε>εt,where fc and ft are the compressive and tensile strength, respectively; εc and εt are the peak strain corresponding to fc and ft; E0 is the initial elastic modulus; Ec is the secant elastic modulus corresponding to 0.7fc; ε0 is the compressive strain corresponding to 0.7fc; αc and αt are the parameters controlling the descending branch of the compressive and tensile stress-strain curve, respectively; and n is a constant and taken as n=E0εc/E0εc−fc.Figure 18
Uniaxial constitutive stress vs. strain relations for the CDP model.The damage evolution is determined by the energy equivalence principle [36] as follows:(6)d=1−σE0ε.(2) Materials Concerning the Beam Element. The beam element also includes two types of materials. For the concrete, the Concrete02 material embedded in OpenSees [37], as shown in Figure 19(a), is used; for the rebar, the modified Clough model accounting for the degradation effect [38], as shown in Figure 19(b), is employed.Figure 19
Materials used in the beam element. (a) Concrete02 material. (b) Modified Clough model.
(a)
(b)


#### 4.1.3. Boundary Condition

For convenience, the gravity load acting on the wall pier is assumed to be distributed uniformly. In addition, the actual lateral cyclic displacement obtained in the test is applied at the right end of loading beam. Since the strength degradation is not obvious, as shown in Figure13, only one cycle for each loading level is taken into account. The other boundary conditions are also applied as seen in Figure 17(b).


### 4.2. Analysis Results

#### 4.2.1. Hysteresis Curves

Figure20(a) presents the comparison between the computed hysteresis curve and the experimental one. In addition, the comparison between the corresponding skeleton curves is also made, as shown in Figure 20(b). It can be seen that on the whole, the computed results agree well with the experimental ones, especially in the elastic range. However, obvious discrepancy can be observed between the computed hysteresis curve and the experimental one, and more significant pinching effect can be found on the latter one. It may be resulted from some simplifications employed in the FE model, e.g., the bond slip between the concrete and rebar is ignored.Figure 20
Comparison between the computed curves and experimental ones. (a) Hysteresis curve. (b) Skeleton curve.
(a)
(b)


#### 4.2.2. Damage Status

Figure21 shows the damage status of the specimen at the end of the test. It can be seen that the ED segments of the SCBs at all the three storeys and the boundary elements of the wall piers at the first storey are damaged seriously. However, only minor damages are found on the LB segments of the SCBs. By comparing Figures 9 and 21, it can be found that the simulated results can well replicate the damage status of the specimen.Figure 21
Damage status of the specimen.From the above comparisons between the analysis results and the experimental ones, it can be concluded to some extent that the FE model established herein can be approximately used to simulate seismic performance of the coupled wall with the SCBs. In addition, the FE model has the appealing advantage of high computational efficiency, since only the shell or beam elements instead of the solid elements are used. Therefore, it is very suitably employed to conduct parametric studies related to the coupled wall with the SCBs.


## 4.1. FE Modeling of the Coupled Wall with the SCBs

### 4.1.1. Overall FE Model

The software ABAQUS [33] is used to establish the FE model of the coupled wall with the SCBs. As shown in Figure 17(a), the wall web, the SCB, and the floor beam are all simulated by the layered shell element S4R, and the rebars are added using the rebar layer. In addition, the loading beam and the boundary element of the wall pier are both modeled by the beam element B31, and the rebars are inputted by editing the keyword ∗rebar. The above elements are simply tied together to construct the overall FE model, as shown in Figure 17(b).Figure 17
Overall FE model of the coupled wall with the SCBs. (a) Element selection. (b) ABAQUS model.
(a)
(b)


