# Insight into the Effect of Adhesive Interface on the Ultimate Capacity of the Double-Superposed Shear Wall

Authors: Wenying Zhang; Lianping Yang; Shaole Yu; Xinxi Chen; Xuewei Zhang
Journal: Advances in Civil Engineering
 (2018)

---

## Abstract

This paper presents the results of a numerical and analytical study to investigate the effect of adhesive interface on the ultimate capacity of a new composite sandwich shear wall: double-superposed shear wall. The effect of adhesive interface on the ultimate capacity of two different wall configurations under different axial compression ratios was studied. The results indicate that, for the two different wall configurations, the bond strength of adhesive interface has a negligible effect on ultimate bearing capacity. As a result of the different intensity grades between cast-in-situ concrete wythe and precast concrete wythe, the double-superposed shear wall with precast boundary elements (wall configuration W3) yields a higher ultimate bearing capacity than that with cast-in-place boundary elements (wall configuration W2), when the axial compression ratio exceeds 0.2, which is contrary to the results under 0.1 axial compression ratio. A new calculation method for ultimate bearing capacity is proposed to take into account the different intensity grades, and the calculation results show a very good agreement with the numerical simulation results.


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## Body

## 1. Introduction

Sandwich structures are layered structural components made up of thin strong exterior and interior precast concrete panels, called wythes, separated by a layer of rigid foam as core materials. The concept behind sandwich construction is that the skins carry the in-plane compressive and tensile stresses resulting from the induced bending moment, while the main function of the lightweight core is to keep the two skins apart, at a desired distance, and also to resist and transmit shear forces to the supporting points [1]. The general concept of sandwich structures has been investigated and developed by many researchers over the past 50 years, and a lot of theoretical analyses and experiments have been done on the sandwich structures, see for instance, Huang et al. [2], Hodicky et al. [3], Gay and Hoa [4], Benayoune et al. [5], Mahendran and Subaaharan [6], Gara et al. [7], and Abdul Hamid and Fudzee [8]. The shear wall structure, with high capacity and lateral stiffness, is an ideal lateral force-resisting structure in high-rise buildings. Therefore, engineers are searching for a new shear wall system that could combine the sandwich structure technology together with the shear wall structure, which is to form a new composite sandwich shear wall—“double-superposed shear wall.” As illustrated in Figure 1, the double-superposed shear wall is a three-wythe element, usually comprising thin wythes with high-strength concrete, which were prefabricated in factory. The two precast wythes are bonded by a truss connector, and a thicker core wythe was filled with lower strength concrete at the construction site. Lap splices are utilized at the horizontal connections which incorporate a 50 mm thick gap between upper and lower panels filled with concrete to make the integrity at the connection. Several experimental studies show the good performance in terms of bearing capacity of the superposed shear wall subjected to axial and lateral loads [9–12]. But, there is little focus on the behavior of adhesive interface between the precast wythes and the core. It has been observed that, under service loads, most sandwich constructions fail due to shear failure of the core or due to disbonding of the skins from the core [13–15]. The double-superposed shear wall is utilized as load-bearing structural elements, and the failure of adhesion between the core and precast wythes can be catastrophic. The research project will conduct a detailed numerical investigation to provide insight into the mechanism of adhesive interface between precast concrete wythes and the inner concrete core wythe and develop an improved calculation method for the ultimate capacity of the double-superposed shear wall.Figure 1
Configuration of the superposed shear wall: (a) cross section forms; (b) lap splice bars across horizontal joints; (c) truss connector.
(a)
(b)
(c)


## 2. Validation of the Finite Element (FE) Simulation Model

### 2.1. General

The numerical simulations of this research were carried out based on the commercial finite element package ABAQUS. Experimental data of Lian et al. [12] were used for validation of the FE simulation model. Figure 2 shows the test setup of [12] schematically. Two different wall configurations were investigated in the test. Figure 3 shows the dimension and details of the double-superposed shear wall. Wall configuration W2 consists of two precast panels with the dimension of 3000 (h) × 1000 (w) × 50 (t) mm, while the boundary elements are poured simultaneously with the core concrete, and U-shaped steel bars are utilized at the vertical connections. Wall configuration W3 consists of two precast panels with the dimension of 3000 (h) × 1800 (w) × 50 (t) mm, with a 3000 (h) × 1800 (w) × 100 (t) mm concrete panel in the core. Cast-in-situ concrete with strength grade of C30 and the precast wall panel intensity rating C35/45 came from the German Silwade Company. The bearing steel inside the precast wall panels is BSt500. Tables 1 and 2 show the mechanical properties of the major materials.Figure 2
Test setup.Figure 3
The dimension and details of the double-superposed shear wall: (a) W2 and (b) W3.
(a)
(b)Table 1
Cubic compressive strength of concrete (MPa).
Strength grade
Specimen 1
Specimen 1
Specimen 1
Average
C30
29.4
29.8
30.7
30.3
German C35/45
53
53
53
53Table 2
Steel mechanical properties.
Diameter (mm)
Grade
Yield strength (MPa)
Ultimate strength (MPa)
Elongation (%)
8
BSt500
589.2
638.9
9.5
10
BSt500
560.5
603.8
15.5


### 2.2. Material Model for the Steel Bar

An idealized double-linear stress-strain curve is employed to model the steel bar. As shown in Figure4, fy is the yield stress of the steel bar, εy is the yield strain of the steel bar, fu is the ultimate stress of the steel bar, and εu is the ultimate strain of the steel bar. The Von Mises yield criterion with associated plastic flow available in ABAQUS was used. Poisson’s ratio and Young’s modulus were assumed to be 0.3 and 200 Gpa. The ultimate strain of steel εu was assumed to be 0.2.Figure 4
Stress-strain curve of the steel bar.


### 2.3. Material Model for the Concrete

In the double-superposed shear wall, the boundary elements are confined by the stirrup, which results in increased ductility and strength of the confined concrete compared to the unconfined concrete. In this research, the Kent-Park model is adopted for the simulations. As shown in Figure5, fc is the compressive strength of unconfined concrete and εc is the strain corresponding to fc. fcc and εcc are the corresponding values of confined concrete. fcc and εcc should be determined in accordance with the following:(1)fcc=Kfc, (2)εcc=0.002K, (3)K=1+ρsfyhfc,where ρs is the stirrup ratio and fyh is the yield strength of stirrup.Figure 5
Kent-Park model.


### 2.4. Boundary Conditions and Load Application

Finite element models of the two different wall configurations W2 and W3 were constructed and shown in Figures6 and 7, respectively. In the experimental test, 730 kN force was axially loaded at the top of the wall through a steel spreader beam which was attached to the loading beam on the wall, and the horizontal load is low cycle repeated loading, which is applied through the load beam. In the FEA model, the applied loads on the wall were simulated in two load steps: in the first step, a vertical concentrated force was applied at a “reference node” located at the center of the loading beam to represent the applied vertical load on the wall; in the second step, the monotonic load (using displacement control) was applied onto the “reference node,” which is substituted as the low cycle repeated load to reduce computational complexity and put more focus on the adhesion between the core and precast wythes. The foundation at the wall base was fixed in all six directions. The connection between the load beam and the wall was simulated using “tie” constraints, and the same constraints were used between the foundation and the wall.Figure 6
Finite element model of W2.
(a)
(b)Figure 7
Finite element model of W3.
(a)
(b)


### 2.5. Finite Element Type and Mesh

Three-dimensional 2-node truss elements (T3D2) were used to model the steel bar so that material yield could be accurately followed. The concrete was modelled using three-dimensional 8-node solid elements (C3D8). A mesh size of 150 mm and 100 mm was employed for modelling the concrete in height direction and width direction, and a size of 20 mm was used for the steel bar. The meshes at the contacting surfaces were matched in order to obtain the best accuracy in contact analysis.


