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Article

Strengthening Reinforced Concrete Walls with Externally Bonded Galvanized Steel Sheets and Near-Surface Mounted Steel Bars

by
Ahmed Hamoda
1,
Alireza Bahrami
2,*,
Aref A. Abadel
3,
Mizan Ahmed
4 and
Mohamed Ghalla
1,*
1
Civil Engineering Department, Faculty of Engineering, Kafrelsheikh University, Kafrelsheikh 6860404, Egypt
2
Department of Building Engineering, Energy Systems and Sustainability Science, Faculty of Engineering and Sustainable Development, University of Gävle, 801 76 Gävle, Sweden
3
Department of Civil Engineering, College of Engineering, King Saud University, Riyadh 11421, Saudi Arabia
4
Centre for Infrastructure Monitoring and Protection, School of Civil and Mechanical Engineering, Curtin University, Kent Street, Bentley, WA 6102, Australia
*
Authors to whom correspondence should be addressed.
Buildings 2025, 15(4), 636; https://doi.org/10.3390/buildings15040636
Submission received: 26 November 2024 / Revised: 3 February 2025 / Accepted: 11 February 2025 / Published: 19 February 2025
(This article belongs to the Section Building Structures)
Browse Figures
Versions Notes

Abstract

Reinforced concrete (RC) walls are mainly used in RC structures to resist gravity and lateral forces. These structural elements may need to be upgraded to withstand additional forces and extend their life cycle. Therefore, it is crucial to provide effective strengthening techniques using low-cost sustainable materials under optimal conditions to rehabilitate RC walls. This study presents an experimental and numerical investigation of reinforced normal concrete (NC) walls strengthened with near-surface mounted (NSM) steel bars, confined with or without an externally bonded reinforced (EBR) galvanized steel sheets (GSSs). A total of six RC walls were constructed, loaded, and tested to failure. The examined parameters included the type of strengthening technique, materials used, and the position and configuration of the strengthening. Both EBR and NSM techniques were applied using GSSs and steel bars, respectively. The configurations were introduced in vertical and horizontal positions to resist gravity and lateral forces, respectively. The experiments revealed that these parameters significantly influenced the crack control, energy absorption, mode of collapse, and ultimate load capacity. Nonlinear three-dimensional finite element models were developed and verified against experimental results, achieving a validation accuracy of 95% on average. This was followed by a parametric study investigating the effect of confinement with or without vertical reinforcements. Both experimental and numerical results confirmed that the strengthening could increase the ultimate load capacity from 20% to 38%.

