Introduction

Masonry infill walls serve as the first line of defense against earthquakes in frame structures. The complex interaction between masonry infill walls and the primary frame has been verified in numerous post-earthquake damage investigations. Infilled walls not only significantly enhance the initial stiffness and load-carrying capacity of the structure but also effectively dissipate seismic energy, playing a non-negligible role in preventing structural collapse1,2,3,4,5. The national codes6,7 require that the constructional column should be set within the walls. In particular, the American standard ASCE 41 − 238 clearly stipulates that the confining effect provided by columns must be considered when conducting out-of-plane performance analysis of infilled walls.

The constructional columns are critical elements for ensuring the integrity and stability of infilled walls. Research has shown that the constructional columns can significantly enhance the structure’s out-of-plane stability9, improve the in-plane and out-of-plane load-carrying capacity of the walls, and mitigate the adverse effects of in-plane cracking damage on its out-of-plane performance10. Classical seismic theory stated that the ductile design of columns was key to controlling the out-of-plane failure modes of infilled walls11. Experimental data had also quantified the impact that a constructional column could increase the structure’s inter-story lateral displacement stiffness by up to 147%12,13,14. However, the damage evolution process in the connection zones directly affected the overall performance of the structure15.

The construction process for a cast-in-situ constructional column is complex, time-consuming, which usually accompanied by some common quality defects such as honeycombing, pitting, and uneven vibration. Therefore, a fabricated constructional column technology was proposed16,17, as shown in Fig. 1. This technology induced the steps of formwork erection and vibration, simplifying the complex construction procedure into a single step in which the fabricated constructional column was cast with the masonry wall. Firstly, the construction period for a single infilled wall was reduced from three days to just one day, and the direct construction cost of a single 2.5-meter-high fabricated constructional column saved approximately 30%. Previous experimental studies had shown12,13 that the lateral stiffness of this new type of column is approximately 46% of that of a cast-in-situ constructional column, which conforms to the ductile design principle as a strong frame and weak wall18, helping to confine potential damage within the infilled wall, thereby protecting the primary structure.

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Construction technology of the fabricated constructional columns17.

The out-of-plane performance of the infilled walls was influenced by multiple factors, and under the effect of in-plane damage was a focal point of current research. Without the in-plane damage, the height-to-thickness ratio of the wall and the compressive strength of the masonry units were the primary factors that affected the out-of-plane performance19. The out-of-plane load-bearing mechanism was typically explained by “arching action”20, wherein the restraint conditions at the top were of critical importance for stability21. Maria et al.22 investigated the influence of the aspect ratio of the wall on the out-of-plane load-bearing capacity. However, after being subjected to cyclic loading, the in-plane damage resulted in a significant deterioration in the out-of-plane performance of the infilled wall23. Researchers have conducted in-depth investigations into this issue. For instance, Furtado et al.24,25 found that openings in the wall weakened the structure’s energy dissipation capacity and reduced the out-of-plane strength by 30%. Studies also indicated that Autoclaved Aerated Concrete (AAC) infilled walls may not simultaneously satisfy both in-plane and out-of-plane seismic requirements26. To quantify the damage degree, the damage index model was proposed by Hossain and Bhowmick27, which can accurately assess the in-plane damage degree. In the latest numerical simulation studies, it was revealed that in-plane inter-story drift would result in through-cracks on the surface of the infilled wall, weaken the out-of-plane arching action, and decrease the out-of-plane load-bearing capacity28. Although the performance could be restored by strengthening techniques such as Glass Fiber Reinforced Polymer (GFRP) mesh29 or Carbon Fiber Reinforced Polymer (CFRP)30, the effectiveness was limited for severely cracked walls, and the costs were relatively high31. Therefore, optimizing constructional measures to enhance the out-of-plane load-bearing capacity of the infilled walls after in-plane damage became a meaningful research direction.

Based on the discrete model validated in the previous research, in this study, the Finite Element Models (FEM) of the steel framed-infilled wall without a constructional column (FW1), with a cast-in-situ constructional column (FW2), and with a fabricated constructional column (FW3) were established. The out-of-plane performance of frame-infilled walls (FI) of different constructional measures after in-plane damage was investigated, including the load-bearing capacity, deformation characteristics, and failure modes. It provided a theoretical foundation for the evaluation of the effectiveness and advantages of the fabricated constructional columns under complex seismic actions. Aiming to lay the foundation for the analysis of more complex structures, the single-layer cantilever frame was used. Therefore, the inter-story interaction in multi-story structures was not explored. Meanwhile, the applicability verification of the model mainly focused on brick-filled partition walls, and the application in other wall types, such as autoclaved aerated concrete (AAC) needed to be studied in the future.