### 2.6. Contact between the Interface of Outer Precast Concrete and Core Concrete

The adhesion between the core and precast wythes can be classified as the issue of bond between new and old concrete, and the load-slip behavior at the interface of new and old concrete has been investigated by many researchers using the push-out test. Hanson [16] performed 62 push-off tests in concrete elements to establish a common basis of comparison between various contact surfaces in the push-off tests, and the nature of failure in these tests is illustrated by the shear-slip curves in Figure 8. Papanicolaou and Triantafillou [17] presented an experimental investigation on the behavior of interfaces between pumice LWAC (lightweight aggregate concrete) and HPC (high-performance concrete with high strength and fiber-reinforced), and typical stress-slip curves are given in Figure 9. Based on these graphs, the stress-slip relationship can be estimated by two straight lines as shown in Figure 10. To model the interaction behavior between the core and precast wythes in ABAQUS, the cohesive property interaction to define the debonding behavior between the two interfaces is utilized. The node-to-surface interaction contact pairs available in ABAQUS were employed to model the interaction between the interfaces. For the interaction between the precast wythes and core wythe, the core wythe was utilized as a master surface and the precast wythe as slave surfaces. The meshes at the contacting surfaces were matched to expedite the convergence of the FE model. The mechanical contact property model assumes an initial linear elastic behavior followed by the initiation and evolution of damage. Once the damage criterion is met, the delamination of the bonded surfaces can be defined by a user-defined damage evolution law. Therefore, the three parameters, as shown in Figure 10, the initial stiffness, the value of the softened contact relationship slope, and the maximum bond stress need calibrating against experiments in order to define the contact model.Figure 8
Typical shear-slip curves from Hanson [16].Figure 9
Typical shear-slip curves from Papanicolaou and Triantafillou [17].Figure 10
Typical traction-separation behavior adopted in the simulations.An elastic constitutive matrix was utilized to relate the normal and tangential shear stresses to the normal and tangential separations across the interface. The nominal traction stress vectorτ consists of three components: τn, τs, and τt, which refer to the normal and tangential directions, respectively, as shown in Figure 11. The corresponding separations are denoted by δn, δs, and δt. The elastic behavior can then be written as [18](4)τ=τnτsτt=KnnKnsKntKnsKssKstKntKstKttδnδsδt=Kδ.Figure 11
Description of normal and tangential directions.Damage modelling is required to simulate degradation and progressive failure of the adhesive interface bond between the core and precast wythes. The criterion for damage initiation has been defined based on maximum nominal stress values at the interface. Damage is assumed to initiate when the maximum contact stress ratio reaches a value of one. This criterion can be represented as(5)maxτnτn0,τsτs0,τtτt0=1,where τn0, τs0, and τt0 are the maximum stresses in the normal and tangential directions. In this investigation, it is assumed that τs0=τt0.The maximum bond stressτs0=τt0 depends on many factors [19–24], such as concrete strength, roughness of the interface, normal stress, and the planted reinforced bar at the interface; moreover, the bond stress values are different based on different design codes. Therefore, different values were used for the maximum bond stress, according to the different design codes, to further investigate the influence of bond strength on ultimate capacity of the double-superposed shear wall. In the normal direction, ABAQUS “hard contact” behavior is defined at the interface between the precast wythes and the core concrete wythe; this means that the resistance to contact pressure is infinite, and they cannot penetrate into each other. However, they are allowed to separate. The maximum bond stress in normal direction is defined as τn0, and the tensile strength of lower strength concrete was employed to define the normal stress values.


#### 2.6.1. Influence of the Initial Stiffness (K)

The initial stiffnessK is required to define the contact property model of the interface between the core and precast concrete wythes, as shown in Figure 10. The initial stiffness in the tangential directions has a significant effect on the behavior of interface; therefore, a sensitivity study was conducted to investigate the influence of the initial stiffness in the tangential directions on the simulation results. The test results of Lian et al. [12] are compared with the simulation results using initial stiffness values ranging from 20 N/mm3 to 200 N/mm3, as shown in Figure 12. The results show that, for the two different wall configurations (W2 and W3), the load-displacement curves were almost the same for K ranging from 20 N/mm3 to 200 N/mm3. Therefore, the average value of 100 N/mm3 was chosen for the initial stiffness in the tangential directions in later analysis. The effect of initial stiffness in the normal direction is negligible, and the same value as in the tangential directions was assigned to the stiffness in the normal direction in order to quicken the convergent speed in FE analysis.Figure 12
Initial stiffness sensitivity analysis: (a) W2 and (b) W3.
(a)
(b)


#### 2.6.2. Influence of the Slope (α)

The value of slopeα is also needed to define the traction-separation model. As shown in Figures 8 and 9, the bond stress decreased with a very low negative stiffness after the peak point. A sensitivity study was conducted to investigate the influence of using different values, as shown in Figure 13. The results show that, for the two different wall configurations (W2 and W3), the load-displacement curves were almost the same for α ranging from 8° to 23°. Therefore, the average value of 15.5° was chosen for the slope in later analysis.Figure 13
Slope angle sensitivity analysis: (a) W2 and (b) W3.
(a)
(b)


#### 2.6.3. Influence of the Maximum Bond Stress

As the bond stressesτn0 and τs0 are influenced by multitudinous factors, the bond stress values are different which were calculated by different design codes. Therefore, the effects of adopting different values of the maximum bond stress were investigated. Available expressions of the most important design codes [25–29] of concrete structures for the bond stress in the interface, which are based on the shear-friction theory, were summarized in Table 3. The test results of Lian et al. [12] are compared with the simulation results using different bond stress values, as shown in Figure 14. The results show that, for the two different wall configurations (W2 and W3), the load-displacement curves were almost the same for the bond stresses τn0 and τs0 ranging from 0.77 MPa to 2.52 MPa. It can be concluded that the bond strength has a negligible effect on ultimate bearing capacity of the double-superposed shear wall under 0.1 axial compression ratio.Table 3
Design expressions of different design codes to calculate the bond strength.
Design code
Design expression
Bond stress
W2 (MPa)
W3 (MPa)
ACI 318 [25]
τ
u
=
ρ
f
y
μ
sin
α
+
cos
α
f
y
≤
414
MPa
0.77
0.86
BS 8110-1 [26]
τ
u
=
0.6
F
b
ρ
tan
α
1.04
1.15
PCI Design Handbook [27]
τ
u
=
ϕ
ρ
f
y
μ
e
f
y
≤
414
MPa
1.19
1.32
CEB-FIP model code [28]
τ
u
=
c
f
ctd
+
μ
σ
n
+
ρ
f
y
sin
α
+
cos
α
1.95
2.06
AASHTO LRFD bridge design specifications [29]
τ
u
=
c
+
μ
ρ
f
y
+
σ
n
2.44
2.52Figure 14
Comparison of simulated and experimental response: (a) W2 and (b) W3.
(a)
(b)


#### 2.6.4. Overall Comparison between Simulation and Test Results

The simulation results were compared with the test results based on the ultimate bearing capacity, as shown in Table4. Fairly consistent agreement is found between the simulation results and the test results with the maximum difference being 1%.Table 4
Comparison of ultimate bearing capacity between experiments and FE simulation using different bond stress values based on different design codes.
Design code
W2
W3
TestFtest (kN)
FE simulationFFE (kN)
F
FE
/
F
test
TestFtest (kN)
FE simulationFFE (kN)
F
FE
/
F
test
ACI 318 [25]
429
425.7
0.99
412
409.8
0.99
BS 8110-1 [26]
429
424.6
0.99
412
408.4
0.99
PCI Design Handbook [27]
429
424.9
0.99
412
414.7
1
CEB-FIP model code [28]
429
429.3
1
412
408.7
0.99
AASHTO LRFD bridge design specifications [29]
429
424.7
0.99
412
409.2
0.99For the two different wall configurations W2 and W3, the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast wythes is shown in Figures15 and 16, respectively. The value of CSMAXSCR exceeding the critical value (one) indicates the adhesive interface debonding. In Figures 15 and 16, the letters (a) to (e) mean the results of the bond stress values ranging from 0.77 MPa to 2.52 MPa; number 1 indicates the adhesive interface between the outer precast wythe and core wythe, and number 2 indicates the adhesive interface between the inner precast wythe and core wythe. It has been found that, for the two different wall configurations W2 and W3, the contact stress of the interfaces between the core and precast wythes exceeds the critical value (one). It indicated the debonding of the core and precast wythes; however, the debonding area is only on a small scale at the bottom, and the debonding scale becomes smaller with the increase in bond stress value. The debonding is caused by the crushing of the bottom concrete of the end column which is subjected to combined axial forces, moment, and shear. Two reference points in different positions of the adhesive interface are selected to compare the variation of CSMAXSCR with top displacement. The variation of CSMAXSCR with top displacement is shown in Figures 17 and 18, respectively. It has been found that the value of CSMAXSCR decreases with the increase in bond strength value. The debonding scale of W3 is wider than that of W2, and it is deduced that the boundary elements casted simultaneously with the core concrete provide a strong constraint to improve the structural integrity. The maximum value of CSMAXSCR at reference point 2 is no more than 0.3 for the two different wall configurations W2 and W3, indicating that the debonding scale is relatively small. It can be concluded that the adhesive interface has a good bonding condition with a truss connector under 0.1 axial compression ratio, which is in agreement with the experimental observations.Figure 15
Maximum traction damage initiation criterion index CSMAXSCR of W2.Figure 16
Maximum traction damage initiation criterion index CSMAXSCR of W3.Figure 17
CSMAXSCR-top displacement curves of W2.Figure 18
CSMAXSCR-top displacement curves of W3.In conclusion, the ABAQUS simulation model is suitable, and the adhesive interface has a negligible effect on ultimate bearing capacity of the double-superposed shear wall under 0.1 axial compression ratio.