1. Introduction

Reinforced concrete (RC) walls are commonly introduced in structural engineering because of their larger load capacity. However, over time, such RC walls may require strengthening due to aging, increased load demands, or damage caused by environmental factors or seismic activity [1,2,3]. One effective method of enhancing the structural performance of RC walls is by retrofitting them with galvanized steel sheets (GSSs). GSSs are coated with zinc, which provides excellent resistance to corrosion, thereby enhancing the durability of the reinforcement. The use of these sheets for strengthening RC walls offers several benefits, including improved load capacity, increased ductility, and enhanced resistance to cracking and buckling. This method is particularly useful in seismic retrofitting, as it allows for the structure to better withstand lateral forces, such as those encountered during earthquakes. This technique is both cost-effective and relatively easy to implement, making it a practical choice for many retrofitting projects in both residential and commercial buildings. In summary, the use of GSSs for RC wall strengthening enhances the structural integrity, extends the service life, and improves the overall performance of the walls under various loading conditions.
RC walls are integral to modern construction, providing essential structural support and stability [4,5,6,7]. Such walls are a critical component in the structural integrity of buildings, providing essential support and stability. The vertical testing of these walls is crucial for understanding their behavior under various loading conditions, particularly in seismic regions where the performance of structural elements can noticeably impact the safety and durability of buildings [8,9,10,11].
Several studies have explored the behavior of RC walls under different loading conditions [7,12,13,14,15]. Doh et al. [12] carried out an experimental program on RC walls made of high-strength concrete and a high slenderness ratio. The study also examined the one-way and two-way actions of the walls. It was found that the axial strength ratios of the walls decreased with increasing slenderness ratios. The reductions in the axial strength ratios for the normal and high-strength concrete were about 10.6% and 27.1% when the slenderness ratio increased from 30 to 40, respectively. The design method given in AS3600 [16] was also evaluated against the test results. Madina Saheb et al. [17] found that the reduction in the axial strength ratios for the normal concrete (NC) was about 41% when the slenderness ratio increased from 9 to 27. However, the tested specimens were moderate in slenderness compared to the ones tested by Doh et al. [12]. Lu et al. [7] conducted experimental tests to study the seismic behavior of RC walls with minimal vertical reinforcements. Their findings highlighted the importance of adequate reinforcement to ensure well-distributed cracking and prevent premature failure. Likewise, the American Concrete Institute (ACI) offers guidelines for testing RC structural elements under gradually applied simulated seismic loads, which are pertinent to this study [18].
The mechanical properties of the materials used in RC walls play a significant role in their performance under vertical loads. Research by Bertolini et al. [19] emphasized the durability of RC structures, pointing out the critical role of using corrosion-resistant materials to prolong the service life of these structures. The study done by Andrade and Alonso [20] on the corrosion of steel reinforcement in concrete provide a comprehensive understanding of the factors affecting the durability of RC structures. These studies underscore the need for materials that can withstand aggressive environmental conditions and reduce maintenance costs.
The use of sustainable materials in concrete strengthening offers several advantages, including superior corrosion resistance, which is particularly beneficial in harsh environmental conditions [21,22,23,24]. Vera et al. [25] assessed the short- and long-term performances of RC beams strengthened with galvanized steel mesh. It was found that this strengthening technique enhanced the ductility and absorbed energy for strengthened beams. Several investigations have been carried out on the application of galvanized steel in concrete elements [26,27,28,29,30,31]. The importance of GSSs in modern industries cannot be overstated. Their ability to resist corrosion, offer cost-effectiveness, provide durability, and remain versatile makes them indispensable in construction, automotive manufacturing, and beyond.
One innovative technique that has gained considerable attention in recent years is the utilization of near-surface mounted (NSM) steel bars for strengthening RC columns and walls [32,33,34,35,36]. Moreover, the technique of externally bonded reinforced (EBR) has been widely employed due to its simplicity of application [37,38,39,40,41,42,43,44]. Such a technique offers several advantages over traditional strengthening techniques. NSM steel bars provide better protection against environmental factors, reduce the risk of de-bonding, and enhance the load capacity of the structure without largely altering its dimensions [44,45,46].
The application of NSM steel bars in RC columns and walls has been extensively studied to understand its effectiveness in improving structural performance. Al-Thairy and Al-Shimarry [47] showed that incorporating NSM steel bars greatly improves the flexural resistance and stiffness of RC columns, particularly when used alongside glass fiber-reinforced polymer (GFRP). Their experimental investigation revealed that the ultimate load capacity of eccentrically loaded NSM-strengthened columns could be increased by up to 79.5% compared to unstrengthened columns.
Numerical simulations have also been used to examine the behavior of NSM-strengthened RC columns. Al-Thairy and Al-Shimarry [48] utilized the finite element ABAQUS 6.0 software to numerically simulate the behavior of eccentrically loaded RC columns reinforced with a combination of NSM steel and GFRP bars. Their results demonstrated good agreement with experimental outcomes, indicating that the ultimate load capacity of hybrid NSM-strengthened columns increased by up to 70% compared to columns strengthened with NSM steel bars only. The use of NSM steel bars in RC walls has also been explored. Additionally, the use of NSM steel bars minimized the impact on the architectural esthetics of the walls, as the bars are embedded within the concrete cover [33].
Although some research has been performed on the strengthening of RC walls, very limited investigations have been conducted on the use of GSS strips confining the reinforced NC walls. Therefore, this article outlines experimental and numerical studies on the strengthening of RC walls that incorporate confining strips of GSSs. The factors introduced herein are the type of strengthening technique (EBR or NSM), strengthening material (GSSs or steel bars), and position of strengthening (vertical and horizontal). Nonlinear three-dimensional finite element models (FEMs) have also been constructed by utilizing the ABAQUS software and were established parallel to the experimentally tested walls. The experimental and numerical models provide a crucial understanding of the performance of the strengthened walls.