### 4.1.2. Materials

(1) Materials Concerning the Layered Shell Element. The layered shell element involves two types of materials, i.e., rebar and concrete. For the rebar, the bilinear kinematic hardening model is used. For the concrete, the concrete damaged plastic (CDP) model embedded in ABAQUS [34] is adopted.As shown in Figure18, the following uniaxial compressive and tensile stress vs. strain relations [35] are used respectively for the CDP model:(5)σ=Ecε,ε≤ε0,nε/εcn−1+ε/εcnfc,ε0≤ε≤εc,ε/εcαcε/εc−12+ε/εcfc,ε>εc,σ=E0ε,ε≤εt,ε/εtαtε/εt−11.7+ε/εtft,ε>εt,where fc and ft are the compressive and tensile strength, respectively; εc and εt are the peak strain corresponding to fc and ft; E0 is the initial elastic modulus; Ec is the secant elastic modulus corresponding to 0.7fc; ε0 is the compressive strain corresponding to 0.7fc; αc and αt are the parameters controlling the descending branch of the compressive and tensile stress-strain curve, respectively; and n is a constant and taken as n=E0εc/E0εc−fc.Figure 18
Uniaxial constitutive stress vs. strain relations for the CDP model.The damage evolution is determined by the energy equivalence principle [36] as follows:(6)d=1−σE0ε.(2) Materials Concerning the Beam Element. The beam element also includes two types of materials. For the concrete, the Concrete02 material embedded in OpenSees [37], as shown in Figure 19(a), is used; for the rebar, the modified Clough model accounting for the degradation effect [38], as shown in Figure 19(b), is employed.Figure 19
Materials used in the beam element. (a) Concrete02 material. (b) Modified Clough model.
(a)
(b)


### 4.1.3. Boundary Condition

For convenience, the gravity load acting on the wall pier is assumed to be distributed uniformly. In addition, the actual lateral cyclic displacement obtained in the test is applied at the right end of loading beam. Since the strength degradation is not obvious, as shown in Figure13, only one cycle for each loading level is taken into account. The other boundary conditions are also applied as seen in Figure 17(b).


## 4.1.1. Overall FE Model

The software ABAQUS [33] is used to establish the FE model of the coupled wall with the SCBs. As shown in Figure 17(a), the wall web, the SCB, and the floor beam are all simulated by the layered shell element S4R, and the rebars are added using the rebar layer. In addition, the loading beam and the boundary element of the wall pier are both modeled by the beam element B31, and the rebars are inputted by editing the keyword ∗rebar. The above elements are simply tied together to construct the overall FE model, as shown in Figure 17(b).Figure 17
Overall FE model of the coupled wall with the SCBs. (a) Element selection. (b) ABAQUS model.
(a)
(b)


## 4.1.2. Materials

(1) Materials Concerning the Layered Shell Element. The layered shell element involves two types of materials, i.e., rebar and concrete. For the rebar, the bilinear kinematic hardening model is used. For the concrete, the concrete damaged plastic (CDP) model embedded in ABAQUS [34] is adopted.As shown in Figure18, the following uniaxial compressive and tensile stress vs. strain relations [35] are used respectively for the CDP model:(5)σ=Ecε,ε≤ε0,nε/εcn−1+ε/εcnfc,ε0≤ε≤εc,ε/εcαcε/εc−12+ε/εcfc,ε>εc,σ=E0ε,ε≤εt,ε/εtαtε/εt−11.7+ε/εtft,ε>εt,where fc and ft are the compressive and tensile strength, respectively; εc and εt are the peak strain corresponding to fc and ft; E0 is the initial elastic modulus; Ec is the secant elastic modulus corresponding to 0.7fc; ε0 is the compressive strain corresponding to 0.7fc; αc and αt are the parameters controlling the descending branch of the compressive and tensile stress-strain curve, respectively; and n is a constant and taken as n=E0εc/E0εc−fc.Figure 18
Uniaxial constitutive stress vs. strain relations for the CDP model.The damage evolution is determined by the energy equivalence principle [36] as follows:(6)d=1−σE0ε.(2) Materials Concerning the Beam Element. The beam element also includes two types of materials. For the concrete, the Concrete02 material embedded in OpenSees [37], as shown in Figure 19(a), is used; for the rebar, the modified Clough model accounting for the degradation effect [38], as shown in Figure 19(b), is employed.Figure 19
Materials used in the beam element. (a) Concrete02 material. (b) Modified Clough model.
(a)
(b)


## 4.1.3. Boundary Condition

For convenience, the gravity load acting on the wall pier is assumed to be distributed uniformly. In addition, the actual lateral cyclic displacement obtained in the test is applied at the right end of loading beam. Since the strength degradation is not obvious, as shown in Figure13, only one cycle for each loading level is taken into account. The other boundary conditions are also applied as seen in Figure 17(b).