## 2.1. General

The numerical simulations of this research were carried out based on the commercial finite element package ABAQUS. Experimental data of Lian et al. [12] were used for validation of the FE simulation model. Figure 2 shows the test setup of [12] schematically. Two different wall configurations were investigated in the test. Figure 3 shows the dimension and details of the double-superposed shear wall. Wall configuration W2 consists of two precast panels with the dimension of 3000 (h) × 1000 (w) × 50 (t) mm, while the boundary elements are poured simultaneously with the core concrete, and U-shaped steel bars are utilized at the vertical connections. Wall configuration W3 consists of two precast panels with the dimension of 3000 (h) × 1800 (w) × 50 (t) mm, with a 3000 (h) × 1800 (w) × 100 (t) mm concrete panel in the core. Cast-in-situ concrete with strength grade of C30 and the precast wall panel intensity rating C35/45 came from the German Silwade Company. The bearing steel inside the precast wall panels is BSt500. Tables 1 and 2 show the mechanical properties of the major materials.Figure 2
Test setup.Figure 3
The dimension and details of the double-superposed shear wall: (a) W2 and (b) W3.
(a)
(b)Table 1
Cubic compressive strength of concrete (MPa).
Strength grade
Specimen 1
Specimen 1
Specimen 1
Average
C30
29.4
29.8
30.7
30.3
German C35/45
53
53
53
53Table 2
Steel mechanical properties.
Diameter (mm)
Grade
Yield strength (MPa)
Ultimate strength (MPa)
Elongation (%)
8
BSt500
589.2
638.9
9.5
10
BSt500
560.5
603.8
15.5


## 2.2. Material Model for the Steel Bar

An idealized double-linear stress-strain curve is employed to model the steel bar. As shown in Figure4, fy is the yield stress of the steel bar, εy is the yield strain of the steel bar, fu is the ultimate stress of the steel bar, and εu is the ultimate strain of the steel bar. The Von Mises yield criterion with associated plastic flow available in ABAQUS was used. Poisson’s ratio and Young’s modulus were assumed to be 0.3 and 200 Gpa. The ultimate strain of steel εu was assumed to be 0.2.Figure 4
Stress-strain curve of the steel bar.


## 2.3. Material Model for the Concrete

In the double-superposed shear wall, the boundary elements are confined by the stirrup, which results in increased ductility and strength of the confined concrete compared to the unconfined concrete. In this research, the Kent-Park model is adopted for the simulations. As shown in Figure5, fc is the compressive strength of unconfined concrete and εc is the strain corresponding to fc. fcc and εcc are the corresponding values of confined concrete. fcc and εcc should be determined in accordance with the following:(1)fcc=Kfc, (2)εcc=0.002K, (3)K=1+ρsfyhfc,where ρs is the stirrup ratio and fyh is the yield strength of stirrup.Figure 5
Kent-Park model.


## 2.4. Boundary Conditions and Load Application

Finite element models of the two different wall configurations W2 and W3 were constructed and shown in Figures6 and 7, respectively. In the experimental test, 730 kN force was axially loaded at the top of the wall through a steel spreader beam which was attached to the loading beam on the wall, and the horizontal load is low cycle repeated loading, which is applied through the load beam. In the FEA model, the applied loads on the wall were simulated in two load steps: in the first step, a vertical concentrated force was applied at a “reference node” located at the center of the loading beam to represent the applied vertical load on the wall; in the second step, the monotonic load (using displacement control) was applied onto the “reference node,” which is substituted as the low cycle repeated load to reduce computational complexity and put more focus on the adhesion between the core and precast wythes. The foundation at the wall base was fixed in all six directions. The connection between the load beam and the wall was simulated using “tie” constraints, and the same constraints were used between the foundation and the wall.Figure 6
Finite element model of W2.
(a)
(b)Figure 7
Finite element model of W3.
(a)
(b)


## 2.5. Finite Element Type and Mesh

Three-dimensional 2-node truss elements (T3D2) were used to model the steel bar so that material yield could be accurately followed. The concrete was modelled using three-dimensional 8-node solid elements (C3D8). A mesh size of 150 mm and 100 mm was employed for modelling the concrete in height direction and width direction, and a size of 20 mm was used for the steel bar. The meshes at the contacting surfaces were matched in order to obtain the best accuracy in contact analysis.


## 2.6. Contact between the Interface of Outer Precast Concrete and Core Concrete

The adhesion between the core and precast wythes can be classified as the issue of bond between new and old concrete, and the load-slip behavior at the interface of new and old concrete has been investigated by many researchers using the push-out test. Hanson [16] performed 62 push-off tests in concrete elements to establish a common basis of comparison between various contact surfaces in the push-off tests, and the nature of failure in these tests is illustrated by the shear-slip curves in Figure 8. Papanicolaou and Triantafillou [17] presented an experimental investigation on the behavior of interfaces between pumice LWAC (lightweight aggregate concrete) and HPC (high-performance concrete with high strength and fiber-reinforced), and typical stress-slip curves are given in Figure 9. Based on these graphs, the stress-slip relationship can be estimated by two straight lines as shown in Figure 10. To model the interaction behavior between the core and precast wythes in ABAQUS, the cohesive property interaction to define the debonding behavior between the two interfaces is utilized. The node-to-surface interaction contact pairs available in ABAQUS were employed to model the interaction between the interfaces. For the interaction between the precast wythes and core wythe, the core wythe was utilized as a master surface and the precast wythe as slave surfaces. The meshes at the contacting surfaces were matched to expedite the convergence of the FE model. The mechanical contact property model assumes an initial linear elastic behavior followed by the initiation and evolution of damage. Once the damage criterion is met, the delamination of the bonded surfaces can be defined by a user-defined damage evolution law. Therefore, the three parameters, as shown in Figure 10, the initial stiffness, the value of the softened contact relationship slope, and the maximum bond stress need calibrating against experiments in order to define the contact model.Figure 8
Typical shear-slip curves from Hanson [16].Figure 9
Typical shear-slip curves from Papanicolaou and Triantafillou [17].Figure 10
Typical traction-separation behavior adopted in the simulations.An elastic constitutive matrix was utilized to relate the normal and tangential shear stresses to the normal and tangential separations across the interface. The nominal traction stress vectorτ consists of three components: τn, τs, and τt, which refer to the normal and tangential directions, respectively, as shown in Figure 11. The corresponding separations are denoted by δn, δs, and δt. The elastic behavior can then be written as [18](4)τ=τnτsτt=KnnKnsKntKnsKssKstKntKstKttδnδsδt=Kδ.Figure 11
Description of normal and tangential directions.Damage modelling is required to simulate degradation and progressive failure of the adhesive interface bond between the core and precast wythes. The criterion for damage initiation has been defined based on maximum nominal stress values at the interface. Damage is assumed to initiate when the maximum contact stress ratio reaches a value of one. This criterion can be represented as(5)maxτnτn0,τsτs0,τtτt0=1,where τn0, τs0, and τt0 are the maximum stresses in the normal and tangential directions. In this investigation, it is assumed that τs0=τt0.The maximum bond stressτs0=τt0 depends on many factors [19–24], such as concrete strength, roughness of the interface, normal stress, and the planted reinforced bar at the interface; moreover, the bond stress values are different based on different design codes. Therefore, different values were used for the maximum bond stress, according to the different design codes, to further investigate the influence of bond strength on ultimate capacity of the double-superposed shear wall. In the normal direction, ABAQUS “hard contact” behavior is defined at the interface between the precast wythes and the core concrete wythe; this means that the resistance to contact pressure is infinite, and they cannot penetrate into each other. However, they are allowed to separate. The maximum bond stress in normal direction is defined as τn0, and the tensile strength of lower strength concrete was employed to define the normal stress values.