2. Experimental Program

2.1. Descriptions of Walls

The reinforced NC walls were all constructed with identical dimensions: 750 mm, 400 mm, and 80 mm in height, width, and thickness, respectively. The size of the specimens was designed based on the study reported by Altin et al. [1], who tested four half-scale RC walls with dimensions of 1500 mm in height and 1000 mm in width. Based on the limitation of the lab equipment, the current investigation was designed approximately half the size of the samples tested by Altin et al. [1]. Vertical reinforcement consisted of two 16 mm diameter bars at each of the two narrow sides and two 12 mm diameter bars at the mid-zone of each wide side. Figure 1 provides schematic details of the dimensions and reinforcements used for all walls, which adhere to the building specifications given by ECP-203-2007 [49]. Horizontal reinforcement comprised 8 mm diameter bars, spaced at 100 mm intervals along the wall’s height. The arrangement of both vertical and horizontal steel reinforcements for all walls is identical. The bottom section in Figure 1 displays that the vertical bars extended from the base and continued up through the wall, enhancing its vertical load capacity.
The experimental program aimed to study three key factors: the type of strengthening technique (EBR or NSM), the strengthening material (GSSs or steel bars), and the position of strengthening (vertical or horizontal). Both horizontal and vertical strengthening techniques were investigated utilizing combinations of external GSSs and internal NSM bars. Table 1 outlines two distinct groups (G1 and G2), detailing the test wall names, the objectives of each group, and the type, configuration, and size of the strengthening materials used.
The experimental program was divided into two groups to evaluate different strengthening techniques and materials.
Group 1: This group included the master wall (W) and three strengthened walls (W-Gv4, W-Gv5, and W-Gv7). The aim was to explore the performance of EBR using a GSS placed horizontally. The walls were strengthened with four, five, and seven horizontal GSS strips, respectively, as depicted in Figure 2a–c. The GSS strips used were 1.00 mm thick and 50 mm wide.
Group 2: This group comprised the master wall (W) and two strengthened walls (W-B2 and W-Gv4-B2). The focus was on assessing the effect of NSM steel bars and the combination of NSM with a GSS. W-B2 was strengthened with two vertical NSM steel bars, each 8 mm in diameter, as illustrated in Figure 2d. W-Gv4-B2 combined NSM bars with horizontal and vertical GSS strengthening, as exhibited in Figure 2e.

2.2. Material Properties

The NC type was delivered herein for casting all RC walls. Such an NC consisted of 350 kg/m3 of cement, 700 kg/m3 of fine aggregate, and 1150 kg/m3 of coarse aggregate, with a water/binder ratio of 0.43. Five cylinders with dimensions of 150 mm in diameter and 300 mm in length were used for obtaining the concrete compressive strength (f’c) according to ASTM C39/C39M [50]. The NC achieved a compressive strength of 25 MPa and a Poisson’s ratio of 0.2. Figure 3a presents the compressive and tensile strength values obtained experimentally and employed for depicting the stress–strain relationship, as recommended by Carreira et al. [51], to be utilized in the numerical study. The tensile stress–strain relationship shown in Figure 3a emphasizes that NC reached its peak tensile stress of about 2.2 MPa and exhibited a brittle failure, with a sharp decline in stress after a very limited strain of less than 0.001.
Table 2 provides the characteristic material properties of the steel elements employed in this study according to uniaxial tensile tests. The uniaxial tensile stress–strain response is depicted in Figure 3b. Three steel elements have been used herein with the yield and ultimate strengths of 293 MPa and 455 MPa, 389 MPa and 603 MPa, 424 MPa and 636 MPa, and 342 MPa and 501 MPa, respectively, for steel components of 8 mm, 12 mm, and 16 mm, and a GSS with 1.00 mm thickness. The steel items were sourced from a local distributor of Ezz steel.

2.3. Casting and Preparation for Strengthening

After 28 days of constructing all the NC walls, the preparation of the strengthening materials involved several steps, as displayed in Figure 4. The strengthened walls of the first group were prepared through three dependent steps, illustrated in Figure 4a–c as follows:
  • Surface preparation and epoxy application: The outer surface of the walls was roughened, and epoxy named Sika was applied to securely attach GSS to the walls’ surface (Figure 4a).
  • GSS confining: The GSS strips were wrapped around the four surfaces of the walls, with both ends overlapping and adhered to ensure continuity (Figure 4b).
  • Anchor bolt installation: Anchor bolts purchased from a local distributor of Ezz steel were embedded inside the walls using epoxy to firmly attach GSS to the walls (Figure 4c).
For walls strengthened with NSM steel bars, as are in the second group (e.g., W-B2), the bars were inserted into prepared grooves and adhered utilizing epoxy for reinforcing (Figure 4d). In W-Gv4-B2, a combination of horizontal and vertical strengthening techniques was employed, involving internal NSM bars followed by external GSS application (Figure 4e).

2.4. Testing Set-Up and Procedure

The testing was carried out using a 2500 kN uniaxial testing machine, as illustrated in Figure 5. The walls were prepared for testing through a three-step process: cleaning, applying white paint, and carefully positioning them in the testing machine with the help of an overhead crane. The white paint was used to visually track and document cracking patterns and failure modes through photographs during testing. To ensure even load distribution and accurate data collection, wide rectangular caps with stiffeners were attached to both ends of each specimen using gypsum, as demonstrated in Figure 5.
The top of the walls remained free but was restrained from lateral movement by the load cell, while the bottom was anchored to a steel base using threaded bolts. The load was applied vertically in the upper cap using a steel I beam. A linear variable displacement transducer (LVDT) was placed on the upper cap to measure vertical displacement, as depicted in Figure 5. Additionally, a strain gauge was horizontally installed on the middle GSS to monitor tensile displacement. The walls were gradually loaded until failure, with their response continuously monitored. At each loading stage, visible cracks were recorded and photographed, and vertical displacement and strains of the GSS data were electronically entered into the data logger.