Finite element model

Model establishment

In the experiment, the span of the cantilever steel frame was 5.4 m, and the story height was 3.0 m. Q235 hot-rolled H-shaped steel was used. The infilled wall size was 5100 mm×2610 mm×200 mm (length×height×thickness). Construction measures were set according to the requirements of the specification6,7. The interface between the frame and the infilled wall was idealized as a rigid connection to highlight the macroscopic nonlinear behavior of FI, the compressive-shear failure of the infilled wall, and the plastic development of the steel frame, which conformed to the experimental design that the tie bars were employed to enhance the composite action32. However, the assumption neglected the energy dissipation mechanism led by interfacial friction and slip33,34. Consequently, the model overestimated the initial stiffness and ultimate load-bearing capacity of the structure and increased inaccuracies in the energy dissipation assessment. Nonetheless, the model exhibited reasonable capability in predicting the overall load-bearing capacity and failure modes of FI. The tie bar was HPB300, with a diameter of 8 mm, which was set on both sides of the wall at intervals of 400 mm. The specimen details are shown in Fig. 217, and the reinforcing bars set in the specimens are presented in Table 1.

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Specimen details17.

Table 1 The reinforcing bars set in the specimens.
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Based on the parameters of the model in the experiment, FEMs of the FW1, FW2, and FW3 were established. The masonry and mortar were modeled as a homogenized equivalent block to enhance computational efficiency, which was widely used to simulate the seismic performance of FI35,36. It has been successfully applied by numerous scholars to the analysis of similar engineering problems37,38. The equivalent blocks, steel frames, blocks of constructional column, tie bars, and constructional column reinforcement mesh were first modeled separately and then assembled as a whole. The specimen and the FEM are shown in Fig. 3.

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Specimen and FEM.

Material properties

In this study, a finite element analysis on the steel frame-infilled wall was conducted using the Abaqus software. The steel frame was modeled by the C3D8R elements, which are 8-node linear brick elements with reduced integration39. The reinforcing bars were modeled by the T3D2 element, the yield strength was considered as the strength grade, and a bilinear model was used as the constitutive relation. The elastic modulus and yield stress of the steel frame were set to 206 GPa and 235 MPa, respectively. A mesh size of 80 mm was adopted for the steel frame and the masonry, while a size of 50 mm was used for the reinforcement bars. The FEM of the three specimens have a node count ranging from approximately 34,232 to 35,376, and a unit count ranging from approximately 13,942 to 14,363. At this mesh density, a converged and stable solution was achieved.

The masonry brick was defined by the Concrete Damage Plasticity (CDP) model, and the element type was C3D8R. The brick blocks were sintered shale hollow bricks with a dimension of 240 mm×190 mm×90 mm (length × thickness× height). The compressive strength of the masonry was calculated according to the “Code for Design of Masonry Structures”6. The compressive stress-strain relationship of masonry was obtained using Equation40. The peak compressive strain of the masonry was 0.0039. The tensile strength of the masonry was taken as 1/10 of the compressive strength41, and the tensile stress-strain curve was calculated based on the tensile constitutive of the concrete material in the code. Since the infilled wall and the frame were regarded as rigidly connected, the infilled wall was connected to the frame by “contact”. In the models, according to code GB 50,003 − 20117, the coefficient of friction between masonry units was 0.7, and that between the infill wall and the frame was 0.45. “Hard” contact was used for the normal behavior, as it is the most physically realistic approach by strictly enforcing “zero penetration” at the contact surfaces. The cohesive behavior of the mortar was simulated by considering one shear stiffness value and two normal stiffness values, which were determined from the shear and tensile strengths of the mortar. The damage model for the mortar adopted a quadratic stress criterion.

