Keywords

1 Introduction

Reinforced concrete wall structures can bear vertical and lateral loads caused by wind or earthquakes. Concrete buildings do not fall easily and stay standing after an earthquake, but the high residual drift ratio makes it much more likely that the buildings will be destroyed [1]. The installation should be demolished after the earthquake, or it might require expensive structural repairs that are neither practical nor cost-effective. In the past ten years, low-damage structural systems have attracted the attention of both academics and practicing engineers. To increase the performance of repairable shear walls, some researchers have suggested using high-strength materials like FRP reinforcement [2, 3], PC strands [4], and SMA (shape memory alloy) [5].

The ability of a concrete structure, subsequent to being unloaded, to revert back to its initial position is known as Self-centeredness aptitude. This capability can be attained through three methods: (a) using unbonded post-tensioning strands[6,7,8,9], (b) memory shape alloy steels[10, 11], and (c) pre-pressed disc springs[12, 13]. Various systems have been developed using these methods, such as a self-centering link beam that is reinforced by post-tensioned Shape Memory Alloy (SMA) rods [14], Unbonded post-tensioned prefabricated concrete moment framework [15], Shear wall made of unbonded post-tensioned concrete [16, 17], The wall is designed with self-centering capabilities and incorporates disc spring devices or SMA bars [13], as well as an unbonded post-tensioned linked wall system [18]. Shen et al. [19, 20] examined the performance of a post-tensioned concrete linked wall system that includes a steel coupling beam. Additionally, these strands contribute to the system’s ability to automatically align itself. Consequently, following the earthquake, the structure would go back to its initial undisturbed position and exhibit either no remaining or minimal remaining displacement. The benefits of unbonded post-tensioned coupling beams, as compared to monolithic cast-in-place RC coupling beams and embedded steel coupling beams, include (a) enhanced aesthetics due to less visible beam and wall details, (b) ability to endure substantial nonlinear displacements without substantial structural harm, (c) self-centering ability that minimizes residual capacity of the structure following a major earthquake, and (d) expedited and simplified post-earthquake repair of the system. Additional ED devices are necessary for this system because of the potential insufficiency of energy dissipation by self-centering concrete walls. The structural deformation behavior can be simplified as “bilinear elastic,” as depicted in Fig. 1(a). To enhance the ability of the self-centering shear wall to dissipate energy, researchers explored the possibility of incorporating a damper element to induce a “flag-shaped” deformation pattern in the structure, as depicted in Fig. 1(b).

To enhance the energy absorption capability of the wall, the hybrid wall, which adds energy absorption fuses to the self-centering wall, is proposed. Restrepo and Rahman[21] first suggested steel rebars embedded in the wall-to-foundation to provide sufficient energy dissipation capacity. Metal devices that presented energy absorption were presented to easily repair hybrid walls after earthquakes. Marriott et al. [22] Suggested an innovative wall design that combines tension-compression elements yielding steel fuses exterior of the wall. Li et al. [23] devised a novel wall-to-foundation connection utilizing buckling-restrained steel sheets through testing methods. For the vertical joints of walls, a unique U-shaped flexural plate (UFP) [24] was designed. Wall rankings and tests on the wall with the O-shaped plates revealed its substantial seismic capacity [25], so Henry et al. [26] proposed welding an O-shaped plate on the wall and using columns to distribute energy.

The current study presents earthquake-resilient RC walls installed with replaceable ED steel angles damper (SC-SAD) to improve earthquake performance. This wall system can produce the following effects: SC capability provided by the unbonded strands, enhanced energy dissipation by external steel angles, limited damage in RC walls with major inelastic deformations concentrated in steel angles, and an earthquake-resilient design requiring little to no repair even after earthquakes. A numerical model of the RC wall was subsequently created and validated using data from representative tests. Last but not least, the computational (finite element) investigation and evaluation of the seismic performance of the RC walls was done in terms of hysteresis curves, skeleton curves, stiffness degradation, residual displacement, and self-centering and energy dissipation capabilities.

Fig. 1.
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Post-tensioned SC wall system with energy dissipaters a) post-tensioning re-centering and energy dissipation b) Hybrid system response.