3. Test Results and Discussion

3.1. Crack Pattern and Failure Mode

The crack pattern and failure mode of the unstrengthened master RC wall are presented in Figure 6. The observed crack pattern shows inclined cracks along the wall, which is typical for RC walls subjected to vertical loads. Figure 6 displays that inclined splitting cracks were majority formed close to the edges of the RC wall, leading to sudden brittle failure and NC crushing. This type of failure is expected in RC walls with minimum reinforcement subjected to gravity loads. The unstrengthened wall demonstrated sudden failure with splitting cracks followed by concrete crushing at Pu of 683 kN.
Figure 7 exhibits the failure modes for walls strengthened with GSSs arranged horizontally along the wall’s height. The key difference between the walls is the number of strips used. W-Gv4, strengthened with four strips, indicated a similar inclined crack pattern to the master wall, as can be seen in Figure 7a. However, the extent of cracking reduced compared to the unstrengthened wall. The four GSS strips provided some resistance to the propagation of shear cracks, but the wall still showed significant cracking. This may suggest that the strengthening was insufficient to fully prevent failure. The wall resisted about 710 kN as a maximum load capacity and failed by a splitting crack followed by concrete damaging and cutting the confining GSS. The crack pattern demonstrated that the four GSS strips delayed, but did not completely stop the shear failure mechanism.
As can be seen in Figure 7b, W-Gv5 (with five GSSs) exhibited a different crack pattern, characterized by multiple smaller inclined cracks rather than one dominant crack. The presence of five GSS strips seemed to distribute the stresses more effectively, resulting in a less severe crack pattern. However, horizontal cracks are also visible, suggesting that the wall experienced an extension of these inclined cracks. This revealed the better contribution caused by the confinement effect. W-Gv5 failed suddenly owing to splitting vertical cracks with concrete crushing, recording Pu as 739 kN.
The presence of seven GSSs, as tested in W-Gv7, presented the least amount of visible damage, as shown in Figure 7c. The crack pattern consisted mainly of horizontal cracks between the strips, suggesting that the strengthening material effectively resisted the inclined splitting cracks observed in the other walls. It is worth mentioning that the horizontal arrangement of seven strips appeared to have provided a noticeable contribution, controlling the spread of the splitting cracks. This has been manifested by changing the failure zone, as depicted in Figure 7c. Therefore, it may be observed that the strengthening configuration with seven strips could change and transfer the failure mode. The presence of seven strips revealed a higher ultimate load capacity, compared to the other counterparts, recording Pu as 764 kN.
Generally, it can be seen that, as the number of strips increased, the crack patterns became less severe. In the master wall, the cracks were larger and predominantly inclined, while in the strengthened walls, the cracks became more distributed and less intense. This indicated that the GSS strips were effective in controlling the crack propagation and in reducing the severity of failure. In addition, the more strips (W-Gv5 and W-Gv7) exhibited a delayed failure and less severe damage compared to the wall with four strips (W-Gv4). This suggests that the additional strips helped increase the ultimate load capacity by providing more resistance to vertical loads. The use of GSS strips for strengthening NC walls has proven effective in controlling crack propagation and enhancing the structural performance of the walls. The number of strips could considerably affect the structural performance since more strips resulted in better crack control, higher load capacity, and shifting failure modes.
W-B2, as shown in Figure 8a, experienced severe vertical cracking and disintegration near the NSM bars’ placement. A splitting crack formed vertically along the height close to the additional steel bar. The localized concentration of cracks at the vertical bar’s placement demonstrated that the reinforcement bars could remarkably resist the applied forces until failure. This is due to the improvement of the tensile strength of concrete in that region owing to the presence of the reinforcement bars. However, a vertical splitting crack and separation at reinforcement were witnessed at the failure occurrence. The failure occurred due to splitting cracks, which led to concrete crushing and were associated with shear cracks along the side of the wall, as displayed in Figure 8a, which may be attributed to the lack of lateral confinement. Therefore, it can be noticed that strengthening using only NSM bars, without confinement, provided limited vertical strengthening and failure due to localized cracking. W-B2 exhibited an ultimate load capacity of 737 kN.
W-Gv4-B2, presented in Figure 8b, indicated a different failure mode compared to W-B2. The cracks were more distributed, and the wall showed both vertical and horizontal fractures. The presence of GSSs could confine the damage and diminish the propagation of cracks into larger sections of the wall. In a similar context, it helped mitigate the spread of cracks and enhance the load distribution through the strengthening system. Steel bars confined with GSSs contributed to a more balanced failure mode, where the wall was able to maintain integrity for a longer period under stress. As a result, the crack pattern remained more controlled, and failure appeared more uniform compared to W-B2. The current combined technique could increase the ultimate load capacity, leading to carrying an ultimate load of 824 kN, which was the largest load capacity compared to other counterparts. W-Gv4-B2 failed due to splitting cracks, which damaged the nearby vertical steel bars and led to a sudden concrete crushing failure.