The concrete of the constructional column was defined by the Concrete Damage Plasticity (CDP) model, and the parameters of the CDP model are shown in Table 2. Based on the recommended parameter settings, which were verified by previous experiments and numerical simulations42, in this study, while maintaining the basic framework unchanged, reasonable ranges of the expansion angle (ψ) and viscosity coefficient (µ) were adjusted according to the experimental data, and the simulation accuracy of the load-displacement curve was improved. The compressive stress-strain curve and tensile stress-strain curve of concrete were selected following the provisions in the “Code for Design of Concrete Structures”43. The elastic modulus of concrete was 2.5 × 104 MPa. To simulate the engaging effect of the horse-tooth joints of the constructional column, a “binding” connection was adopted with the infilled wall. It was embedded in the constructional column through the “embedded region” after the reinforcing bars were assembled to form a reinforcing mesh. The bottom surface of the floor beam of the frame infill wall was subjected to completely fixed constraints (fixing all translational and rotational degrees of freedom) to simulate the rigid connection between the structure and the foundation.

Table 2 CDP model parameters.
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Test conditions

Based on the accuracy of the FEM validated against experimental results, the in-plane performance of the FI was obtained, and the effect of drift ratios (0.33%, and 0.53%) on the stress and strain of the FI was analyzed. Subsequently, the out-of-plane performance of the FI, which was in-plane pre-damaged, was studied. The in-plane load was applied incrementally under displacement control. The loading increment was set to 2 mm per step before yielding and was increased to 4 mm per step post-yielding. The loading schedule is shown in Fig. 4.

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Loading schedule of in-plane.

As shown in Fig. 5, the out-of-plane load was applied incrementally under displacement control, which is perpendicular to the wall surface.

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Loading scheme of out-of-plane.

Model verification

To validate the accuracy of the separated model, the finite element simulation results of the FW1, FW2, and FW3 were compared with the in-plane experimental results of the full-scale model. The variation trends observed in the load-displacement curves from both the experiments and simulations were basically consistent. The correlation coefficients, R, were 0.974, 0.964, and 0.952, respectively. (The closer the value of R approaches 1, the more accurate the fitting effect becomes)44. The skeleton curves are shown in Fig. 617.

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Skeleton curve17.

The compressive direction was defined as positive and the tensile direction as negative. The in-plane peak bearing capacity of the FW1 was 537.49 kN, and the load-displacement curve exhibited a decline when the lateral displacements reached 106 mm (positive) and 102 mm (negative). The in-plane peak bearing capacity of the FW2 was 950.71kN when the lateral displacements were 84 mm (positive) and 80 mm (negative). In contrast, FW3 performed an in-plane peak bearing capacity of 607.50 kN, when the lateral displacements were at 106 mm (positive) and 102 mm (negative), the load-displacement curve exhibited a declining section. The in-plane peak load capacity of FW2 was 176.88% of that of FW1, a 76.88% increase. Compared to FW3, the peak capacity of FW2 was 156.50% of that of FW3. Indicating that the confinement and stiffness effects of a cast-in-situ constructional column improved the in-plane bearing capacity of the FI. The peak in-plane bearing capacity of the FW3 was 113.02% of that of the FW1, indicating that a fabricated constructional column exerted a relatively minor confinement and stiffness effect on the FI when compared to the cast-in-situ constructional column. The horizontal displacements of the FW1 and the FW3 at the onset of the decline section were 126.19% (positive) and 127.5% (negative), respectively, relative to those of the FW2, indicating that the incorporation of a cast-in-situ constructional column results in a reduction in peak displacement and a decrease in ductility in the plane. In conclusion, the constructional column improves the in-plane bearing capacity of the FI. In comparison to the cast-in-situ constructional column, the fabricated constructional column has less influence on the in-plane bearing capacity of the FI, and does not reduce the peak displacement. It can prevent excessive stiffness from generating and increase the ductility of FI.

Analysis of finite element results

In-plane stress and strain

Stress analysis

The stress cloud diagrams of the FI are shown in Fig. 7. When the inter-story drift angle of FW1 reached 0.33%, the infilled wall exhibited a distinct zoning characteristic. The triangular regions located at the lower left and upper right corners correspond to the formation of a left strut and a right strut, respectively, which segregated the central region of the wall. Because the area of the triangular zone in the lower left corner was relatively large, the length of the left strut was long, and the width was long. However, the area of the triangular zone in the upper right corner was small, the length of the right strut was short, and the width was narrow. The FW1 withstood horizontal loading, mainly depending on the triangular zone at the left lower corner adjacent to the loading side and the central zone of the infilled wall. With the load increasing, the triangular zone at the lower left corner of the wall was gradually crushed. The location of the right strut shifted towards the loading side and suffered a certain load. Finally, the overall load resistance capacity of the infilled wall was reduced.

