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

,is 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. ,e effect of adhesive interface on the ultimate capacity of two different wall configurations under different axial compression ratios was studied.,e 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 castin-place boundary elements (wall configurationW2), 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.


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.e 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].e 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].e shear wall structure, with high capacity and lateral stiffness, is an ideal lateral force-resisting structure in high-rise buildings.
erefore, 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.e 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][10][11][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][14][15].e 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.e 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.

Validation of the Finite Element (FE) Simulation Model
2.1.General.e numerical simulations of this research were carried out based on the commercial nite 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 di erent wall con gurations were investigated in the test.Figure 3 shows the dimension and details of the double-superposed shear wall.Wall con guration 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 con guration 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.
e bearing steel inside the precast wall panels is BSt500.Tables 1 and 2 show the mechanical properties of the major materials.

Material Model for the Steel
Bar.An idealized doublelinear stress-strain curve is employed to model the steel bar.As shown in Figure 4, f y is the yield stress of the steel bar, ε y is the yield strain of the steel bar, f u is the ultimate stress of the steel bar, and ε u is the ultimate strain of the steel bar.e Von Mises yield criterion with associated plastic ow available in ABAQUS was used.Poisson's ratio and Young's modulus were assumed to be 0.3 and 200 Gpa.e ultimate strain of steel ε u was assumed to be 0.2.

Material Model for the Concrete.
In the doublesuperposed shear wall, the boundary elements are con ned by the stirrup, which results in increased ductility and strength of the con ned concrete compared to the uncon ned concrete.In this research, the Kent-Park model is adopted for the simulations.As shown in Figure 5, f c is the compressive strength of uncon ned concrete and ε c is the strain corresponding to f c .f cc and ε cc are the corresponding values of con ned concrete.f cc and ε cc should be determined in accordance with the following: 2 Advances in Civil Engineering where ρ s is the stirrup ratio and f yh is the yield strength of stirrup.

Boundary Conditions and Load
Application.Finite element models of the two di erent wall con gurations W2 and W3 were constructed and shown in Figures 6 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 rst 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.e foundation at the wall base was xed in all six directions.e 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.

Finite Element Type and Mesh.
ree-dimensional 2-node truss elements (T3D2) were used to model the steel bar so that material yield could be accurately followed.
e concrete was modelled using three-dimensional 8node 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.e meshes at the contacting surfaces were matched in order to obtain the best accuracy in contact analysis.

Contact between the Interface of Outer Precast Concrete and Core Concrete.
e adhesion between the core and precast wythes can be classi ed as the issue of bond between new and old concrete, and the load-slip behavior at the   Advances in Civil Engineering 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 fiberreinforced), 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.e 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.e meshes at the contacting surfaces were matched to expedite the convergence of the FE model.e 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.erefore, 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.
An elastic constitutive matrix was utilized to relate the normal and tangential shear stresses to the normal and tangential separations across the interface.e nominal traction stress vector τ consists of three components: τ n , τ s , and τ t , which refer to the normal and tangential directions, respectively, as shown in Figure 11.
e corresponding separations are denoted by δ n , δ s , and δ t .e elastic behavior can then be written as [18] [τ] � Damage modelling is required to simulate degradation and progressive failure of the adhesive interface bond between 4 Advances in Civil Engineering the core and precast wythes.e criterion for damage initiation has been de ned 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.is criterion can be represented as where τ 0 n , τ 0 s , and τ 0 t are the maximum stresses in the normal and tangential directions.In this investigation, it is assumed that τ 0 s τ 0 t .e maximum bond stress (τ 0 s τ 0 t ) depends on many factors [19][20][21][22][23][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 di erent based on di erent design codes.erefore, di erent values were used for the maximum bond stress, according to the di erent design codes, to further investigate the in uence of bond strength on ultimate capacity of the doublesuperposed shear wall.In the normal direction, ABAQUS "hard contact" behavior is de ned at the interface between the precast wythes and the core concrete wythe; this means that the resistance to contact pressure is in nite, and they cannot penetrate into each other.However, they are allowed to separate.e maximum bond stress in normal direction is de ned as τ 0 n , and the tensile strength of lower strength concrete was employed to de ne the normal stress values.

