Finite Element Analysis of Self-centering Reinforced Concrete Shear Walls

Abstract

Post-tensioned precast concrete walls are an attractive research trend in structural engineering, which replaces cast-in-place concrete walls in earthquake-prone buildings. Precast concrete walls use mild steel and high-strength post-tensioning steel for flexural resistance. Mild steel reinforcement yields in tension and compression, dissipating inelastic energy. Unbounded tendons are used inside the wall to give self-centering capability, which lowers residual displacements. At the wall-foundation, horizontal slots are installed equally. Meanwhile, the middle-wall concrete is still anchored to the base. A three-dimensional finite element (FE) model is developed in this study to assess the lateral load response of shear walls with horizontal bottom slots. The seismic performance of three distinct walls is evaluated using the Abaqus software FEA. The model is validated by comparing the experimental data accessible in the literature. Furthermore, we investigate the effects of bottom slit length, steel strand position, initial prestressing level, and concrete strength. All of these criteria are critical for constructing structures with the new concept. The results of this study show that the three-dimensional finite element model accurately predicts all of the above-mentioned properties, including the lateral force–displacement response and toe area damage of self-centering shear walls.

1 Introduction

Shear walls are structural elements that provide both lateral force resistance and drift control to buildings during seismic events. Conventional concrete shear walls that are part of monolithic structures are highly likely to suffer extensive damage from flexural and shear cracking. Its toe crushing, rebar fracture, buckling, and residual lateral displacement respond to reversed cyclic loading during design intensity or higher seismic events. Reinforcing steel and base concrete collapse in concrete shear walls, dissipating energy. Self-centering (SC) earthquake-resistant systems are innovative. SC structural systems are designed to decompress at a certain level of lateral loading, contradicting conventional systems. The recently proposed self-centering (SC) structural systems are a feasible alternative to traditional structural systems as they can make structures usable and repairable after strong earthquakes. The SC systems have important advantages in terms of their overall earthquake performance. They can reduce damage to the main structural components to minimal levels and eliminate residual lateral deformations due to strong earthquakes. Recent research on the PRESSS (Precast Seismic Structural Systems) project has shown that precast concrete wall and frame structures that use high-strength post-tensioning (PT) steel and mild steel reinforcement have good seismic properties during a severe earthquake. In earthquake-prone regions, precast concrete walls have been created as an alternative to cast-in-place reinforced concrete (RC) shear walls for building lateral-force resisting systems [1,2,3,4,5,6]

These precast concrete walls incorporate unbonded post-tensioning (PT) tendons extending from the roof to the foundation level (see Fig. 1). The self-centering response of precast concrete walls is achieved by restoring forces provided by gravity loading and the PT force. Precast wall systems have been subject to numerous pseudo-static lateral load tests [1, 3, 7]and extensive analytical investigations [2, 3, 7,8,9] Restrope and Rahman [8] researched a hybrid shear wall while subjecting it to quasi-static reversed cyclic loading tests. Holden et al. [9] studied a hybrid shear wall with carbon fiber tendons and steel fiber concrete, and the reinforcements of the walls were reduced compared with conventional precast walls. Sritharan et al. [10] developed an end-column precast wall that was unbonded and post-tensioned to the base. PreWEC can be built at a low cost while limiting damage and providing self-centering capability.

Fig. 1

Self-centering wall with horizontal bottom slots [12]

Finite element (FE) analysis is widely adopted in earthquake engineering, particularly when dealing with systems with a high number of degrees of freedom (DOF), which represent the structural configuration of buildings. On the other hand, the simulation of the seismic response of RC structures through finite element analysis can be complex and challenging. This is mostly because of how the different mechanical responses of concrete and steel rebars cause them to work together in a complicated way. Although many tests on self-centering shear walls have been conducted, the authors have limited knowledge on how to numerically model these structures in order to represent the usual nonlinear response associated with self-centering shear wall behavior. To anticipate the behavior of self-centering shear walls, most earlier studies used rotational spring, fiber, and multi-spring models [11].

While these simplified FE modeling techniques can estimate the global behaviors of self-centering shear walls, they are lacking in predicting the damage to the concrete of these walls under extreme loading conditions. To cope with these issues and bridge the gap in the modeling for self-centering, the current study proposes a novel model based on moment-rotation analysis using Abaqus to provide a reference and foundation for the design of self-centering concrete walls. This article uses ABAQUS FEA to model self-centering shear walls with horizontal bottom slots. Horizontal slots are made by inserting separating steel plates at the wall-foundation joint of prestressed shear walls and maintaining the reinforced concrete in the center of the wall width linked with the foundation. Additionally, this study examines the effects of slot length, steel strand positioning, initial pretension level, and concrete strength. Applying the new idea to engineering structures required consideration of all these factors. This work is organized as follows: Sect. 2 is intended to describe the method, including the procedures for modeling reinforced concrete post-tensioned precast shear walls. In Sect. 3, the analytical analysis is described, and the discussion and results analysis are described in Sect. 4. Finally, conclusions drawn from the study are summarized in Sect. 5.