3.2. Load-Vertical Displacement Relationships

The load versus vertical displacement behavior of two groups of walls, G1 and G2, under load testing are depicted in Figure 9a,b, respectively. The absorbed energy (E) together with the ultimate vertical displacement values (Δu) measured at the peak are provided in Table 3.
The control wall, W, exhibited the lowest load capacity among the first group. The peak load occurred at a vertical displacement of around 2–3 mm, and the load suddenly dropped with increasing displacement, resulting in sudden crushing.
The first group, displayed in Figure 9a, emphasized that the strengthened NC walls demonstrated varying degrees of load–vertical displacement responses depending on the number of strengthening strips. W-Gv4 indicated higher load capacity and slightly improved energy absorption compared to the master wall W. Also, the ultimate load was reached earlier at a lower vertical displacement (Δpu = 2.36 mm), presenting enhanced stiffness due to strengthening with GSS strips. Strengthening with five or seven strips (i.e., W-Gv5 and W-Gv7, respectively) progressively illustrated more pronounced load capacities and vertical displacements, reaching the peak at higher values than the control wall, especially for W-Gv7. Related to the linear response, the enhanced load–vertical displacement behavior may refer to the finding that the addition of more strips (from four to seven) improved the load capacity while slightly reduced the vertical displacement, reflecting a stiffer behavior. Beyond the peak, the load dropped more gradually post-peak, reflecting the better energy dissipation properties for W-Gv7. The energy absorbed by the strengthened walls progressively increased with the number of strengthening strips, recording an enhancement within a range from 24% to 59% when using a confinement ratio from about 0.8% to 1.4%, respectively. In summary, increasing the number of GSS strips resulted in higher load capacity and energy absorption, with W-Gv7 showing better performance.
The use of EBR and NSM was tested in the second group with the load–vertical displacement response depicted in Figure 9b. The load–vertical displacement curve demonstrated a significant augmentation in both load capacity and vertical displacement compared to the master wall W. W-b2 with two NSM steel bars reached a slightly higher load than the unstrengthened wall with an increased vertical displacement of 3.56 mm. This may indicate that the use of vertical reinforcements could enhance the wall’s resistance and ductility. Moreover, this strengthened wall reflected an energy absorption enhancement ratio of 55%. The combination of vertical reinforcements nearly mounted on the wall’s surface confined with GSS strips (i.e., W-Gv4-B2) led to the best performance compared to other counterparts. This can be evidenced by exhibiting a much greater load capacity, with the peak load extending beyond 900 kN, and the vertical displacement at failure being the highest at 4.23 mm. In addition, W-Gv4-B2 generated the highest E value, with an enhancement ratio of 190%, illustrating the superior performance of this hybrid strengthening method. Therefore, the use of both steel bars and GSSs provided a dual mechanism for enhancing load capacity and energy absorption, making W-Gv4-B2 the most efficient wall in terms of energy absorption and structural performance.

3.3. Impact of Strengthening Technique on Ultimate Load Capacity

Table 3 summarizes the results of testing various wall specimens, focusing on their ultimate load capacity (Pu) and their corresponding vertical displacement (Δu). The ultimate load capacity displays the contribution of different strengthening techniques utilized in this study.
Table 3 outlines that the strengthening using EBR with GSSs, as tested in G1, led to an increase in the ultimate load capacity of the NC walls. However, the ultimate load capacity has significantly been impressed with the ratio of lateral strengthening. The gained enhancement can range between 4% and 12% for lateral GSS strengthening from 0.8% to 1.4%. This shows a clear correlation between the number of GSS strips used and the increase in the load capacity, likely owing to the higher resistance provided by the additional reinforcement.
The second group also demonstrated that strengthening employing vertical steel bars with/without closed GSSs could upgrade the ultimate load capacity. W-B2 upgraded the ultimate load capacity of the NC walls by about 9%, as presented in Table 3. However, combining NSM vertical steel bars along with confining GSSs gave the highest load capacity, exhibiting a 20% improvement and producing higher vertical displacement values as well. In other words, this technique could provide a balance between the strength and ductility. Also, the better enhancement gained by this combination indicated a synergistic effect between the two strengthening methods (bars and GSSs).
Comparing both techniques used herein revealed a gradual improvement in the ultimate load capacity with an increased number of GSS strips. Also, the utilization of horizontal GSS strips appeared to enhance the load capacity and reduce vertical displacements slightly. On the other hand, the use of NSM steel bars is preferred to be confined with lateral GSSs. This has been evidenced by the combination of NSM bars and GSSs, which resulted in the most significant improvements in the ultimate load capacities, vertical displacements, failure modes, and energy dissipations.