During the initial loading phase, the stress evolution pattern of FW2 was similar to that of FW1, and the in-plane load was mainly borne by the central region of the infilled wall. When the inter-story drift angle was 0.33%, because the infilled wall was divided into two sections by a constructional column, left and right, the diagonal strut at the center of the infilled wall was separated, thereby two distinct diagonal struts were created on either side. When the inter-story drift angle was 0.53%, a left distinct diagonal strut and a distinct diagonal strut appeared on the FW2, and the cast-in-situ constructional column changed the stress development path on the wall surface. Since the construction column provided a high lateral resistance stiffness, it could effectively impose a restraining effect on the infilled wall under horizontal loading. Consequently, an infilled wall with a constructional column can be considered as two independently deformed walls.

The stress evolution process of the FW3 was similar to that of FW1. The stress development mode on the wall surface was not influenced by a fabricated constructional column, and the stress was transmitted through the mortar joints between the precast blocks of the fabricated constructional column. When the inter-story drift angle was 0.53%, the wall exhibited a three-brace failure mode. As the horizontal displacement increased, the area of the lower left triangular zone in FW3 gradually decreased, whereas that of the upper right triangular zone expanded. So the length of the left diagonal strut decreased, and the right diagonal strut increased. The FW3 withstood horizontal loading, mainly depending on the triangular zone at the left lower corner adjacent to the loading side and the central zone of the infilled wall. But some small diagonal braces emerge on both sides of the fabricated construction column.

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Stress cloud diagram (MPa).

Equivalent plastic strain cloud diagram

The equivalent plastic strain cloud diagram (PEEQ) of the FI is shown in Fig. 8. When the inter-story drift angle of FW1 was 0.33%, the failure initially occurred at the contact areas of beams and wall, and the center of the wall. When the inter-story drift angle was 0.53%, as the drift angle increased, the failure at the contact areas of beams and wall, and the center of the wall, was worse. The damage in the middle of the wall extended to both sides, thereby increasing the failure area. The diagonal crack initiated in the center of the wall and propagated to the four corners. When the inter-story drift angle of FW2 was 0.33%, little damage appeared on the wall. When the inter-story drift angle was 0.53%, the damage increased and was mainly concentrated on both sides of the constructional column. The failure occurred at the corners of the left and right walls, which developed diagonally along the diagonal direction. When the inter-story drift angle of FW3 was 0.53%, the damage on the wall was mainly characterized as horizontal, accompanied by a few diagonal cracks, and the wall presented a layering phenomenon.

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Equivalent plastic strain cloud diagram.

Out-of-plane behaviour

Failure mode

The out-of-plane displacement cloud diagram of FI is shown in Fig. 9. The FI yielded when the out-of-plane displacement was between 10.00 mm and 20.00 mm. The displacement cloud diagram of the FW1 exhibited a distinct bidirectional arching mechanism, that is, both the vertical wall and horizontal wall presented an arched state. Under the out-of-plane load, the masonry bricks in the middle of the wall were pushed out, and the maximum out-of-plane displacement area was concentrated in the middle of the wall. Moreover, as the out-of-plane load increased, the area of the maximum out-of-plane displacement gradually decreased towards in the middle of the wall, and the maximum displacement regions of the FW2 and FW3 were located in the central portions of the walls on both sides of the constructional column, suggesting that the constructional column and its construction measures divided the infilled wall into the left and right segments. Nevertheless, the failure mode of the infilled-wall under out-of-plane load remains presented as a distinct bidirectional arching mechanism, bbut the constructional colum altered the out-of-plane failure mode of the FI.

According to the failure mode of the FI under out-of-plane load, it is proposed that during the construction of the infilled wall frames, continuous reinforcing bars can be adopted instead of the original construction method, where each frame column and constructional column extend 1 m of reinforcing bars to the wall.

This not only reduces the process of reinforcing bar cutting but also ensures that the structure has a better out-of-plane strength. In the case of the infilled wall frames without a constructional column, it is recommended to install continuous tie bars near the half-height of the infilled wall to reduce the displacement of the structure under out-of-plane loads.