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2 Material Properties

The ABAQUS concrete damaged plasticity model (CDP) was used for the concrete materials in the FEM. This model was mainly made for reinforced concrete structures that are loaded cyclically or dynamically. The concrete damage plasticity model is generally built on two primary uniaxial concrete data sets and five plasticity parameters. The yield surface function, the potential flow, and the material’s viscosity are all determined by the five parameters φ, e, fb0/fc0, Kc, and λ, Multiple calculations were performed to increase the analysis’s precision and convergence, and the results show that the model’s plasticity parameter values are 38,0.1,1.16, 0.6667, and 0.0005, respectively. The elastic modulus and Poisson’s ratio are two more variables that must be defined to define the concrete material. The classical elastic-perfectly plastic stress-strain material model is adopted for the steel reinforcements and pre-stress tendons, and tests obtain the essential properties. In addition, the ED angle devices are made mainly of steel. The Q345 strength grade describes the angle made of steel. This investigation uses a model that is elastically and exhibits excellent plasticity to mimic the behavior of steel angles accurately. Table 1 and Fig. 2 outlines the particular characteristics of all of the materials.

Fig. 2.
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Mechanical properties of concrete material.

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Table 1. Properties of concrete, reinforced bars, ED steel angle, and strands.
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Fig. 3.
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Specifications of specimens’ construction.

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Fig. 4.
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Design details of the ED steel angle.

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3 Test Specimen

Restrepo et al. [21] tested three self-centering shear walls that had been pre-stressed to look into how well self-centering concrete wall structures handle earthquakes. The prototype for a 4-story building structure was used to design the test specimens. The tested samples were called “Unit1, Unit2, and Unit3.“ This research paper uses Unit 1 as an example, and Fig. 3 displays the wall’s design details. The wall is 3700 mm tall and 125 mm thick. The shear wall has two sets of pre-stressed tendons (PTs). They are set up 175 mm from the centerline of the wall. Each pre-stressed tendon comprises a steel strand that is 12.7 mm wide and has a cross-sectional area of 100 mm2. Their starting level of pre-stress is 0.5. The two corners of the test sample have additional enhancements to strengthen the local concrete and prevent the concrete’s premature failure at the wall toe while the wall is moving back and forth.

First, Unit 1 has no ED bars or other energy-dissipating devices at the joints. It means it is a typical pre-stressed rocking wall structure written as SC in this study. Second, this research shows a brand-new precast self-centering concrete wall structure made of ED steel angles device. It is called SC-SAD. In Fig. 4, you can see more information about the design parameters. The angle damper made of steel used in this study has a cross-section that is L75 mm × 75 mm × 4 mm. It was done with an angle width of b = 10 mm. The ED steel angle dampers’ legs were attached to the corners of the walls and the foundation. It can create stable hysteretic loops that can handle more ED loads.

4 Finite Element Analysis

This study presents a numerical simulation analysis using the ABAQUS software to investigate the energy dissipation of the proposed system. Consequently, the proposed method parameters conduct a finite element analysis (FEA), as shown in Fig. 7. The strong portion of the sample utilizes the C3D8R part, while the pre-stressed and stressed reinforcements adjust the truss element. A small pad simulates the anchor at the top of the wall and the bottom end of the foundation, corresponding to the pre-stressed tendons. Regular rebar and concrete are embedded in regions. Concrete is hardened into a damaged flexibility in concrete. The touch interfaces of further elements are formed with hard contact in the desired direction and the circumferential contact characteristic direction. The coefficient of specific friction is established based on the physical characteristics of the touching layer. The experimental parameters, including loading approaches and environment at borders, are identical to those of the subsequent studies. The bond slip occurs among steel. Bars and concrete are ignored when the precast concrete wall contacts reinforcing steel bars and profiled steel. The tie partially simulates wall contact with ED steel angle damper legs. A “surface-to-surface” connection models the wall to the foundation. The contact surface is “contact hard,” meaning it can be Split off from the outer layer. The perpendicular attribute is “penalty,” and the percentage of interaction is 0.5. This method can mimic the self-centering rocking wall’s corner lifting characteristics while avoiding concrete tension to make the structure more logical. We investigate the seismic response of a self-centering rocking wall subjected to cyclic horizontal forces on the upper wall. Figure 5 depicts the horizontal cyclic load-displacement loading system. The SC and SC-steel angle damper (SC-SAD) models are analyzed numerically. Figure 6 shows the first step in validating the precision of the mathematical models by comparing the simulation findings of SC with the test results. This diagram depicts the nonlinear elastic response typical of a rocking body. Almost no residual lateral displacements were detected during the reaction, even after applying drift ratios of 3%. According to test results, [21]: As shown in Fig. 1(a), the hysteresis curve of the SC specimen without any energy absorption device is of the typical “rocking wall” type, indicating that its energy dissipation capacity is poor. Figure 6 demonstrates that the overall patterns of the two hysteresis curves have a high degree of unity with one another. Numerical simulation and experimental results agree well and show similar trends, so they can accurately reflect the proposed system’s mechanical properties like bearing and energy dissipation capacities in Fig. 7.