### 2.6.1. Influence of the Initial Stiffness (K)

The initial stiffnessK is required to define the contact property model of the interface between the core and precast concrete wythes, as shown in Figure 10. The initial stiffness in the tangential directions has a significant effect on the behavior of interface; therefore, a sensitivity study was conducted to investigate the influence of the initial stiffness in the tangential directions on the simulation results. The test results of Lian et al. [12] are compared with the simulation results using initial stiffness values ranging from 20 N/mm3 to 200 N/mm3, as shown in Figure 12. The results show that, for the two different wall configurations (W2 and W3), the load-displacement curves were almost the same for K ranging from 20 N/mm3 to 200 N/mm3. Therefore, the average value of 100 N/mm3 was chosen for the initial stiffness in the tangential directions in later analysis. The effect of initial stiffness in the normal direction is negligible, and the same value as in the tangential directions was assigned to the stiffness in the normal direction in order to quicken the convergent speed in FE analysis.Figure 12
Initial stiffness sensitivity analysis: (a) W2 and (b) W3.
(a)
(b)


### 2.6.2. Influence of the Slope (α)

The value of slopeα is also needed to define the traction-separation model. As shown in Figures 8 and 9, the bond stress decreased with a very low negative stiffness after the peak point. A sensitivity study was conducted to investigate the influence of using different values, as shown in Figure 13. The results show that, for the two different wall configurations (W2 and W3), the load-displacement curves were almost the same for α ranging from 8° to 23°. Therefore, the average value of 15.5° was chosen for the slope in later analysis.Figure 13
Slope angle sensitivity analysis: (a) W2 and (b) W3.
(a)
(b)


### 2.6.3. Influence of the Maximum Bond Stress

As the bond stressesτn0 and τs0 are influenced by multitudinous factors, the bond stress values are different which were calculated by different design codes. Therefore, the effects of adopting different values of the maximum bond stress were investigated. Available expressions of the most important design codes [25–29] of concrete structures for the bond stress in the interface, which are based on the shear-friction theory, were summarized in Table 3. The test results of Lian et al. [12] are compared with the simulation results using different bond stress values, as shown in Figure 14. The results show that, for the two different wall configurations (W2 and W3), the load-displacement curves were almost the same for the bond stresses τn0 and τs0 ranging from 0.77 MPa to 2.52 MPa. It can be concluded that the bond strength has a negligible effect on ultimate bearing capacity of the double-superposed shear wall under 0.1 axial compression ratio.Table 3
Design expressions of different design codes to calculate the bond strength.
Design code
Design expression
Bond stress
W2 (MPa)
W3 (MPa)
ACI 318 [25]
τ
u
=
ρ
f
y
μ
sin
α
+
cos
α
f
y
≤
414
MPa
0.77
0.86
BS 8110-1 [26]
τ
u
=
0.6
F
b
ρ
tan
α
1.04
1.15
PCI Design Handbook [27]
τ
u
=
ϕ
ρ
f
y
μ
e
f
y
≤
414
MPa
1.19
1.32
CEB-FIP model code [28]
τ
u
=
c
f
ctd
+
μ
σ
n
+
ρ
f
y
sin
α
+
cos
α
1.95
2.06
AASHTO LRFD bridge design specifications [29]
τ
u
=
c
+
μ
ρ
f
y
+
σ
n
2.44
2.52Figure 14
Comparison of simulated and experimental response: (a) W2 and (b) W3.
(a)
(b)


### 2.6.4. Overall Comparison between Simulation and Test Results

The simulation results were compared with the test results based on the ultimate bearing capacity, as shown in Table4. Fairly consistent agreement is found between the simulation results and the test results with the maximum difference being 1%.Table 4
Comparison of ultimate bearing capacity between experiments and FE simulation using different bond stress values based on different design codes.
Design code
W2
W3
TestFtest (kN)
FE simulationFFE (kN)
F
FE
/
F
test
TestFtest (kN)
FE simulationFFE (kN)
F
FE
/
F
test
ACI 318 [25]
429
425.7
0.99
412
409.8
0.99
BS 8110-1 [26]
429
424.6
0.99
412
408.4
0.99
PCI Design Handbook [27]
429
424.9
0.99
412
414.7
1
CEB-FIP model code [28]
429
429.3
1
412
408.7
0.99
AASHTO LRFD bridge design specifications [29]
429
424.7
0.99
412
409.2
0.99For the two different wall configurations W2 and W3, the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast wythes is shown in Figures15 and 16, respectively. The value of CSMAXSCR exceeding the critical value (one) indicates the adhesive interface debonding. In Figures 15 and 16, the letters (a) to (e) mean the results of the bond stress values ranging from 0.77 MPa to 2.52 MPa; number 1 indicates the adhesive interface between the outer precast wythe and core wythe, and number 2 indicates the adhesive interface between the inner precast wythe and core wythe. It has been found that, for the two different wall configurations W2 and W3, the contact stress of the interfaces between the core and precast wythes exceeds the critical value (one). It indicated the debonding of the core and precast wythes; however, the debonding area is only on a small scale at the bottom, and the debonding scale becomes smaller with the increase in bond stress value. The debonding is caused by the crushing of the bottom concrete of the end column which is subjected to combined axial forces, moment, and shear. Two reference points in different positions of the adhesive interface are selected to compare the variation of CSMAXSCR with top displacement. The variation of CSMAXSCR with top displacement is shown in Figures 17 and 18, respectively. It has been found that the value of CSMAXSCR decreases with the increase in bond strength value. The debonding scale of W3 is wider than that of W2, and it is deduced that the boundary elements casted simultaneously with the core concrete provide a strong constraint to improve the structural integrity. The maximum value of CSMAXSCR at reference point 2 is no more than 0.3 for the two different wall configurations W2 and W3, indicating that the debonding scale is relatively small. It can be concluded that the adhesive interface has a good bonding condition with a truss connector under 0.1 axial compression ratio, which is in agreement with the experimental observations.Figure 15
Maximum traction damage initiation criterion index CSMAXSCR of W2.Figure 16
Maximum traction damage initiation criterion index CSMAXSCR of W3.Figure 17
CSMAXSCR-top displacement curves of W2.Figure 18
CSMAXSCR-top displacement curves of W3.In conclusion, the ABAQUS simulation model is suitable, and the adhesive interface has a negligible effect on ultimate bearing capacity of the double-superposed shear wall under 0.1 axial compression ratio.


## 2.6.1. Influence of the Initial Stiffness (K)

The initial stiffnessK is required to define the contact property model of the interface between the core and precast concrete wythes, as shown in Figure 10. The initial stiffness in the tangential directions has a significant effect on the behavior of interface; therefore, a sensitivity study was conducted to investigate the influence of the initial stiffness in the tangential directions on the simulation results. The test results of Lian et al. [12] are compared with the simulation results using initial stiffness values ranging from 20 N/mm3 to 200 N/mm3, as shown in Figure 12. The results show that, for the two different wall configurations (W2 and W3), the load-displacement curves were almost the same for K ranging from 20 N/mm3 to 200 N/mm3. Therefore, the average value of 100 N/mm3 was chosen for the initial stiffness in the tangential directions in later analysis. The effect of initial stiffness in the normal direction is negligible, and the same value as in the tangential directions was assigned to the stiffness in the normal direction in order to quicken the convergent speed in FE analysis.Figure 12
Initial stiffness sensitivity analysis: (a) W2 and (b) W3.
(a)
(b)


## 2.6.2. Influence of the Slope (α)

The value of slopeα is also needed to define the traction-separation model. As shown in Figures 8 and 9, the bond stress decreased with a very low negative stiffness after the peak point. A sensitivity study was conducted to investigate the influence of using different values, as shown in Figure 13. The results show that, for the two different wall configurations (W2 and W3), the load-displacement curves were almost the same for α ranging from 8° to 23°. Therefore, the average value of 15.5° was chosen for the slope in later analysis.Figure 13
Slope angle sensitivity analysis: (a) W2 and (b) W3.
(a)
(b)