In uence of the Initial Sti ness (K).
e initial sti ness K is required to de ne the contact property model of the interface between the core and precast concrete wythes, as shown in Figure 10.e initial sti ness in the tangential directions has a signi cant e ect on the behavior of interface; therefore, a sensitivity study was conducted to investigate the  Advances in Civil Engineering in uence of the initial sti ness in the tangential directions on the simulation results.e test results of Lian et al. [12] are compared with the simulation results using initial sti ness values ranging from 20 N/mm 3 to 200 N/mm 3 , as shown in Figure 12. e results show that, for the two di erent wall con gurations (W2 and W3), the load-displacement curves were almost the same for K ranging from 20 N/mm 3 to 200 N/mm 3 .erefore, the average value of 100 N/mm 3 was chosen for the initial sti ness in the tangential directions in later analysis.e e ect of initial sti ness in the normal direction is negligible, and the same value as in the tangential directions was assigned to the sti ness in the normal direction in order to quicken the convergent speed in FE analysis.

In uence of the Slope (α).
e value of slope α is also needed to de ne the traction-separation model.As shown in Figures 8 and 9, the bond stress decreased with a very low negative sti ness after the peak point.A sensitivity study was conducted to investigate the in uence of using di erent values, as shown in Figure 13.e results show that, for the two di erent wall con gurations (W2 and W3), the loaddisplacement curves were almost the same for α ranging from 8 °to 23 °.erefore, the average value of 15.5 °was chosen for the slope in later analysis.

In uence of the Maximum Bond Stress.
As the bond stresses τ 0 n and τ 0 s are in uenced by multitudinous factors, the bond stress values are di erent which were calculated by di erent design codes.
erefore, the e ects of adopting di erent values of the maximum bond stress were investigated.Available expressions of the most important design codes [25][26][27][28][29] of concrete structures for the bond stress in the interface, which are based on the shear-friction theory, were summarized in Table 3. e test results of Lian 6 Advances in Civil Engineering et al. [12] are compared with the simulation results using di erent bond stress values, as shown in Figure 14. e results show that, for the two di erent wall con gurations (W2 and W3), the load-displacement curves were almost the same for the bond stresses τ 0 n and τ 0 s ranging from 0.77 MPa to 2.52 MPa.It can be concluded that the bond strength has a negligible e ect on ultimate bearing capacity of the doublesuperposed shear wall under 0.1 axial compression ratio.

Overall Comparison between Simulation and Test
Results.
e simulation results were compared with the test results based on the ultimate bearing capacity, as shown in Table 4. Fairly consistent agreement is found between the simulation results and the test results with the maximum di erence being 1%.
For the two di erent wall con gurations W2 and W3, the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast wythes is shown in Figures 15 and 16, respectively.
e 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

Design code
Design expression Bond stress W2 (MPa) W3 (MPa) ACI 318 [25] τ u ρf y (μ sin α + cos α) (f y ≤ 414 MPa) 0.77 0.86 BS 8110-1 [26] τ u 0.6F b ρ tan α 1.04 1.15 PCI Design Handbook [27] τ u ϕρf y μ e (f y ≤ 414 MPa) 1.19 1.32 CEB-FIP model code [28] τ u cf ctd + μ[σ n + ρf y (sin α + cos α)] 1.95 2.06 AASHTO LRFD bridge design speci cations [29] τ u c + μ(ρf y + σ n ) 2.44  Advances in Civil Engineering been found that, for the two di erent wall con gurations 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.e 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 di erent positions of the adhesive interface are selected to compare the variation of CSMAXSCR with top displacement.e 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.e 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.e maximum value of CSMAXSCR at reference point 2 is no more than 0.3 for the two di erent wall con gurations 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.
In conclusion, the ABAQUS simulation model is suitable, and the adhesive interface has a negligible e ect on ultimate bearing capacity of the double-superposed shear wall under 0.1 axial compression ratio.