5 Result Analysis

The loading process was modeled through the force system, which consists of the pre-stress tendons and axial force to the wall body, resisting the bending moment caused by the horizontal load before the self-centering rocking wall begins to rotate. When the wall starts to turning, the right and left devices of energy absorption, which have more significant force, begin to yield tension in the left. As the turning continues to increase, the two instruments of energy absorption begin to yield in. To evaluate the FEM’s accuracy even further, regional variables for reaction like the unbonded tendon stress are looked into. To make it possible to compare the FEM calculations and test results. The FEM results showed a good correlation with the experimental results. The inaccurate estimation of strand stress during lateral force, as depicted in Fig. 8, may have been caused by minor seating losses at the post-tensioning anchor and the test-related deformation of the loading beam, which were not considered in the Finite Element Model (FEM).

5.1 Analysis of Hysteresis Curve

The hysteresis loop of the load-movement is shown in Fig. 9. In Fig. 9a, the starting stage of loading, the structure is in an entirely elastic step, the hysteresis loop is almost a straight path, and the area of energy absorption is tiny; with the increase of the load, the uplifting of the wall increases, the energy dissipation capacity little increases.

Fig. 5.
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Displacement control process of numerical model.

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Fig. 6.
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Differences between the predicted hysteretic curves and the experimental findings.

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Fig. 7.
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Finite element model loading

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Fig. 8.
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Relationship between modelling and test outcomes: (a) The stresses of the PT1 bars; (b) The stresses of the PT2 rods.

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5.2 Influence of Thickness of Steel Angle Damper on Energy Dissipation Capacity

Figure 9 (a, b, c, d, and e) shows the hysteresis curve of the load-sway. With the augment in the load, the energy dissipation capacity of the steel angle damper starts to play; The structure’s rotation angle is increasing, causing the steel angle devices in the corners of the wall to enter the plastics phase; the energy absorption capacity augment until it attended its peak. Based on the above analysis, the energy absorption capacity of the steel angle device is dominant for the SC-SAD under cyclic loading. So, it is essential to look into how SAD’s thickness affects SC-SAD’s mechanical properties when it is loaded and unloaded many times. To accomplish this goal, five cases have been chosen to investigate the effect that varying thicknesses of SAD have on the energy dissipation of SC-SAD. These results can be found in Fig. 9. For a small angle thickness of 10mm, the energy dissipation is about 2.5 KN-m. For the case of an angle thickness of 12.5mm, the energy dissipation is about 8 KN-m. In the case of an angle with a thickness of 15mm, the energy dissipation is approximately 11 KN-m. For an angle thickness of 17.5mm, the energy dissipation is about 15 KN-m. In the case of an angle with a thickness of 20mm, the energy dissipation is approximately 19 KN-m. For all cases, the energy absorption gradually increases with the displacement increase δ. For the same shape and strength as the angle damper, the selection of the thickness of the angle damper will help determine energy dissipation, which is quite crucial to the design of the angle damper. The deformation for the angle thickness of 10 mm to 20 mm in the FEA simulation is shown in Fig. 9 (a, b, c, d, and e) and Fig. 10, respectively.

Fig. 9.
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Lateral force-top displacement hysteretic curves of the (a) angle plate thickness 10 mm (b) angle plate thickness 12.5 mm (c) angle plate thickness 15 mm (d) angle plate thickness 17.5 mm(e) angle plate thickness 20 mm.