## 2.6.3. Influence of the Maximum Bond Stress

As the bond stressesτn0 and τs0 are influenced by multitudinous factors, the bond stress values are different which were calculated by different design codes. Therefore, the effects of adopting different values of the maximum bond stress were investigated. Available expressions of the most important design codes [25–29] of concrete structures for the bond stress in the interface, which are based on the shear-friction theory, were summarized in Table 3. The test results of Lian et al. [12] are compared with the simulation results using different bond stress values, as shown in Figure 14. The results show that, for the two different wall configurations (W2 and W3), the load-displacement curves were almost the same for the bond stresses τn0 and τs0 ranging from 0.77 MPa to 2.52 MPa. It can be concluded that the bond strength has a negligible effect on ultimate bearing capacity of the double-superposed shear wall under 0.1 axial compression ratio.Table 3
Design expressions of different design codes to calculate the bond strength.
Design code
Design expression
Bond stress
W2 (MPa)
W3 (MPa)
ACI 318 [25]
τ
u
=
ρ
f
y
μ
sin
α
+
cos
α
f
y
≤
414
MPa
0.77
0.86
BS 8110-1 [26]
τ
u
=
0.6
F
b
ρ
tan
α
1.04
1.15
PCI Design Handbook [27]
τ
u
=
ϕ
ρ
f
y
μ
e
f
y
≤
414
MPa
1.19
1.32
CEB-FIP model code [28]
τ
u
=
c
f
ctd
+
μ
σ
n
+
ρ
f
y
sin
α
+
cos
α
1.95
2.06
AASHTO LRFD bridge design specifications [29]
τ
u
=
c
+
μ
ρ
f
y
+
σ
n
2.44
2.52Figure 14
Comparison of simulated and experimental response: (a) W2 and (b) W3.
(a)
(b)


## 2.6.4. Overall Comparison between Simulation and Test Results

The simulation results were compared with the test results based on the ultimate bearing capacity, as shown in Table4. Fairly consistent agreement is found between the simulation results and the test results with the maximum difference being 1%.Table 4
Comparison of ultimate bearing capacity between experiments and FE simulation using different bond stress values based on different design codes.
Design code
W2
W3
TestFtest (kN)
FE simulationFFE (kN)
F
FE
/
F
test
TestFtest (kN)
FE simulationFFE (kN)
F
FE
/
F
test
ACI 318 [25]
429
425.7
0.99
412
409.8
0.99
BS 8110-1 [26]
429
424.6
0.99
412
408.4
0.99
PCI Design Handbook [27]
429
424.9
0.99
412
414.7
1
CEB-FIP model code [28]
429
429.3
1
412
408.7
0.99
AASHTO LRFD bridge design specifications [29]
429
424.7
0.99
412
409.2
0.99For the two different wall configurations W2 and W3, the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast wythes is shown in Figures15 and 16, respectively. The value of CSMAXSCR exceeding the critical value (one) indicates the adhesive interface debonding. In Figures 15 and 16, the letters (a) to (e) mean the results of the bond stress values ranging from 0.77 MPa to 2.52 MPa; number 1 indicates the adhesive interface between the outer precast wythe and core wythe, and number 2 indicates the adhesive interface between the inner precast wythe and core wythe. It has been found that, for the two different wall configurations W2 and W3, the contact stress of the interfaces between the core and precast wythes exceeds the critical value (one). It indicated the debonding of the core and precast wythes; however, the debonding area is only on a small scale at the bottom, and the debonding scale becomes smaller with the increase in bond stress value. The debonding is caused by the crushing of the bottom concrete of the end column which is subjected to combined axial forces, moment, and shear. Two reference points in different positions of the adhesive interface are selected to compare the variation of CSMAXSCR with top displacement. The variation of CSMAXSCR with top displacement is shown in Figures 17 and 18, respectively. It has been found that the value of CSMAXSCR decreases with the increase in bond strength value. The debonding scale of W3 is wider than that of W2, and it is deduced that the boundary elements casted simultaneously with the core concrete provide a strong constraint to improve the structural integrity. The maximum value of CSMAXSCR at reference point 2 is no more than 0.3 for the two different wall configurations W2 and W3, indicating that the debonding scale is relatively small. It can be concluded that the adhesive interface has a good bonding condition with a truss connector under 0.1 axial compression ratio, which is in agreement with the experimental observations.Figure 15
Maximum traction damage initiation criterion index CSMAXSCR of W2.Figure 16
Maximum traction damage initiation criterion index CSMAXSCR of W3.Figure 17
CSMAXSCR-top displacement curves of W2.Figure 18
CSMAXSCR-top displacement curves of W3.In conclusion, the ABAQUS simulation model is suitable, and the adhesive interface has a negligible effect on ultimate bearing capacity of the double-superposed shear wall under 0.1 axial compression ratio.


## 3. The Effect of Bond Strength of Adhesive Interface on Ultimate Bearing Capacity under Different Axial Compression Ratios

The performance of the adhesive interfaces is crucial in developing a monolithic action for the double-superposed shear wall under different axial compression ratios, especially under high axial compression ratio. However, very little test data are available about the effect of adhesive interface on ultimate bearing capacity under high axial compression ratio. To further investigate the effect of adhesive interface on ultimate bearing capacity under different axial compression ratios, a parametric simulation study has been carried out to examine the effect of interface bond stress on ultimate bearing capacity. The bond stress ranges from 0.77 MPa to 2.52 MPa according to design codes [25–29]. The validated numerical model is used to generate the parametric study.


### 3.1. The Effect of Bond Strength of Adhesive Interface on Ultimate Bearing Capacity under 0.3 Axial Compression Ratio

The effect of different bond stresses on ultimate capacity under 0.3 axial compression ratio is investigated. The simulation results are showed in Table5, and it indicates that the wall configuration W3 yields a 5% higher ultimate bearing capacity than the wall configuration W2. As shown in Figure 19, the load-displacement curves are almost the same for bond stress values ranging from 0.77 MPa to 2.52 MPa for the two different wall configurations W2 and W3. It can be concluded that the variation of adhesive interface bond strength has a negligible effect on ultimate bearing capacity of the superposed shear wall under 0.3 axial compression ratio.Table 5
Comparison of the ultimate bearing capacity based on different design codes under 0.3 axial compression ratio.
Design code
W2
W3
Bond strength (MPa)
FE simulationFFE (kN)
Bond strength (MPa)
FE simulationFFE (kN)
ACI 318 [25]
0.77
623.7
0.86
650.35
BS 8110-1 [26]
1.04
624.21
1.15
656.34
PCI Design Handbook [27]
1.19
625.5
1.32
652.97
CEB-FIP model code [28]
1.95
624.95
2.06
654.38
AASHTO LRFD bridge design specifications [29]
2.44
624.62
2.52
654.14Figure 19
Comparison of load-displacement curves under 0.3 axial compression ratio: (a) W2 and (b) W3.
(a)
(b)For the two different wall configurations W2 and W3, Figures20 and 21, respectively, show the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast concrete wythes using different values of the bond strength under 0.3 axial compression ratio. It has been found that, for the two different wall configurations W2 and W3, although the debonding scale is wider than that under 0.1 axial compression ratio, contact stress between the core and precast concrete wythes exceeds the critical value (one) still on a small scale at the bottom, and the debonding scale becomes smaller with the increase in bond strength value. The debonding is caused by the crushing of the bottom concrete which is subjected to combined axial forces, moment, and shear. The variation of CSMAXSCR with top displacement at two reference points is shown in Figures 22 and 23, respectively, and it has been found that the value of CSMAXSCR decreases with the increase in bond strength value. The maximum value of CSMAXSCR at reference point 2 is no more than 0.3 for the two different wall configurations W2 and W3, indicating that the debonding is relatively small in scale. It can be concluded that the adhesive interface has a good bonding condition with a truss connector under 0.3 axial compression ratio.Figure 20
Maximum traction damage initiation criterion index CSMAXSCR of W2 under 0.3 axial compression ratio.Figure 21
Maximum traction damage initiation criterion index CSMAXSCR of W3 under 0.3 axial compression ratio.Figure 22
CSMAXSCR-top displacement curves of W2 under 0.3 axial compression ratio.Figure 23
CSMAXSCR-top displacement curves of W3 under 0.3 axial compression ratio.