The Effect of Bond Strength of Adhesive Interface on Ultimate Bearing Capacity under Different Axial Compression Ratios
e performance of the adhesive interfaces is crucial in developing a monolithic action for the double-superposed shear wall under di erent axial compression ratios, especially under high axial compression ratio.However, very little test data are available about the e ect of adhesive interface on ultimate bearing capacity under high axial compression ratio.To further investigate the e ect of adhesive interface on ultimate bearing capacity under di erent axial compression ratios, a parametric simulation study has been carried out to examine the e ect of interface bond stress on ultimate bearing capacity.

e E ect of Bond Strength of Adhesive Interface on Ultimate Bearing Capacity under 0.3 Axial Compression
Ratio.
e e ect of di erent bond stresses on ultimate capacity under 0.3 axial compression ratio is investigated.Advances in Civil Engineering e simulation results are showed in Table 5, and it indicates that the wall con guration W3 yields a 5% higher ultimate bearing capacity than the wall con guration 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 di erent wall con gurations W2 and W3.It can be concluded that the variation of adhesive interface bond strength has a negligible e ect on ultimate bearing capacity of the superposed shear wall under 0.3 axial compression ratio.
For the two di erent wall con gurations W2 and W3, Figures 20 and 21, respectively, show the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast concrete wythes using di erent values of the bond strength under 0.3 axial compression ratio.It has been found that, for the two di erent wall con gurations 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.e debonding is caused by the crushing of the bottom concrete which is subjected to combined axial forces, moment, and shear.e 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.
e maximum value of CSMAXSCR at reference point 2 is no more than 0.3 for the two di erent wall con gurations W2 and W3, indicating that 10 Advances in Civil Engineering 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.

e E ect of Bond Strength of Adhesive Interface on Ultimate Bearing Capacity under 0.5 Axial Compression
Ratio. e e ect of di erent bond strengths on ultimate capacity under 0.5 axial compression ratio is investigated.
e simulation results show that the wall con guration W3 yielded a 10% higher ultimate bearing capacity than the wall con guration W2, which is provided in Table 6.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 di erent wall con gurations W2 and W3.It can be concluded that the variation of the adhesive interface bond strength has no obvious e ect on ultimate bearing capacity of the double-superposed shear wall under 0.5 axial compression ratio.
For the two di erent wall con gurations W2 and W3, the maximum traction damage initiation criterion index (CSMAXSCR) for the adhesive interface between the core and precast wythes using di erent values of the bond strength under 0.5 axial compression ratio was shown in Figures 25 and 26, respectively.It has been found that, for the two di erent wall con gurations, 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.
e debonding scale becomes smaller with the increase in bond strength value.
e debonding was caused by the crushing of the bottom concrete of the end column which was subjected to combined axial forces, moment, and shear.e 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.e maximum value of CSMAXSCR at reference point 2 is no more than 0.5 for the two di erent wall con gurations.

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It can be concluded that the adhesive interface has a good bonding condition with a truss connector under 0.5 axial compression ratio.

Comparison of the Ultimate Bearing Capacity under
Di erent Axial Compression Ratios