## 4.2. Analysis Results

### 4.2.1. Hysteresis Curves

Figure20(a) presents the comparison between the computed hysteresis curve and the experimental one. In addition, the comparison between the corresponding skeleton curves is also made, as shown in Figure 20(b). It can be seen that on the whole, the computed results agree well with the experimental ones, especially in the elastic range. However, obvious discrepancy can be observed between the computed hysteresis curve and the experimental one, and more significant pinching effect can be found on the latter one. It may be resulted from some simplifications employed in the FE model, e.g., the bond slip between the concrete and rebar is ignored.Figure 20
Comparison between the computed curves and experimental ones. (a) Hysteresis curve. (b) Skeleton curve.
(a)
(b)


### 4.2.2. Damage Status

Figure21 shows the damage status of the specimen at the end of the test. It can be seen that the ED segments of the SCBs at all the three storeys and the boundary elements of the wall piers at the first storey are damaged seriously. However, only minor damages are found on the LB segments of the SCBs. By comparing Figures 9 and 21, it can be found that the simulated results can well replicate the damage status of the specimen.Figure 21
Damage status of the specimen.From the above comparisons between the analysis results and the experimental ones, it can be concluded to some extent that the FE model established herein can be approximately used to simulate seismic performance of the coupled wall with the SCBs. In addition, the FE model has the appealing advantage of high computational efficiency, since only the shell or beam elements instead of the solid elements are used. Therefore, it is very suitably employed to conduct parametric studies related to the coupled wall with the SCBs.


## 4.2.1. Hysteresis Curves

Figure20(a) presents the comparison between the computed hysteresis curve and the experimental one. In addition, the comparison between the corresponding skeleton curves is also made, as shown in Figure 20(b). It can be seen that on the whole, the computed results agree well with the experimental ones, especially in the elastic range. However, obvious discrepancy can be observed between the computed hysteresis curve and the experimental one, and more significant pinching effect can be found on the latter one. It may be resulted from some simplifications employed in the FE model, e.g., the bond slip between the concrete and rebar is ignored.Figure 20
Comparison between the computed curves and experimental ones. (a) Hysteresis curve. (b) Skeleton curve.
(a)
(b)


## 4.2.2. Damage Status

Figure21 shows the damage status of the specimen at the end of the test. It can be seen that the ED segments of the SCBs at all the three storeys and the boundary elements of the wall piers at the first storey are damaged seriously. However, only minor damages are found on the LB segments of the SCBs. By comparing Figures 9 and 21, it can be found that the simulated results can well replicate the damage status of the specimen.Figure 21
Damage status of the specimen.From the above comparisons between the analysis results and the experimental ones, it can be concluded to some extent that the FE model established herein can be approximately used to simulate seismic performance of the coupled wall with the SCBs. In addition, the FE model has the appealing advantage of high computational efficiency, since only the shell or beam elements instead of the solid elements are used. Therefore, it is very suitably employed to conduct parametric studies related to the coupled wall with the SCBs.


## 5. Parametric Study

### 5.1. Parameters Involved in the Study

Due to the limited number of specimens involved in the test, a comprehensive parametric study on seismic performance of the coupled wall with the SCBs is conducted here utilizing the above proposed FE model. A variety of design parameters, including the axial compressive ratio of the wall pierμN, the concrete strength fc, and especially the sectional height of the SCB hLB/hED, are taken into account, where hLB and hED denote the sectional height of the LB segment and ED segment of the SCB, respectively. The axial compressive ratio of the wall pier is defined as follows:(7)μN=NfcA,where N is the axial force imposed on the wall pier and A is the sectional area. The values of the parameters involved in this study are listed in Table 5.Table 5
Parameter values used in this study.
Parameter
Values
μ
N
0.10
0.20
0.30
h
LB/hED (mm/mm)
275/125
275/175
275/225
f
c (N/mm2)
30
50
70