### 3.2. The Effect of Bond Strength of Adhesive Interface on Ultimate Bearing Capacity under 0.5 Axial Compression Ratio

The effect of different bond strengths on ultimate capacity under 0.5 axial compression ratio is investigated. The simulation results show that the wall configuration W3 yielded a 10% higher ultimate bearing capacity than the wall configuration W2, which is provided in Table6. As shown in Figure 24, the load-displacement curves are almost the same for bond stress values ranging from 0.77 MPa to 2.52 MPa for the two different wall configurations W2 and W3. It can be concluded that the variation of the adhesive interface bond strength has no obvious effect on ultimate bearing capacity of the double-superposed shear wall under 0.5 axial compression ratio.Table 6
Comparison of the ultimate bearing capacity based on different design codes under 0.5 axial compression ratio.
Design code
W2
W3
Bond strength (MPa)
FE simulationFFE (kN)
Bond strength (MPa)
FE simulationFFE (kN)
ACI 318 [25]
0.77
737.72
0.86
815.26
BS 8110-1 [26]
1.04
740.75
1.15
817.95
PCI Design Handbook [27]
1.19
738.82
1.32
815.83
CEB-FIP model code [28]
1.95
735.93
2.06
817.51
AASHTO LRFD bridge design specifications [29]
2.44
736.51
2.52
819.13Figure 24
Comparison of load-displacement curves under 0.5 axial compression ratio: (a) W2 and (b) W3.
(a)
(b)For the two different wall configurations W2 and W3, the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast wythes using different values of the bond strength under 0.5 axial compression ratio was shown in Figures25 and 26, respectively. It has been found that, for the two different wall configurations, although the debonding spreads to a wider scale than that under 0.3 axial compression ratio, the debonding area is still on a small scale at the bottom. The debonding scale becomes smaller with the increase in bond strength value. The debonding was caused by the crushing of the bottom concrete of the end column which was subjected to combined axial forces, moment, and shear. The variation of CSMAXSCR with top displacement at 2 reference points is shown in Figures 27 and 28, respectively. It has been found that the value of CSMAXSCR decreases with increase in bond strength value. The maximum value of CSMAXSCR at reference point 2 is no more than 0.5 for the two different wall configurations. It can be concluded that the adhesive interface has a good bonding condition with a truss connector under 0.5 axial compression ratio.Figure 25
Maximum traction damage initiation criterion index CSMAXSCR of W2 under 0.5 axial compression ratio.Figure 26
Maximum traction damage initiation criterion index CSMAXSCR of W3 under 0.5 axial compression ratio.Figure 27
CSMAXSCR-top displacement curves of W2 under 0.5 axial compression ratio.Figure 28
CSMAXSCR-top displacement curves of W3 under 0.5 axial compression ratio.


### 3.3. Comparison of the Ultimate Bearing Capacity under Different Axial Compression Ratios

#### 3.3.1. Comparison of the Ultimate Bearing Capacity between Theoretical and Numerical Results under Different Axial Compression Ratios

On the basis of the plane section assumption and strain compatibility condition, the theory analysis result of the ultimate bearing capacity was conducted, as shown in Figure29. The triangle distribution of stresses assumed for confined concrete is estimated by a uniform stress equal to 0.85fcc in order to simplify the calculation. The section ultimate bending moment Mu should be determined in accordance with the following.Figure 29
The stress-strain distribution of the section.For the depth of compressionxn > the boundary element length lc,(6)Mu=Pychw−lc2+Pchw2−xn3−2lc3+2Pysthw2−as+Pfbt1.5xn−lc2,Pyc=0.85bwfcclc,Pc=0.5fcbwxn−lc,Pyst=fyAs,Pfbt=ffbbwρvhw−1.5xn.For the depth of compressionxn < the boundary element length lc,(7)Mu=Pyc′hw−lc2+Pysthw2−as+Pyschw2−as′+Pfbt1.5xn−lc2,Pyc′=0.85fccbwxn,Pysc=σsAs=Esεcu1−as′xnAs,where bw is the section width, fcc is the compressive strength of confined concrete, which is calculated through (1), hw is the effective depth of the section, as is the distance from the resultant force point of tensile reinforcement to the tensile edge, fc is the compressive strength of concrete, fy is the yield strength of longitudinal reinforcement, As is the longitudinal reinforcement area, ffb is the yield strength of longitudinal distributed reinforcement, ρv is the longitudinal distributed reinforcement ratio, Es is the elastic modulus of longitudinal reinforcement, εcu is the ultimate compression strain of concrete, and as′ is the distance from the resultant force point of compressive reinforcement to the compressive edge.The ultimate bearing capacityFu should be determined in accordance with the following:(8)Fu=MuH,where H = height of the shear wall.Table7 shows the comparison between the theoretical results Fu,calc using (8) and the mean values of numerical simulation results Fu,FE. The results show a good agreement with the maximum difference being 14%. However, the simulations results show that when the axial compression ratio exceeds 0.3, the wall configuration W3 yields a higher ultimate bearing capacity than the wall configuration W2. The variation trend of the theoretical results Fu,calc is inconsistent with the numerical simulation results Fu,FE, as shown in Figures 30 and 31. The obvious differences can be deduced from the different intensity grades between the cast-in-situ concrete layer and the precast concrete layer, which is not taken into account in the theoretical calculation formula.Table 7
Comparison of the ultimate bearing capacity between calculations and simulations.
Axial compression ratio
W2
W3
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (8) Fu,calc
F
u,calc
/
F
u,FE
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (1) Fu,calc
F
u,calc
/
F
u,FE
0.1
425.84
379.34
0.89
410.16
351.13
0.86
0.3
624.596
658.37
1.05
653.636
631.37
0.97
0.5
737.946
743.16
1.01
817.136
723.9
0.89Figure 30
Variation of the calculated ultimate bearing capacity with axial compression ratio.Figure 31
Variation of the simulated ultimate bearing capacity with axial compression ratio.


#### 3.3.2. A New Calculation Method for Ultimate Bearing Capacity of the Double-Superposed Shear Wall

As a result of the different intensity grades between the cast-in-situ concrete layer and precast concrete layer, the same strain on the different concrete layers yields different stresses, as shown in Figure32. A new calculation method for ultimate bearing capacity is proposed to take into account the different stresses on the different concrete layers, and the section ultimate bending moment MuN should be determined in accordance with the following.Figure 32
The stress-strain distribution of the section considering the different intensity grades.For the depth of compressionxn > the boundary element length lc,(9)MnN=PycNhw−lc2+PcNhw2−xn3−2lc3+⁡2Pysthw2−as+Pfbt1.5xn−lc2,PycN=0.85bwlcfccP+fccR2,PcN=0.5bwxn−lcfcP+fcR2.For the depth of compressionxn < the boundary element length lc,(10)MuN=PycN′hw−lc2+Pysthw2−as+Pyschw2−as′+Pfbt1.5xn−lc2,PycN′=0.85bwxnfccP+fccR2,where fccP is the compressive strength of confined precast concrete, fccR is the compressive strength of confined reinforced concrete, fcP is the compressive strength of unconfined precast concrete, and fcR is the compressive strength of unconfined reinforced concrete.Ultimate bearing capacityFu should be determined in accordance with the following:(11)Fu=MuNH.Table8 shows the comparison between the theoretical results Fu,calc using (11) and the mean values of numerical simulation results Fu,FE. The results show that the maximum difference is within 11%, and the variation trend of the theoretical results Fu,calc shows a very good agreement with the numerical simulation results Fu,FE as the increase in axial compression ratio, as shown in Figure 33.Table 8
Comparison of the ultimate bearing capacity between calculations and simulations.
Axial compression ratio
W2
W3
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (11) Fu,calc
F
u,calc
/
F
u,FE
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (1) Fu,calc
F
u,calc
/
F
u,FE
0.1
425.84
379.34
0.89
410.16
371.13
0.91
0.3
624.596
658.9
1.05
653.636
669.54
1.02
0.5
737.946
770.2
1.01
817.136
834.1
1.02Figure 33
Variation of the ultimate bearing capacity under different axial compression ratios. (a) Simulated results. (b) Calculated results.
(a)
(b)