4. Numerical Analysis

The walls tested in the experiment were reconstructed using the ABAQUS 14 software [52], employing explicit calculation. Verifying the accuracy of FEMs was accomplished by comparing their results with their corresponding experimental ones. By applying FEM, this section gains a comprehensive understanding of the performance characteristics of RC walls strengthened with EB GSS and NSM steel bars.

4.1. Mechanical Properties Considered in Modeling

The concrete damage plasticity (CDP) model was utilized to describe the characteristics of the NC body. This model includes isotropic damage, tensile plasticity, and isotropic compression to more precisely capture the nonlinear behavior in both tension and compression, as documented in prior studies.
Figure 3a depicts the stress–strain curve for NC fitted with respect to previous research [51,53,54,55]. Key parameters in the CDP model included the ratio of biaxial to uniaxial compressive strengths (fbo/fco), the ratio of tensile stress to the compressive meridian (Kc), eccentricity (e), and the viscosity parameter (μ). The CDP parameters for NC were 1.16, 0.67, 0.10, and 0.00, respectively, which closely aligned with previous studies [56,57]. Figure 10 displays the effects of various dilation angles on the accuracy of the FEM prediction. Based on the sensitivity analysis, the dilation angle (ψ) is taken as 29°. To minimize computational costs, the modeled stress–strain relationship for steel bars and GSSs was simplified by adopting piecewise linear curves idealized from the actual experimental curves, as illustrated in Figure 3b. It should be noted that the initial imperfections for the steel bars were not modeled.
In accordance with the CDP model, the softening behavior of concrete was represented through two damage variables [58]. These variables, denoted as d c and d t , ranged from 0 to 1, where 0 signifies an undamaged state and 1 indicates a complete loss of strength. The values of these damage parameters were determined using Equations (1) and (2), with the following definitions: σ c and ε c represent the concrete compressive strength and the corresponding strain; σ t and ε t denote the concrete tensile strength and the corresponding strain; and E 0 , ε c p l , and ε t p l represent the modulus of elasticity, equivalent plastic strain in compression, and equivalent plastic strain in tension, respectively [58].
σ c = ( 1 − d c ) E 0 ( ε c − ε c p l )
σ t = ( 1 − d t ) E 0 ( ε t − ε t p l )

4.2. Model Set-Up

Figure 11 shows the use of an eight-node element (C3D8R) to model the NC wall and caps, with reinforcing bars modeled using two-node linear truss elements (T3D2). However, the steel bolts were introduced as solid parts utilizing the C3D8R element type. A four-node shell element with reduced integration (S4R) was chosen to model GSSs.
The interaction between the steel bars and the NC wall was modeled employing an embedded element mechanism, ensuring a full bond. The steel bars were embedded as truss elements within the NC wall, which served as the host region. The surface-to-surface tie constraint in ABAQUS was used to simulate the interaction between GSS and wall surfaces. The wall surface acted as the master, and GSSs were the slaves. The interaction was modeled utilizing a traction–separation constitutive model, assuming linear elastic behavior followed by damage evolution. The additional steel bars employed for strengthening were simulated via three steps. Firstly, grooves were trimmed along the wall height, as conducted experimentally. Secondly, the epoxy interacted inside the groove’s surface through a surface-to-surface tie constraint, since the wall surface was the master and the epoxy was the slave. A traction–separation constitutive model was considered, assuming linear elastic behavior followed by damage evolution. Thirdly, the steel bars were embedded inside the epoxy element, which was assumed to be the host region. Based on the mesh sensitivity analysis presented in Figure 12, a 5 mm mesh size was adopted. The analysis type was static standard, as the maximum number of increments was 10,000, initial increment size was 0.001, minimum increment size was 1 × 10−35, and maximum increment size was 1.