### 5.2. Results and Discussions

#### 5.2.1. Effect of the Axial Compressive Ratio of the Wall Pier

To investigate the effect of the axial compressive ratio of the wall pier on seismic performance of the coupled wall with the SCBs, its values are varied as listed in Table5. The other parameter values are kept constant as follows: hLB/hED = 275 mm/175 mm and fc = 50 MPa.Figure22 shows the effect of the axial compressive ratio of the wall pier on the hysteresis curves and the corresponding equivalent viscous damping ratio. From Figure 22(a), it can be seen that the strength of the coupled wall increases as the axial compressive ratio increases. However, from Figure 22(b), it can be found that the equivalent viscous damping ratio reduces with the increase of the axial compressive ratio. The above observations show that although the lateral strength of the coupled wall with the SCBs improves with the increase of the axial compressive ratio of the wall pier, its energy-dissipating capacity gets reduced.Figure 22
Effect of the axial compression ratio of the wall pier. (a) Hysteresis curves. (b) Equivalent viscous damping ratio.
(a)
(b)


#### 5.2.2. Effect of the Concrete Strength

To investigate the influence of the concrete strength on seismic performance of the coupling wall with the SCBs, the values of the concrete strength are changed as listed in Table5. The other parameter values are kept as the same as follows: μN = 0.2 and hLB/hED = 275 mm/175 mm.Figure23 shows the effect of the concrete strength on the hysteresis curves and the corresponding equivalent viscous damping ratio. It can be seen that both the strength and the equivalent viscous damping ratio increase on the whole as the concrete strength increases. However, from Figure 23(b), it can be noticed that for a relatively larger displacement amplitude, the equivalent viscous damping ratio decreases with the increase of the concrete strength.Figure 23
Effect of concrete strength. (a) Hysteresis curves. (b) Equivalent viscous damping ratio.
(a)
(b)


#### 5.2.3. Effect of the Sectional Height of the SCB

To study the effect of the sectional height of the SCB on seismic performance of the coupling wall with the SCBs, the values of the sectional height of the SCB are changed according to Table5. The other parameter values remain unchanged as follows: μN = 0.2 and fc = 50 MPa.Figure24 presents the effect of the sectional height of the SCB on the hysteresis curve and the corresponding equivalent viscous damping ratio. Form Figure 24(a), it can be found that as the sectional height of the ED segment increases, the strength of the coupled wall improves obviously. From Figure 24(b), it can be seen that the equivalent viscous damping ratio also increases as the sectional height of the ED segment increases, showing that energy-dissipating capacity of the coupled wall with the SCBs is enhanced.Figure 24
Effect of the sectional heights of the SCB. (a) Hysteresis curves. (b) Equivalent viscous damping ratio.
(a)
(b)To further explore the underlying mechanism, the compressive damage contours of the concrete of the SCB corresponding to different sectional heights of the ED segment are plotted in Figure25. It can be seen that the damage pattern of the SCB changes essentially as the sectional height of the ED segment increases. When the height of the ED segment is close to that of the LB segment, as seen in Figure 25(c), the LB segment also takes part in consuming energy by means of plastic deformations. Consequently, it results in the improvement of energy-dissipating capacity of the coupled wall with the SCBs on the whole. However, this may deviate from the original design philosophy of the SCB, since the LB segment is desired only to support the gravity load while undergoing no or minimal damage.Figure 25
Compressive damage contour of the concrete of the SCB corresponding to different sectional heights. (a) 275/125. (b) 275/175. (c) 275/225.
(a)
(b)
(c)


## 5.1. Parameters Involved in the Study

Due to the limited number of specimens involved in the test, a comprehensive parametric study on seismic performance of the coupled wall with the SCBs is conducted here utilizing the above proposed FE model. A variety of design parameters, including the axial compressive ratio of the wall pierμN, the concrete strength fc, and especially the sectional height of the SCB hLB/hED, are taken into account, where hLB and hED denote the sectional height of the LB segment and ED segment of the SCB, respectively. The axial compressive ratio of the wall pier is defined as follows:(7)μN=NfcA,where N is the axial force imposed on the wall pier and A is the sectional area. The values of the parameters involved in this study are listed in Table 5.Table 5
Parameter values used in this study.
Parameter
Values
μ
N
0.10
0.20
0.30
h
LB/hED (mm/mm)
275/125
275/175
275/225
f
c (N/mm2)
30
50
70