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Out-of-plane displacement cloud diagram (mm).

The effect of a construction column on the failure mode of the FI is shown in Fig. 10. Along the span direction, under the out-of-plane load, cracks initiated on the wall of FW1, and the wall was separated into three. The wall rotated around the cracking position and was tightly abutting against the adjacent column and wall to transfer the out-of-plane load, forming an arching mechanism. The crack initiation position on the wall of the FW2 and FW3 was at one-fourth of the wall length. The middle part of the wall was constrained by the construction column and corresponding construction measures, resulting in high integrity. The crack initiation position on the wall was changed, causing two arching phenomena on both sides of a construction column formed under the out-of-plane load.

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Out-of-plane failure modes of the FI.

Damage analysis

When the friction coefficients between the brick blocks are uniform and there is no in-plane damage to the FI, the out-of-plane compressive and tensile deformations are shown in Fig. 11.

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Compressive damage and tensile damage.

The compressive damage of the FI was relatively lower than the tensile damage. The distribution of the compression damage was consistent with the large out-of-plane displacement in the displacement nephogram. As the out-of-plane displacement increased, the area of compressive damage increased and exhibited a certain symmetry. The compressive damage on the FW1 was mainly concentrated in the middle of the wall. When the out-of-plane displacement was 20.00 mm, the damage degree of the upper left and upper right corners of the FW1 was higher than that of the lower left and lower right corners. No obvious compressive damage was observed on the construction column of the FW2, whereas compressive damage was mainly concentrated in the middle of the left and right wall sections near the frame side. The compressive damage on the FW3 was mainly concentrated in the middle of the left and right sidewalls, and slight compressive damage occurred at the connection of the precast blocks in the middle of the fabricated construction column.

The tensile damage on the FW1 initiated at the mid-region of the wall and propagated toward the corners, exhibiting an X-shaped failure pattern. For specimen FW2, when the out-of-plane displacement reached 20.00 mm, tensile failure was predominantly localized along the frame-side regions at the mid-height of the left and right walls. As the out-of-plane displacement increased, the tensile damage area extended toward the construction column, and the tensile damage on the middle of the constructional column was the most severe. The development process of tensile damage in FW3 was similar to that in FW2. However, the tensile damage on the fabricated construction column was primarily concentrated at the junctions of each precast block. This is because precast blocks are connected by mortar, which is prone to failure under out-of-plane loads.

Notably, the damage observed in this paper, including X-shaped cracking, horizontal delamination, and concentration of out-of-plane displacement, exhibited a high degree of consistency with the experimental results observed by Kaya et al.45. It provided strong corroborative support for the ability of our finite element model to reasonably capture the key out-of-plane failure mechanisms. The underlying mechanism of the coupling effect, where in-plane damage led to out-of-plane strength degradation, was consistent with the URM damage patterns that progressively develop under combined dynamic actions, as demonstrated by Kaya et al.46. It also revealed that in-plane cracking weakens the overall integrity of the wall, thereby reducing the capacity to resist out-of-plane loads, which was verified in the analysis in this paper.

Load-displacement curve

In-pane undamaged

The out-of-plane load-displacement curve and stiffness degradation curve when the in-plane inter-story drift angle is zero are shown in Fig. 12. The constructional column enhanced the out-of-plane bearing capacity and stiffness of the FI. The out-of-plane bearing capacities of the FW2 and FW3 were 271.49% (out-of-plane displacement was 50 mm) and 199.09% of that of FW1, respectively, and the initial maximum stiffness of FW1 was 41.19% and 55.35% of that of FW2 and FW3, respectively. The constructional column played a significant role in improving the out-of-plane performance of the FI. The out-of-plane bearing capacity of FW3 was 72.25% of that of FW2, indicating that the cast-in-place constructional column provides a greater out-of-plane restraint effect on the FI compared to the fabricated construction column. When the out-of-plane displacement was 17 mm, the peak bearing capacity of the FW1 occurred, whereas for FW2, the out-of-plane displacement was 50 mm, and for FW3, the out-of-plane displacement was 24 mm. This indicated that the incorporation of the constructional column enhances the out-of-plane ductility of the FI. In conclusion, the constructional column increases both the in-plane bearing capacity and ductility of the FI. Furthermore, the enhancement effects of a fabricated constructional column on the out-of-plane bearing capacity and ductility are less than those of a cast-in-situ constructional column.