4.3. Verifications of FEMs

This section highlights the accuracy of the constructed FEMs by evaluating them against their experimental counterparts. The comparison includes the crack patterns visualized in Figure 13, the load–vertical displacement curves depicted in Figure 14, and the ultimate load capacity values presented in Table 4.
Similar to the major cracks observed experimentally, FEMs could reflect the splitting major cracks, as can be observed in Figure 13a,e,f for walls W0, W-B2, and W-Gv4-B2, respectively. In addition, the contribution of a number of strips (i.e., the ratio of additional lateral reinforcement) appeared in confining the crack propagation. In this context, the larger number of strips could control stress widening, as seen when comparing the three walls W-Gv-4, W-Gv-5, and W-Gv-7, respectively, presented in Figure 13b–d, respectively. As displayed the experimental and finite element predictions in Figure 13, it is witnessed that, generally, FEMs can identify the critical stressed region of the tested specimens. For specimens W-Gv5, W-Gv7, W-B2, and W-Gv4-B2, FEMs can reasonably identify the highly stressed regions. However, for W-Gv4, there is a slight discrepancy from the actual observation. The discrepancies between the experimental and finite element predictions can be attributed to the uncertainty of the actual strength and stiffness of the concrete and steel materials, where only the average values obtained from the experimental material tests were adopted. The mean ratio between the experimental and finite element predicted results was about 0.95 for the ultimate capacity, with coefficients of variation (COV) of 0.002 and a standard deviation of 0.011, as indicated in Table 4. The load-vertical displacement responses developed by FEMs could closely exhibit the experimental behavior, as demonstrated in Figure 14. In the linear zone, the models’ behavior was found to be close to their experimental counterparts. Then, all models entered the nonlinear zone, confirming the experimental performance with the same variation caused by the effect of strengthening.
These results show that the created FEMs precisely predicted the actual mode of collapse for strengthened and unstrengthened RC walls subjected to gravity and static forces with a variation not exceeding 6% and 9% for the ultimate load capacity and vertical displacement, respectively. The smaller values of the standard deviation (SD) and coefficient of variance (COV) provide confidence from a statistical point of view.

5. Parametric Study

The verified models have been re-used to conduct a parametric study on RC walls strengthened with confined GSSs with different size (aspect) ratios (μ%) with or without vertical additional reinforcing bars. The effect of GSSs as a lateral reinforcement along with a combination of lateral GSSs confining vertical bars were the two major studied systems which were categorized into the two groups displayed in Figure 15a,b, respectively. Figure 16 presents the crack pattern observed numerically, demonstrating the performance of the two groups. Figure 17 summarizes the reflection of both parameters on the ultimate load capacity.
The first group studied the effect of GSSs confining the RC wall as lateral reinforcement acted for strengthening. The GSSs varied from zero ratios up to the maximum ratio recommended by ACI 318-19 [59]. According to ACI 318-19, the minimum ratio of lateral reinforcement and the maximum ratio should not exceed 2.5% of the wall cross-section. This limit ensures that the wall maintains adequate ductility and avoids issues related to the congestion of reinforcement, which can complicate concrete placement and reduce the overall effectiveness of the reinforcement. The first group indicated that the increase in GSSs exhibited an increase in the ultimate load capacity.
The second group examined the combination of lateral and vertical additional reinforcements employed for strengthening. The vertical reinforcement was considered as a constant value, which was 1.47%, while the lateral confinement varied from zero up to 2.5%, as recommended by ACI 318-19 [59]. The numerical models emphasized that a combination of GSSs confining steel bars could achieve better efficiency compared to the previous technique.
To study the effects of the slenderness ratio of the walls in G1 and G2, the slenderness ratio of the walls varied from 9.3 to 18.8 by reducing the thickness of the walls. The μ ratio of GSSs was constant as 2.5% (Figure 17). As can be seen from Figure 18, increasing the slenderness ratio decreased the ultimate load capacity of the walls regardless of their strengthening methods. When the slenderness ratio increased from 9.3 to 18.8, the ultimate load capacity of the walls in G1 and G2 reduced by 21% and 16%, respectively. Interestingly, it is seen that for walls in G1, the reduction due to the increase in the slenderness ratio became negligible after a slenderness ratio of 12.5. However, for walls in G2, the effects of changing slenderness ratio beyond 15 are still distinguishable from Figure 18.

6. Conclusions

The current investigation provides experimental and numerical insights into the structural behavior of RC walls strengthened with GSSs with or without embedded steel bars. The factors introduced herein were the type of strengthening technique (EBR or NSM), strengthening material (GSSs or steel bars), and position of strengthening (vertical and horizontal). Then, nonlinear three-dimensional FEMs were created, exemplifying the tested walls followed by the parametric study. The following conclusions are drawn from this study:
  • Walls strengthened with more GSS strips demonstrated less severe cracking and higher load capacities. Walls confined with a ratio of 1.4% of GSS (as in W-Gv7) well upgraded the NC walls, effectively controlling the crack propagation and increasing the ultimate load capacity by about 15%. However, the combined use of EBR GSS strips and NSM bars with ratios of 0.8% and 0.628%, respectively, (as in W-Gv4-B2), further improved the performance, leading to a more balanced failure mode and the highest load capacity of 22% kN.
  • Strengthened walls with GSS strip ratios from 0.8% to 1.4% could increase the absorbed energy within a range from 24% to 59%. The combination of EBR GSS strips and NSM bars with ratios of 0.8% and 0.628%, respectively, provided the highest energy absorption by about 190%. This yielded the best results in terms of the energy absorption and load capacity, indicating the effectiveness of hybrid strengthening methods.
  • The integration of GSSs and steel bars greatly enhanced the crack resistance and loa capacity. Using EBR GSSs at a ratio of 0.8% to confine NSM steel bars at a ratio of 0.628% effectively delayed the crack propagation, controlled the damage, and improved the overall structural performance. This combination led to higher ultimate loads by 22% compared to the master wall.
  • The estimation from the developed FEMs closely matched the experimental results, with a numerical-to-experimental ratio of 0.95 for the ultimate load stage and for the corresponding vertical displacement.
  • The results showed that increasing the GSS ratio enhanced the ultimate load capacity of the walls by about 45%, while combinations with vertical bars significantly enhanced the ultimate load capacity by about 65% and the overall structural performance of the RC walls.