2 Sample Study

2.1 Shear Walls with Horizontal Bottom Slots

This study used one typical shear wall and walls with horizontal bottom slots from [12]. The specimens were all the same size, with the wall dimension (2 * 1 * 0.125) mm. The reinforcement features of the examples for various arrangements (sw0 through sw1-3) in regard to elevation are shown in Fig. 2. The aspect ratio of 2.3 was chosen to obtain wall specimen reaction rather than shear slip ACI ITG-5.1 (ACI 2007). The quantity of reinforcement crossing the wall-foundation joint defined the slot length, which was equal to the dividing steel plate (Fig. 2). The initial prestressing values of the various specimens, as well as the slot lengths, are reported in Fig. 2. The reinforcement quantities across the joint in sw1-1, sw1-2, and sw1-3 were varied. Steel strands with total area of 140 mm² were employed in the prestressed element examinations. To improve the performance of concrete in compression, with closely spaced stirrups, the concrete at the specimens' toes was confined (spacing 50 mm). The strands' unbonded length was 3 m, which was equivalent to the specimen's overall height.

Fig. 2

The experimental reinforcement detailing [12]

2.2 Experimental Setup

Figure 3 shows the experimental set-up. Out-of-plane braces prevented wall panel deformations. Table 1 reveals that vertical weights were added to the specimens by hydraulic jacks at the top. Figure 4 shows that all specimens were subjected to cyclic lateral displacement. The average concrete compressive strength of each specimen was 20.8 MPa. fy = 527 MPa, fu = 683 MPa for 6 mm reinforcement; fy = 448 MPa, fu = 576 MPa for 10 mm reinforcement. Figure 6 shows the yield stress of the steel strand is 1,740 MPa, while the ultimate tensile strength is 1,950 MPa.

Fig. 3

Test setup [12]

Table 1 Wall configurations tested [12].

Fig. 4

Cyclic loading used for test

3 Finite Element Modelling

ABAQUS software is used to generate a nonlinear three-dimensional (3D) finite element (FE) model of the self-centering reinforced concrete shear walls. The 3D FE model was developed to mimic the test scenario more precisely (Fig. 5). In all of the produced models, all concrete components, including the precast concrete wall and the concrete base, were constructed using an eight-node 3D brick element. ABAQUS software's concrete damage plasticity model, which is a common concrete structure analysis model, was used to define concrete material. This model includes concrete elements subjected to monotonic or cyclic loads.

Fig. 5

3 D view of the FE model

Fig. 6

Steel and strands stress–strain

In this investigation, the CDP input data was defined using a newly suggested a model of the damage made to softened concrete's plasticity by Feng et al. [13]. This model takes into account the impact of compress softens on the estimated stress–strain data as well as concrete material degradation. The specimen's ultimate concrete compressive strength is displayed in Fig. 7. Assume all concrete materials’ ultimate strain is 0.003. The concrete damaged plasticity model in ABAQUS involves the definition of five criteria related to plasticity. These factors are the dilation angle ψ, the flow potential eccentricity ∊, the biaxial to uniaxial strength ratio b0/c0, the yield function Kc second stress invariant on the tensile to compressive meridian, and the viscosity parameter. These parameters were expected to be 30, 0.1, 1.16, 0.667, and 0.005. This assumption is based on program documentation suggestions (SIMULIA 2008) and past research [16, 17]. The pre-stressed strands, energy dissipation bars, and vertical and horizontal reinforcements of the shear wall were simulated using the truss element T3D2

Unbonded tendons were embedded in a cap beam and foundation. Concrete had connected tendons, longitudinal and transverse reinforcing bars. Model the gap between a precast wall and foundation using surface-to-surface contact. 0.5 friction determined tangential contact behavior [15]. Hard contact was employed to avoid penetration upon contact between solid parts, allowing shear wall and foundation surfaces to easily separate and compress. To emulate fixing, the footing's bottom was completely constrained.

The produced models were analyzed in three steps to imitate the real sequence of load for the experiment operation. The initial stress was applied to the unbonded tendons as the first stage. The vertical load was then applied to the model using the same way as in the test. Finally, the predetermined lateral drifts were applied.