## 3.1. The Effect of Bond Strength of Adhesive Interface on Ultimate Bearing Capacity under 0.3 Axial Compression Ratio

The effect of different bond stresses on ultimate capacity under 0.3 axial compression ratio is investigated. The simulation results are showed in Table5, and it indicates that the wall configuration W3 yields a 5% higher ultimate bearing capacity than the wall configuration W2. As shown in Figure 19, the load-displacement curves are almost the same for bond stress values ranging from 0.77 MPa to 2.52 MPa for the two different wall configurations W2 and W3. It can be concluded that the variation of adhesive interface bond strength has a negligible effect on ultimate bearing capacity of the superposed shear wall under 0.3 axial compression ratio.Table 5
Comparison of the ultimate bearing capacity based on different design codes under 0.3 axial compression ratio.
Design code
W2
W3
Bond strength (MPa)
FE simulationFFE (kN)
Bond strength (MPa)
FE simulationFFE (kN)
ACI 318 [25]
0.77
623.7
0.86
650.35
BS 8110-1 [26]
1.04
624.21
1.15
656.34
PCI Design Handbook [27]
1.19
625.5
1.32
652.97
CEB-FIP model code [28]
1.95
624.95
2.06
654.38
AASHTO LRFD bridge design specifications [29]
2.44
624.62
2.52
654.14Figure 19
Comparison of load-displacement curves under 0.3 axial compression ratio: (a) W2 and (b) W3.
(a)
(b)For the two different wall configurations W2 and W3, Figures20 and 21, respectively, show the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast concrete wythes using different values of the bond strength under 0.3 axial compression ratio. It has been found that, for the two different wall configurations W2 and W3, although the debonding scale is wider than that under 0.1 axial compression ratio, contact stress between the core and precast concrete wythes exceeds the critical value (one) still on a small scale at the bottom, and the debonding scale becomes smaller with the increase in bond strength value. The debonding is caused by the crushing of the bottom concrete which is subjected to combined axial forces, moment, and shear. The variation of CSMAXSCR with top displacement at two reference points is shown in Figures 22 and 23, respectively, and it has been found that the value of CSMAXSCR decreases with the increase in bond strength value. The maximum value of CSMAXSCR at reference point 2 is no more than 0.3 for the two different wall configurations W2 and W3, indicating that the debonding is relatively small in scale. It can be concluded that the adhesive interface has a good bonding condition with a truss connector under 0.3 axial compression ratio.Figure 20
Maximum traction damage initiation criterion index CSMAXSCR of W2 under 0.3 axial compression ratio.Figure 21
Maximum traction damage initiation criterion index CSMAXSCR of W3 under 0.3 axial compression ratio.Figure 22
CSMAXSCR-top displacement curves of W2 under 0.3 axial compression ratio.Figure 23
CSMAXSCR-top displacement curves of W3 under 0.3 axial compression ratio.


## 3.2. The Effect of Bond Strength of Adhesive Interface on Ultimate Bearing Capacity under 0.5 Axial Compression Ratio

The effect of different bond strengths on ultimate capacity under 0.5 axial compression ratio is investigated. The simulation results show that the wall configuration W3 yielded a 10% higher ultimate bearing capacity than the wall configuration W2, which is provided in Table6. As shown in Figure 24, the load-displacement curves are almost the same for bond stress values ranging from 0.77 MPa to 2.52 MPa for the two different wall configurations W2 and W3. It can be concluded that the variation of the adhesive interface bond strength has no obvious effect on ultimate bearing capacity of the double-superposed shear wall under 0.5 axial compression ratio.Table 6
Comparison of the ultimate bearing capacity based on different design codes under 0.5 axial compression ratio.
Design code
W2
W3
Bond strength (MPa)
FE simulationFFE (kN)
Bond strength (MPa)
FE simulationFFE (kN)
ACI 318 [25]
0.77
737.72
0.86
815.26
BS 8110-1 [26]
1.04
740.75
1.15
817.95
PCI Design Handbook [27]
1.19
738.82
1.32
815.83
CEB-FIP model code [28]
1.95
735.93
2.06
817.51
AASHTO LRFD bridge design specifications [29]
2.44
736.51
2.52
819.13Figure 24
Comparison of load-displacement curves under 0.5 axial compression ratio: (a) W2 and (b) W3.
(a)
(b)For the two different wall configurations W2 and W3, the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast wythes using different values of the bond strength under 0.5 axial compression ratio was shown in Figures25 and 26, respectively. It has been found that, for the two different wall configurations, although the debonding spreads to a wider scale than that under 0.3 axial compression ratio, the debonding area is still on a small scale at the bottom. The debonding scale becomes smaller with the increase in bond strength value. The debonding was caused by the crushing of the bottom concrete of the end column which was subjected to combined axial forces, moment, and shear. The variation of CSMAXSCR with top displacement at 2 reference points is shown in Figures 27 and 28, respectively. It has been found that the value of CSMAXSCR decreases with increase in bond strength value. The maximum value of CSMAXSCR at reference point 2 is no more than 0.5 for the two different wall configurations. It can be concluded that the adhesive interface has a good bonding condition with a truss connector under 0.5 axial compression ratio.Figure 25
Maximum traction damage initiation criterion index CSMAXSCR of W2 under 0.5 axial compression ratio.Figure 26
Maximum traction damage initiation criterion index CSMAXSCR of W3 under 0.5 axial compression ratio.Figure 27
CSMAXSCR-top displacement curves of W2 under 0.5 axial compression ratio.Figure 28
CSMAXSCR-top displacement curves of W3 under 0.5 axial compression ratio.


## 3.3. Comparison of the Ultimate Bearing Capacity under Different Axial Compression Ratios

### 3.3.1. Comparison of the Ultimate Bearing Capacity between Theoretical and Numerical Results under Different Axial Compression Ratios

On the basis of the plane section assumption and strain compatibility condition, the theory analysis result of the ultimate bearing capacity was conducted, as shown in Figure29. The triangle distribution of stresses assumed for confined concrete is estimated by a uniform stress equal to 0.85fcc in order to simplify the calculation. The section ultimate bending moment Mu should be determined in accordance with the following.Figure 29
The stress-strain distribution of the section.For the depth of compressionxn > the boundary element length lc,(6)Mu=Pychw−lc2+Pchw2−xn3−2lc3+2Pysthw2−as+Pfbt1.5xn−lc2,Pyc=0.85bwfcclc,Pc=0.5fcbwxn−lc,Pyst=fyAs,Pfbt=ffbbwρvhw−1.5xn.For the depth of compressionxn < the boundary element length lc,(7)Mu=Pyc′hw−lc2+Pysthw2−as+Pyschw2−as′+Pfbt1.5xn−lc2,Pyc′=0.85fccbwxn,Pysc=σsAs=Esεcu1−as′xnAs,where bw is the section width, fcc is the compressive strength of confined concrete, which is calculated through (1), hw is the effective depth of the section, as is the distance from the resultant force point of tensile reinforcement to the tensile edge, fc is the compressive strength of concrete, fy is the yield strength of longitudinal reinforcement, As is the longitudinal reinforcement area, ffb is the yield strength of longitudinal distributed reinforcement, ρv is the longitudinal distributed reinforcement ratio, Es is the elastic modulus of longitudinal reinforcement, εcu is the ultimate compression strain of concrete, and as′ is the distance from the resultant force point of compressive reinforcement to the compressive edge.The ultimate bearing capacityFu should be determined in accordance with the following:(8)Fu=MuH,where H = height of the shear wall.Table7 shows the comparison between the theoretical results Fu,calc using (8) and the mean values of numerical simulation results Fu,FE. The results show a good agreement with the maximum difference being 14%. However, the simulations results show that when the axial compression ratio exceeds 0.3, the wall configuration W3 yields a higher ultimate bearing capacity than the wall configuration W2. The variation trend of the theoretical results Fu,calc is inconsistent with the numerical simulation results Fu,FE, as shown in Figures 30 and 31. The obvious differences can be deduced from the different intensity grades between the cast-in-situ concrete layer and the precast concrete layer, which is not taken into account in the theoretical calculation formula.Table 7
Comparison of the ultimate bearing capacity between calculations and simulations.
Axial compression ratio
W2
W3
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (8) Fu,calc
F
u,calc
/
F
u,FE
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (1) Fu,calc
F
u,calc
/
F
u,FE
0.1
425.84
379.34
0.89
410.16
351.13
0.86
0.3
624.596
658.37
1.05
653.636
631.37
0.97
0.5
737.946
743.16
1.01
817.136
723.9
0.89Figure 30
Variation of the calculated ultimate bearing capacity with axial compression ratio.Figure 31
Variation of the simulated ultimate bearing capacity with axial compression ratio.