## 5.2. Results and Discussions

### 5.2.1. Effect of the Axial Compressive Ratio of the Wall Pier

To investigate the effect of the axial compressive ratio of the wall pier on seismic performance of the coupled wall with the SCBs, its values are varied as listed in Table5. The other parameter values are kept constant as follows: hLB/hED = 275 mm/175 mm and fc = 50 MPa.Figure22 shows the effect of the axial compressive ratio of the wall pier on the hysteresis curves and the corresponding equivalent viscous damping ratio. From Figure 22(a), it can be seen that the strength of the coupled wall increases as the axial compressive ratio increases. However, from Figure 22(b), it can be found that the equivalent viscous damping ratio reduces with the increase of the axial compressive ratio. The above observations show that although the lateral strength of the coupled wall with the SCBs improves with the increase of the axial compressive ratio of the wall pier, its energy-dissipating capacity gets reduced.Figure 22
Effect of the axial compression ratio of the wall pier. (a) Hysteresis curves. (b) Equivalent viscous damping ratio.
(a)
(b)


### 5.2.2. Effect of the Concrete Strength

To investigate the influence of the concrete strength on seismic performance of the coupling wall with the SCBs, the values of the concrete strength are changed as listed in Table5. The other parameter values are kept as the same as follows: μN = 0.2 and hLB/hED = 275 mm/175 mm.Figure23 shows the effect of the concrete strength on the hysteresis curves and the corresponding equivalent viscous damping ratio. It can be seen that both the strength and the equivalent viscous damping ratio increase on the whole as the concrete strength increases. However, from Figure 23(b), it can be noticed that for a relatively larger displacement amplitude, the equivalent viscous damping ratio decreases with the increase of the concrete strength.Figure 23
Effect of concrete strength. (a) Hysteresis curves. (b) Equivalent viscous damping ratio.
(a)
(b)


### 5.2.3. Effect of the Sectional Height of the SCB

To study the effect of the sectional height of the SCB on seismic performance of the coupling wall with the SCBs, the values of the sectional height of the SCB are changed according to Table5. The other parameter values remain unchanged as follows: μN = 0.2 and fc = 50 MPa.Figure24 presents the effect of the sectional height of the SCB on the hysteresis curve and the corresponding equivalent viscous damping ratio. Form Figure 24(a), it can be found that as the sectional height of the ED segment increases, the strength of the coupled wall improves obviously. From Figure 24(b), it can be seen that the equivalent viscous damping ratio also increases as the sectional height of the ED segment increases, showing that energy-dissipating capacity of the coupled wall with the SCBs is enhanced.Figure 24
Effect of the sectional heights of the SCB. (a) Hysteresis curves. (b) Equivalent viscous damping ratio.
(a)
(b)To further explore the underlying mechanism, the compressive damage contours of the concrete of the SCB corresponding to different sectional heights of the ED segment are plotted in Figure25. It can be seen that the damage pattern of the SCB changes essentially as the sectional height of the ED segment increases. When the height of the ED segment is close to that of the LB segment, as seen in Figure 25(c), the LB segment also takes part in consuming energy by means of plastic deformations. Consequently, it results in the improvement of energy-dissipating capacity of the coupled wall with the SCBs on the whole. However, this may deviate from the original design philosophy of the SCB, since the LB segment is desired only to support the gravity load while undergoing no or minimal damage.Figure 25
Compressive damage contour of the concrete of the SCB corresponding to different sectional heights. (a) 275/125. (b) 275/175. (c) 275/225.
(a)
(b)
(c)


## 5.2.1. Effect of the Axial Compressive Ratio of the Wall Pier

To investigate the effect of the axial compressive ratio of the wall pier on seismic performance of the coupled wall with the SCBs, its values are varied as listed in Table5. The other parameter values are kept constant as follows: hLB/hED = 275 mm/175 mm and fc = 50 MPa.Figure22 shows the effect of the axial compressive ratio of the wall pier on the hysteresis curves and the corresponding equivalent viscous damping ratio. From Figure 22(a), it can be seen that the strength of the coupled wall increases as the axial compressive ratio increases. However, from Figure 22(b), it can be found that the equivalent viscous damping ratio reduces with the increase of the axial compressive ratio. The above observations show that although the lateral strength of the coupled wall with the SCBs improves with the increase of the axial compressive ratio of the wall pier, its energy-dissipating capacity gets reduced.Figure 22
Effect of the axial compression ratio of the wall pier. (a) Hysteresis curves. (b) Equivalent viscous damping ratio.
(a)
(b)