Fig. 7

Definitions of stress–strain for concrete instate of: a Compression; b Tension

3.1 Hysterical Behavior

Based upon numerical and experimental findings, the hysteretic responses of shear wall specimens Sw0 and Sw1-3 are shown in Figs. 8 and 9. After going through rebar failure, the specimens lost strength and failed. The black lines indicate the experimental test findings, and the red curves represent the numerical model results. Generally, the newly created F.E. models predict hysterical curves effectively. The results from the diagrams show that the concrete wall modeling in Abaqus is accurate enough.

Fig. 8

Hysteretic curves SW0

Fig. 9

SW1-3 Hysteretic curves

3.2 Damage Mode

The concrete wall FEM behaved similarly to test specimen. Wall toe stresses and strains were high; however, the restricted concrete area was strong enough to avoid crushing. The strain distribution and deformation mode simulation findings at 3.65% drift levels (Δ = 3.65%) are shown in Fig. 10, along with the plastic deformation of the wall panel. When the lateral force that was being applied to the (sw0 through sw1-3) specimens wase eliminated, for sw1-3 specimen, the gap closed in completely.

Fig. 10

Comparison between FEM and Test results Damage

3.3 Local Response

For the purpose of evaluating the FEM's accuracy, characteristics of the local response were examined.; further, the comparisons of envelope curves generated from peaks of the cycle are given in Fig. 12 to compare findings visually. The uplift shape at the wall toe of Units 1–3 of the FEM results and the Von-Mises stress contour of the steel bars reinforced by Sw0, were shown in Fig. 11. Local responding (a) Gap opening (b) SW0 Rebar model (c)Von-Mises stress contour of the steel bars reinforced sw-0.

Fig. 11

Local responding (a) Gap opening (b) SW0 Rebar model (c) Von-Mises stress contour of the steel bars reinforced sw-0

Fig. 12

FEM and test envelope curves

Regarding all local response variables, the FEM findings generally exhibited a good match with the experimental results. The accuracy of the global lateral force–displacement response was most importantly confirmed by the precisely predicted local response characteristics. They gave the 3D finite element model used to model the self-centering concrete wall more confidence.

3.4 The Viscous Damping Ratio

Viscous damping ratios are used to measure a system's energy dissipation capacity. For a typical hysteretic loop, given in Fig. 13, Eq. 1 [16] was utilized to determine the wall's equivalent viscous damping (sw 0, sw 1-3). Figure 14 a comparison between both the equivalent viscous damping ratio of the hysterical analytical curve and the corresponding experimental data. As demonstrated in Fig. 14, the equivalent viscous damping ratio of computational models corresponds well to experiments, indicating that the model can predict the hysteretic response of such structural systems with reasonable accuracy. Moreover, the accurately predicted local response characteristics verified the accuracy found in the global lateral force–displacement response and increased confidence in the 3D FEM utilized to model the self-centering concrete wall Eq. 1:

$$ \zeta_{ei} = \frac{1}{4\pi }\frac{{E_{i} }}{{E_{si} }} $$

(1)

Fig. 13

Typical hysteresis loop of SC-PSBCs

Fig. 14

Eq. viscous damping coefficient of the Sw0, Sw1-3 specimen

4 Parametric Studies

A parametric analysis of the effect of important structural variables on the earthquake characteristics of self-centering concrete walls with bottom slots was carried out using provided FEA models. The inverted cyclic model and its drift in Fig, 4 were used to validate and compare the influence of the parameters. Bottom slot size, location of steel strands, initial level of post - tensioned, and concrete compressive strength were studied. The effect of these parameters is shown below.

Figure 15 demonstrates the impact of concrete's compressive strength, Fc. The compressive strength of concrete should have a substantial effect on the crushing of concrete at the toes (bottom shear wall), which touches the foundation, and the rocking behavior of entire walls. Given that the proposed walls are for four-story low-rise buildings, the values of Fc were set between 30 and 60 MPa, and C75 concrete was used to confirm the influence of high-strength concrete on the hysteretic behavior of the walls, particularly their rocking behavior. It is demonstrated that increasing the concrete's strength slightly increases the shear walls' elasticity; however, the increase in concrete strength slightly affects the yield and ultimate loads. Figure 16 depicts the lateral load vs displacement for three different prestressing forces. It is observed that as the effective prestressing force ${\mathbf{f}}_{\mathbf{P}\mathbf{T}\mathbf{i}}$ is raised, the lateral load values improve and have minor effects on the energy dissipation capacity. However, by increasing tendon forces, the values of lateral displacement related to yielding were reduced, and it has essentially no effect on behaviors under massive deformations. In order to establish the optimal balance between the self-centering capacity and the energy dissipation capacity of the wall, it is crucial to effectively control the initial prestress level of the PTs during the design stage.