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Out-of-plane load-displacement curve and stiffness degradation curve.

In-plane damaged

When the in-plane inter-story drift angle was 0.33% and 0.53% (with displacements of 10 mm and 16 mm, respectively), the load-displacement curve is shown in Fig. 13. The in-plane damage of FI has a considerable impact on the out-of-plane performance. When the inter-story drift angle was 0.53%, the out-of-plane bearing capacity of FW1 was 39.50% of that when the inter-story drift angle was 0, decreased by 60.50%. Under the same working conditions, the out-of-plane bearing capacity of FW2 decreased by 29.48%, and that of FW3 decreased by 25.31%, indicating that a constructional column can mitigate the influence of the in-plane damage of the FI on the out-of-plane strength, and the out-of-plane bearing capacity of FW3 decreased with the increase of the in-plane damage. However, the strength reduction rate decreased with the increase in in-plane displacement. The out-of-plane load-displacement curves corresponding to inter-story drift angles of 0.33% and 0.53% were nearly coincident. This phenomenon can be attributed to the presence of steel bars within the wall, which effectively limited the out-of-plane displacement under in-plane damage conditions.

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Out-of-plane performance of FI after in-plane damage.

The out-of-plane displacement cloud diagram of FI after in-plane damage is shown in Fig. 14. The out-of-plane bearing capacity of the FI was affected by the in-plane damage. As the in-plane displacement increased from 10 mm to 16 mm, when the out-of-plane displacements were identical, the failure of the wall became worse. When the in-plane displacement and out-of-plane displacement were the same, the out-of-plane failure of the FW2 was markedly worse than that observed in FW1 and FW3. The maximum out-of-plane displacement of FW2 reached 43 mm. This is because the in-plane stiffness of the FW2 was higher than that of FW1 and FW3, which results in a larger in-plane load being sustained. Furthermore, under similar conditions of in-plane and out-of-plane displacements, the out-of-plane failure of the FW3 was much better than that of FW1. The maximum out-of-plane displacement of FW3 was 6.6 mm, while that of FW1 reached 16.69 mm. Indicating that a fabricated constructional column can substantially reduce the damage to the wall induced by out-of-plane loads. Meanwhile, the experimental observations of Hossain et al.27 are consistent with the damage evolution observed in the simulation. It is essential to acknowledge the potential sources of error inherent in numerical simulations. These errors stem from several factors: firstly, the material constitutive model employed is a simplification of complex material behavior. Secondly, the precision of the mesh and the selection of element types can influence the accuracy of local stress calculations. Lastly, the boundary conditions and loading paths used in the simulation are idealized and may deviate from complex real-world conditions.

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Out-of-Plane displacement cloud diagram of FI after in-plane damage (mm).

Conclusions

In this study, based on finite element simulations, the influence of the constructional columns on the out-of-plane seismic performance of infilled walls after experiencing in-plane damage was investigated, the main conclusions are as follows.

  1. (1)

    Through the finite element analysis, the in-plane load-displacement curves were validated, and which demonstrated a strong correlation with the experimental data. The finite element models can accurately reflect the mechanical behavior of infilled walls under in-plane damage, thereby providing a reliable basis for out-of-plane performance analysis.

  2. (2)

    The cast-in-situ constructional columns improved the in-plane bearing capacity of FI. In contrast, the fabricated constructional column provided a relatively limited enhancement to the in-plane bearing capacity of FI, but the ductility was improved.

  3. (3)

    The constructional columns enhanced the out-of-plane bearing capacity and improved the out-of-plane failure mode of the FI after in-plane damage. It is because the constructional columns exerted a pronounced restraint effect on the out-of-plane displacement in the middle of the infilled wall, the overall out-of-plane stability of the FI was improved.

It should be noted that the findings of this study were primarily based on a single-story cantilever frame. Consequently, the current conclusions may possess certain limitations when applied to multi-story structures, especially given that the complex interlayer interaction mechanisms in such structures require further in-depth investigation. Furthermore, the applicability and generality of the proposed finite element models to other wall types, such as autoclaved aerated concrete (AAC) infilled walls, necessitate further validation through additional experiments and simulations.