Comparison of the Ultimate Bearing Capacity between eoretical and Numerical Results under Di erent 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 Figure 29.e triangle distribution of stresses assumed for con ned concrete is estimated by a uniform stress equal to 0.85f cc in order to simplify the calculation.
e section ultimate bending moment M u should be determined in accordance with the following.Advances in Civil Engineering 13 For the depth of compression x n > the boundary element length l c , For the depth of compression x n < the boundary element length l c , where b w is the section width, f cc is the compressive strength of con ned concrete, which is calculated through (1), h w is the e ective depth of the section, a s is the distance from the resultant force point of tensile reinforcement to the tensile edge, f c is the compressive strength of concrete, f y is the yield strength of longitudinal reinforcement, A s is the longitudinal reinforcement area, f fb is the yield strength of longitudinal distributed reinforcement, ρ v is the longitudinal distributed reinforcement ratio, E s is the elastic modulus of longitudinal reinforcement, ε cu is the ultimate compression strain of concrete, and a ′ s is the distance from the resultant force point of compressive reinforcement to the compressive edge.
where H height of the shear wall.
Table 7 shows the comparison between the theoretical results F u,calc using (8) and the mean values of numerical simulation results F u,FE .e results show a good agreement with the maximum di erence being 14%.However, the simulations results show that when the axial compression ratio exceeds 0.3, the wall con guration W3 yields a higher ultimate bearing capacity than the wall con guration W2. e variation trend of the theoretical results F u,calc is inconsistent with the numerical simulation results F u,FE , as shown in Figures 30 and 31.e obvious di erences can be deduced from the di erent 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.

A New Calculation Method for Ultimate Bearing
Capacity of the Double-Superposed Shear Wall.As a result of the di erent intensity grades between the cast-in-situ concrete layer and precast concrete layer, the same strain on the di erent concrete layers yields di erent stresses, as shown in Figure 32.A new calculation method for ultimate bearing capacity is proposed to take into account the di erent stresses on the di erent concrete layers, and the section ultimate bending moment M N u should be determined in accordance with the following.
For the depth of compression x n > the boundary element length l c , For the depth of compression x n < the boundary element length l c ,

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where f P cc is the compressive strength of con ned precast concrete, f R cc is the compressive strength of con ned reinforced concrete, f P c is the compressive strength of uncon ned precast concrete, and f R c is the compressive strength of uncon ned reinforced concrete.
Ultimate bearing capacity F u should be determined in accordance with the following: Table 8 shows the comparison between the theoretical results F u,calc using (11) and the mean values of numerical simulation results F u,FE .e results show that the maximum di erence is within 11%, and the variation trend of the theoretical results F u,calc shows a very good agreement with the numerical simulation results F u,FE as the increase in axial compression ratio, as shown in Figure 33.

Conclusions
e e ect 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 di erent concrete grades on the di erent concrete layers.Based on the results, the following conclusions have been drawn: (1) e bond strength of the adhesive surface has a negligible e ect on ultimate bearing capacity of the double-superposed shear wall under di erent axial compression ratios.(2) e double-superposed shear wall with cast-in-place boundary elements (wall con guration W2) yields a higher ultimate capacity than that with precast  boundary elements (wall con guration W3) under 0.1 axial compression ratio.When the axial compression ratio exceeds 0.2, the wall con guration W3 yields a higher ultimate capacity than the wall con guration 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 di erent strength grades on the di erent concrete layers and gives accurate results compared to FE simulation results.

Figure 3 :
Figure 3: e dimension and details of the double-superposed shear wall: (a) W2 and (b) W3.

Figure 32
Figure32: e stress-strain distribution of the section considering the di erent intensity grades.

Figure 33 :
Figure 33: Variation of the ultimate bearing capacity under di erent axial compression ratios.(a) Simulated results.(b) Calculated results.

Table 3 :
Design expressions of di erent design codes to calculate the bond strength.

Table 4 :
Comparison of ultimate bearing capacity between experiments and FE simulation using di erent bond stress values based on di erent design codes.

Table 5 :
Comparison of the ultimate bearing capacity based on di erent design codes under 0.3 axial compression ratio.

Table 6 :
Comparison of the ultimate bearing capacity based on di erent design codes under 0.5 axial compression ratio.MPa) FE simulation F FE (kN) Bond strength (MPa) FE simulation F FE (kN)

Table 7 :
Comparison of the ultimate bearing capacity between calculations and simulations.

Table 8 :
Comparison of the ultimate bearing capacity between calculations and simulations.