## 5.2.2. Effect of the Concrete Strength

To investigate the influence of the concrete strength on seismic performance of the coupling wall with the SCBs, the values of the concrete strength are changed as listed in Table5. The other parameter values are kept as the same as follows: μN = 0.2 and hLB/hED = 275 mm/175 mm.Figure23 shows the effect of the concrete strength on the hysteresis curves and the corresponding equivalent viscous damping ratio. It can be seen that both the strength and the equivalent viscous damping ratio increase on the whole as the concrete strength increases. However, from Figure 23(b), it can be noticed that for a relatively larger displacement amplitude, the equivalent viscous damping ratio decreases with the increase of the concrete strength.Figure 23
Effect of concrete strength. (a) Hysteresis curves. (b) Equivalent viscous damping ratio.
(a)
(b)


## 5.2.3. Effect of the Sectional Height of the SCB

To study the effect of the sectional height of the SCB on seismic performance of the coupling wall with the SCBs, the values of the sectional height of the SCB are changed according to Table5. The other parameter values remain unchanged as follows: μN = 0.2 and fc = 50 MPa.Figure24 presents the effect of the sectional height of the SCB on the hysteresis curve and the corresponding equivalent viscous damping ratio. Form Figure 24(a), it can be found that as the sectional height of the ED segment increases, the strength of the coupled wall improves obviously. From Figure 24(b), it can be seen that the equivalent viscous damping ratio also increases as the sectional height of the ED segment increases, showing that energy-dissipating capacity of the coupled wall with the SCBs is enhanced.Figure 24
Effect of the sectional heights of the SCB. (a) Hysteresis curves. (b) Equivalent viscous damping ratio.
(a)
(b)To further explore the underlying mechanism, the compressive damage contours of the concrete of the SCB corresponding to different sectional heights of the ED segment are plotted in Figure25. It can be seen that the damage pattern of the SCB changes essentially as the sectional height of the ED segment increases. When the height of the ED segment is close to that of the LB segment, as seen in Figure 25(c), the LB segment also takes part in consuming energy by means of plastic deformations. Consequently, it results in the improvement of energy-dissipating capacity of the coupled wall with the SCBs on the whole. However, this may deviate from the original design philosophy of the SCB, since the LB segment is desired only to support the gravity load while undergoing no or minimal damage.Figure 25
Compressive damage contour of the concrete of the SCB corresponding to different sectional heights. (a) 275/125. (b) 275/175. (c) 275/225.
(a)
(b)
(c)


## 6. Conclusions

In this paper, one scaled RC coupled wall specimen with the proposed SCBs is tested under cyclic loading. Subsequently, the FE analysis model of the coupled wall with the SCBs is proposed and verified by comparing the analysis results with the experimental ones. Finally, the parametric study is conducted to investigate various design parameters on seismic performance of the coupled wall with the SCBs. Based on the findings in this study, the following conclusions can be drawn:(1)
At the end of the test, a large quantity of cracks concentrate at the ED segment of the SCB while only a few cracks occur at the LB segment, showing that the ED segment plays a primary role in energy dissipation. In addition, the maximum roof drift is about 1/40, showing that the coupled wall specimen with the SCBs has an excellent deformation capacity.(2)
During the loading, the ED segment of the SCB yields first and works as the first defense, whereas the LB segment yields much later. It shows that the LB segment of the SCB can always reliably support the gravity load transferred from the floor beam.(3)
The numerical analysis model of the RC coupled wall specimen proposed in this paper has an appealing advantage of both high computational accuracy and efficiency. It can be further used to perform numerical analysis of the framed core tube structure employing the RC coupled wall with the SCBs. It can be of great significance in performing numerical analysis of the framed core tube structure employing the RC coupled wall with the SCBs.(4)
As the axial compressive ratio of the wall pier increases, the strength of the coupled wall with the SCBs increases while the energy dissipating capacity decreases. In addition, the strength of the coupled wall also increases as the concrete strength increases. Besides, as the sectional height of the ED segment increases, the energy-dissipating capacity of the coupled wall may improve, whereas the ability of supporting the gravity load is reduced.However, due to the limited number of test specimens involved in this study, there are still some studies, especially regarding the design approach and detailing requirements of the proposed SCB, to be further conducted in the future.



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*Source: 1520375-2019-06-03.xml*