Fig. 15

Effect of unbounded tendon initial stress on the lateral force versus top lateral displacement of precast wall

Fig. 16

Impact of concrete strength

Figure 17 indicates that when the tendons were positioned near to the specimen's centerline, the lateral capacity decreased. To investigate the influence of tendons position, specimens with 220 and 420 mm tendons, as well as specimens with two tendons 220 and 420 mm separated from the center line, were studied. The cross-sections of all the wall specimens were 2000, 1000, and 125 mm, with the first model (220 mm) interior, the second model (420 mm) exterior, and the third model (220 and 420 mm) double. Figure 17a illustrates the cross-sectional model for all specimens; a prestressing force of 0.24 ${\mathrm{f}}_{\mathrm{Pu}}$ i is induced in all cases, and the walls are examined under monotonic incremental loading. Figure `17b exhibits the lateral load vs drift relationships for the three spacemen's models of the shear wall. The base shear value is lower in the shear wall with interior tendons than in the shear wall with external tendons, but higher in double tendons. Both models have about the same effective stiffness (before system yield) and have minor influence on the energy dissipation capacity. Changing the tendon location, however, has the slightest impact on the self-centering property.

Fig. 17

Effect of s distance from centering of wall

Figure 18 the aperture of the joint between the wall and foundation, which started approximately at the load stages, predominated the responses of (sw1-1 through sw1-3). When the joint-crossing rebars were put under tension and bonded with the wall panel's concrete, horizontal stresses were created. With an increase in the lateral load displacement, these stresses grew horizontally. However, as a result of that the nonlinear deformation was concentrated at the wall panel-to-base joint, the amount of stress was relatively low. Figure 10 depicts the pictures of sw0 through sw1-3 after the application of loads with respective drift ratios of 0.025, 0.45, 0.9, 1.35, 1.8, 2.65, 3.15, and 3.65%. It is discussed how the performance of the specimens is affected by various slit lengths. The deformation range decreased as the number of slits rose. Due to the positioning of the steel plates, sw1-1 through sw1-3 exhibit minimal deformations. The wall exhibited low strain because sw1-3 lacked rebars that crossed at joints. There was no considerable tension created because the breach opened. Therefore, the crushing of the concrete at the base of the walls is to fault for the decrease in strength. According to Fig.10, the damage shapes of FEM specimens with bottom slots matched those of the experiments. The specimen's maximum load can be enhanced by shortening the bottom slot.

Fig. 18

Effect of bottom slits

5 Conclusions

This paper investigates the earthquake performance of self-centering concrete walls with bottom slots under seismic loads. A 3D detailed model was built to predict the lateral load behavior of a shear wall, which we tested against experimental data [12] Comprehensive parametric analyses were carried out after the numerical models were validated. An FEA model was used to analyze factors such as bottom slit length, steel strand location, the initial level of prestressing and concrete strength on the damage pattern, and lateral capacity. The main conclusions are drawn as below:

• The results indicate that the three-dimensional finite element model proposed in this study is accurate in predicting the lateral force–displacement response and the local response observed during the experimental testing. The impacts of concrete walls configurations, such as the length of the bottom slit, the place of the tendons, the level of initial post - tensioned, and the strength of the concrete, on the damage pattern and lateral capacity are shown.

• Wall-foundation gap interface causes high stresses and strains in a localized region of the wall toe, which were mitigated by the steel plate.

• The results in this paper show that the shear capacity increased slightly when strength of concrete was raised.

• Prestressed steel tendons added vertical restoring load for self-centering.

• Prestressing can affect shear wall response to seismic forces. According to this study, f-PTi affects wall behavior under minor and medium deformations but not large ones. Effective prestressing increases a structure's lateral deformation resistance. PTs must be designed with an appropriate starting prestress level. The wall's self-centering and energy dissipation capacities must be balanced.

• It is suggested that slits should be put in places where there is a lot of bending during an earthquake.

• As the length of the bottom slit got shorter, the number of cracks and the range of where they were found got smaller. The specimens' remaining drifts also got smaller; it confirms that the self-centering capacity performed as predicted.

• Making the bottom slot shorter, placing the steel strands closer to the specimen's center line, and raising the initial stress in the steel strands all will enhance the specimen's maximum load capacity.

• The corresponding viscous damping coefficient with the highest value is found in the traditional shear wall specimen.

• The outcomes also revealed that the specimen with bottom slits's ability to dissipate energy was not significantly affected by the placement of steel tendons or the initial prestress amount.

The analytical model accurately represented the total lateral load displacement, wall gap opening and closing behavior, PT tendon behavior, and stress on reinforced steel bars. Engineers can use the FEM model that was used in the research as a useful tool in their daily work. More information was required in order to fully understand the behavior of the concrete structures.