### 3.3.2. A New Calculation Method for Ultimate Bearing Capacity of the Double-Superposed Shear Wall

As a result of the different intensity grades between the cast-in-situ concrete layer and precast concrete layer, the same strain on the different concrete layers yields different stresses, as shown in Figure32. A new calculation method for ultimate bearing capacity is proposed to take into account the different stresses on the different concrete layers, and the section ultimate bending moment MuN should be determined in accordance with the following.Figure 32
The stress-strain distribution of the section considering the different intensity grades.For the depth of compressionxn > the boundary element length lc,(9)MnN=PycNhw−lc2+PcNhw2−xn3−2lc3+⁡2Pysthw2−as+Pfbt1.5xn−lc2,PycN=0.85bwlcfccP+fccR2,PcN=0.5bwxn−lcfcP+fcR2.For the depth of compressionxn < the boundary element length lc,(10)MuN=PycN′hw−lc2+Pysthw2−as+Pyschw2−as′+Pfbt1.5xn−lc2,PycN′=0.85bwxnfccP+fccR2,where fccP is the compressive strength of confined precast concrete, fccR is the compressive strength of confined reinforced concrete, fcP is the compressive strength of unconfined precast concrete, and fcR is the compressive strength of unconfined reinforced concrete.Ultimate bearing capacityFu should be determined in accordance with the following:(11)Fu=MuNH.Table8 shows the comparison between the theoretical results Fu,calc using (11) and the mean values of numerical simulation results Fu,FE. The results show that the maximum difference is within 11%, and the variation trend of the theoretical results Fu,calc shows a very good agreement with the numerical simulation results Fu,FE as the increase in axial compression ratio, as shown in Figure 33.Table 8
Comparison of the ultimate bearing capacity between calculations and simulations.
Axial compression ratio
W2
W3
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (11) Fu,calc
F
u,calc
/
F
u,FE
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (1) Fu,calc
F
u,calc
/
F
u,FE
0.1
425.84
379.34
0.89
410.16
371.13
0.91
0.3
624.596
658.9
1.05
653.636
669.54
1.02
0.5
737.946
770.2
1.01
817.136
834.1
1.02Figure 33
Variation of the ultimate bearing capacity under different axial compression ratios. (a) Simulated results. (b) Calculated results.
(a)
(b)


## 3.3.1. Comparison of the Ultimate Bearing Capacity between Theoretical and Numerical Results under Different Axial Compression Ratios

On the basis of the plane section assumption and strain compatibility condition, the theory analysis result of the ultimate bearing capacity was conducted, as shown in Figure29. The triangle distribution of stresses assumed for confined concrete is estimated by a uniform stress equal to 0.85fcc in order to simplify the calculation. The section ultimate bending moment Mu should be determined in accordance with the following.Figure 29
The stress-strain distribution of the section.For the depth of compressionxn > the boundary element length lc,(6)Mu=Pychw−lc2+Pchw2−xn3−2lc3+2Pysthw2−as+Pfbt1.5xn−lc2,Pyc=0.85bwfcclc,Pc=0.5fcbwxn−lc,Pyst=fyAs,Pfbt=ffbbwρvhw−1.5xn.For the depth of compressionxn < the boundary element length lc,(7)Mu=Pyc′hw−lc2+Pysthw2−as+Pyschw2−as′+Pfbt1.5xn−lc2,Pyc′=0.85fccbwxn,Pysc=σsAs=Esεcu1−as′xnAs,where bw is the section width, fcc is the compressive strength of confined concrete, which is calculated through (1), hw is the effective depth of the section, as is the distance from the resultant force point of tensile reinforcement to the tensile edge, fc is the compressive strength of concrete, fy is the yield strength of longitudinal reinforcement, As is the longitudinal reinforcement area, ffb is the yield strength of longitudinal distributed reinforcement, ρv is the longitudinal distributed reinforcement ratio, Es is the elastic modulus of longitudinal reinforcement, εcu is the ultimate compression strain of concrete, and as′ is the distance from the resultant force point of compressive reinforcement to the compressive edge.The ultimate bearing capacityFu should be determined in accordance with the following:(8)Fu=MuH,where H = height of the shear wall.Table7 shows the comparison between the theoretical results Fu,calc using (8) and the mean values of numerical simulation results Fu,FE. The results show a good agreement with the maximum difference being 14%. However, the simulations results show that when the axial compression ratio exceeds 0.3, the wall configuration W3 yields a higher ultimate bearing capacity than the wall configuration W2. The variation trend of the theoretical results Fu,calc is inconsistent with the numerical simulation results Fu,FE, as shown in Figures 30 and 31. The obvious differences can be deduced from the different intensity grades between the cast-in-situ concrete layer and the precast concrete layer, which is not taken into account in the theoretical calculation formula.Table 7
Comparison of the ultimate bearing capacity between calculations and simulations.
Axial compression ratio
W2
W3
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (8) Fu,calc
F
u,calc
/
F
u,FE
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (1) Fu,calc
F
u,calc
/
F
u,FE
0.1
425.84
379.34
0.89
410.16
351.13
0.86
0.3
624.596
658.37
1.05
653.636
631.37
0.97
0.5
737.946
743.16
1.01
817.136
723.9
0.89Figure 30
Variation of the calculated ultimate bearing capacity with axial compression ratio.Figure 31
Variation of the simulated ultimate bearing capacity with axial compression ratio.


## 3.3.2. A New Calculation Method for Ultimate Bearing Capacity of the Double-Superposed Shear Wall

As a result of the different intensity grades between the cast-in-situ concrete layer and precast concrete layer, the same strain on the different concrete layers yields different stresses, as shown in Figure32. A new calculation method for ultimate bearing capacity is proposed to take into account the different stresses on the different concrete layers, and the section ultimate bending moment MuN should be determined in accordance with the following.Figure 32
The stress-strain distribution of the section considering the different intensity grades.For the depth of compressionxn > the boundary element length lc,(9)MnN=PycNhw−lc2+PcNhw2−xn3−2lc3+⁡2Pysthw2−as+Pfbt1.5xn−lc2,PycN=0.85bwlcfccP+fccR2,PcN=0.5bwxn−lcfcP+fcR2.For the depth of compressionxn < the boundary element length lc,(10)MuN=PycN′hw−lc2+Pysthw2−as+Pyschw2−as′+Pfbt1.5xn−lc2,PycN′=0.85bwxnfccP+fccR2,where fccP is the compressive strength of confined precast concrete, fccR is the compressive strength of confined reinforced concrete, fcP is the compressive strength of unconfined precast concrete, and fcR is the compressive strength of unconfined reinforced concrete.Ultimate bearing capacityFu should be determined in accordance with the following:(11)Fu=MuNH.Table8 shows the comparison between the theoretical results Fu,calc using (11) and the mean values of numerical simulation results Fu,FE. The results show that the maximum difference is within 11%, and the variation trend of the theoretical results Fu,calc shows a very good agreement with the numerical simulation results Fu,FE as the increase in axial compression ratio, as shown in Figure 33.Table 8
Comparison of the ultimate bearing capacity between calculations and simulations.
Axial compression ratio
W2
W3
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (11) Fu,calc
F
u,calc
/
F
u,FE
Ultimate bearing capacity by FE modelFu,FE
Ultimate bearing capacity by using (1) Fu,calc
F
u,calc
/
F
u,FE
0.1
425.84
379.34
0.89
410.16
371.13
0.91
0.3
624.596
658.9
1.05
653.636
669.54
1.02
0.5
737.946
770.2
1.01
817.136
834.1
1.02Figure 33
Variation of the ultimate bearing capacity under different axial compression ratios. (a) Simulated results. (b) Calculated results.
(a)
(b)


## 4. Conclusions

The effect of adhesive behavior between the core and precast concrete wythes on the ultimate capacity of the double-superposed shear wall has been investigated using FE simulation, and a new calculation method for ultimate capacity is proposed to take into account the different concrete grades on the different concrete layers. Based on the results, the following conclusions have been drawn:(1)
The bond strength of the adhesive surface has a negligible effect on ultimate bearing capacity of the double-superposed shear wall under different axial compression ratios.(2)
The double-superposed shear wall with cast-in-place boundary elements (wall configuration W2) yields a higher ultimate capacity than that with precast boundary elements (wall configuration W3) under 0.1 axial compression ratio. When the axial compression ratio exceeds 0.2, the wall configuration W3 yields a higher ultimate capacity than the wall configuration W2 due to the higher strength grade of precast concrete wythes.(3)
A new calculation method for ultimate capacity is proposed to take into account the different strength grades on the different concrete layers and gives accurate results compared to FE simulation results.



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*Source: 1913902-2018-04-02.xml*