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5.3 Analysis of Skeleton Curve

The skeleton loops and cumulative energy dissipators coefficient ξ loops eshedtablis on the hysteresis loops for walls with the ED angle thickness of 10 mm, 12.5 mm, 15 mm, 17.5 mm, and 20 mm are illustrated in Figs. 11 and 12, indicating that the early stiffness and force, as well as the energy absorption ability of SC-SAD, are substantially improved with the augment of SAD’s thickness under the premise of other conditions being the same. However, the self-centering capability was decreased. It is because the same recovery forces presented by the pre-stressed tendons should overcome the different SAD’s resistances due to varying thicknesses of SADs, resulting in higher starting stiffness, larger bearing capacity, and energy absorption capacity but more obvious residual malformation with the increased thickness of SADs. The envelope curves extracted from the cycle peaks are shown in Fig. 11.

The equivalent viscous dampening proportion assesses the structure’s ability to dissipate energy. Figure 13 depicts how the same amount of damping viscous alters depending on the displacement that is being measured. Overall, the same viscous damping proportion increases with the increase in displacement of the SC-SAD system. For example, if the angle thickness is 20 mm, the comparable viscous pressure damping proportion of the sample reaches a peak value of 0.01274 importance the drift is 0.0025%. When the drift is 0.0075%, the same viscous damping proportion of the sample gets a maximum importance of 0.02196. When the drift is 0.01575%, the comparable viscous damping ratio of the model reaches a maximum importance of 0.02612. When the drift is 0.025%, the same viscous damping proportion of the model gets a maximum importance of 0.0259. To better understand the variation of the system cyclic response of an SC-SAD with different angle thickness parameters, residual drift is presented here, as shown in Fig. 14. The variation in selected thickness parameters of the SAD (10, 12.5, 15, 17.5, and 20 mm) It is observed that the residual drift increases noticeably with an increase in the thickness of the SAD. However, this comes at a penalty of reduced re-centering capabilities. The reduction in re-centering is more apparent in more thickness angles, but for a low and medium range of thickness of the SAD, the SC-SAD can re-center after the complete cycle. Increasing the thickness of the angle damper is beneficial to improving the self-centering wall’s lateral stiffness, strength, and energy absorption capacity. Still, it simultaneously causes a significant residual drift.

Fig. 10.
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Load-displacement curves of specimens with different angle thickness ratios.

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Fig. 11.
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Backbone curves.

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Fig. 12.
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Energy dissipation results.

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Fig. 13.
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Equivalent viscous damping ratio.

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Fig. 14.
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Residual Drift ratio.

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6 Summary and Conclusions

This study suggests using replaceable ED devices to create an earthquake-resistant RC wall. The structure and design of this innovative precast RC wall were presented. The post-tensioned wall was investigated. Steel-angle dampers were used on the wall to dissipate the energy. The numerical modeling samples included a control specimen without an energy dissipation damper and five specimens with steel angle dampers with different damper thicknesses were tested under cyclic loading. The main findings of this study are summarized as follows:

The control sample with no energy absorption damper under cyclic loading showed bilinear-elastic load-movement behavior. At the same time, the models equipped with steel angle dampers presented flag-shaped hysteresis loops. In these models, PT strands played the role of self-centering, and steel angle devices played the role of energy absorption in the system. The angle damper self-centering wall suggested in the paper is straightforward and clearly defined. It is possible to achieve the following: no damage to the primary wall structure, replaceable members, simple installation, and quick restoration of structure-function. The force-displacement curve for the suggested system showed an ordinary “flag-shaped” hysteretic response, and it has excellent energy dissipation and self-centering capabilities. Based on the numerical results, the damper provided a completely stable behavior without increasing damage. The specimen showed regular hysteresis behavior up to the thickness of 15 mm, but with thicknesses 17.5 mm and 20 mm, the residual of the sample increased significantly. At the same time, the models had excellent energy dissipation, load-carrying capacities, and lateral stiffness under cyclic loads. They could withstand large nonlinearities without additional damage to wall and angle dampers. Increasing the ED device thickness is beneficial to improving the energy absorption and the self-centering wall’s lateral stiffness. Still, it simultaneously causes a significant residual drift.

The plastic deformation of the structure is concentrated in the energy absorption device. The proposed precast RC walls with ED steel angle will provide a promising solution for performance seismic-resisting structural systems suitable for resilient and sustainable civil infrastructure.