Author Contributions

Conceptualization, A.H., A.B. and M.G.; Methodology, A.H., A.B. and M.G.; Validation, A.H., A.B. and M.G.; Formal analysis, A.H., A.B. and M.G.; Investigation, A.H., A.B., A.A.A., M.A. and M.G.; Data curation, A.H., A.B. and M.G.; Writing—original draft, A.H., A.B. and M.G.; Writing—review and editing, A.H., A.B., A.A.A. and M.A.; Visualization, A.H., A.B., A.A.A. and M.G. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Data Availability Statement

The original contributions presented in this study are included in the article; further inquiries can be directed to the corresponding authors.

Acknowledgments

The authors thank the support provided by King Saud University, Riyadh, Saudi Arabia, through project RSP2025R343.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Geometric and reinforcement details of all walls (units: mm).
Figure 1. Geometric and reinforcement details of all walls (units: mm).
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Figure 2. Geometric and reinforcement details of strengthened walls: (a) W-Gv4, (b) W-Gv5, (c) W-Gv7, (d) W-B2, and (e) W-Gv4-B2 (units: mm).
Figure 2. Geometric and reinforcement details of strengthened walls: (a) W-Gv4, (b) W-Gv5, (c) W-Gv7, (d) W-B2, and (e) W-Gv4-B2 (units: mm).
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Figure 3. Stress–strain relationship for all used materials: (a) NC [24] and (b) steel elements.
Figure 3. Stress–strain relationship for all used materials: (a) NC [24] and (b) steel elements.
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Figure 4. Strengthening preparation: (a) installation of GSSs with adhesive epoxy, (b) overlapping two ends of each GSS, (c) positioning anchors with chemical epoxy, (d) application of NSM bars with epoxy after cover removal for W-B2, and (e) preparation of W-Gv4-B2.
Figure 4. Strengthening preparation: (a) installation of GSSs with adhesive epoxy, (b) overlapping two ends of each GSS, (c) positioning anchors with chemical epoxy, (d) application of NSM bars with epoxy after cover removal for W-B2, and (e) preparation of W-Gv4-B2.
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Figure 5. Test set-up and details of instrumentations: (a) schematic of tested wall and (b) image of wall during testing.
Figure 5. Test set-up and details of instrumentations: (a) schematic of tested wall and (b) image of wall during testing.
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Figure 6. Failure mode of master NC wall (W).
Figure 6. Failure mode of master NC wall (W).
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Figure 7. Failure modes of G1: (a) W-Gv4, (b) W-Gv5, and (c) W-Gv7.
Figure 7. Failure modes of G1: (a) W-Gv4, (b) W-Gv5, and (c) W-Gv7.
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Figure 8. Failure modes of G2: (a) W-B2 and (b) W-Gv4-B2.
Figure 8. Failure modes of G2: (a) W-B2 and (b) W-Gv4-B2.
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Figure 9. Load–vertical displacement relationships for all tested walls: (a) G1 and (b) G2.
Figure 9. Load–vertical displacement relationships for all tested walls: (a) G1 and (b) G2.
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Figure 10. Effects of various dilation angles on accuracy of FEM prediction.
Figure 10. Effects of various dilation angles on accuracy of FEM prediction.
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Figure 11. FEM: (a) element types and (b) loading and boundary conditions.
Figure 11. FEM: (a) element types and (b) loading and boundary conditions.
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Figure 12. Results of mesh sensitivity analysis.
Figure 12. Results of mesh sensitivity analysis.
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Figure 13. Experimental and numerical failure patterns for all tested walls: (a) NC wall W, (b) W-Gv4, (c) W-Gv5, (d) W-Gv7, (e) W-B2, and (f) W-Gv4-B2.
Figure 13. Experimental and numerical failure patterns for all tested walls: (a) NC wall W, (b) W-Gv4, (c) W-Gv5, (d) W-Gv7, (e) W-B2, and (f) W-Gv4-B2.
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Figure 14. Experimental and FE load–vertical displacement relationships for all tested walls: (a) master wall, (b) G1, and (c) G2.
Figure 14. Experimental and FE load–vertical displacement relationships for all tested walls: (a) master wall, (b) G1, and (c) G2.
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Figure 15. Datils of specimens used for parametric study: (a) G1-FE and (b) G2-FE.
Figure 15. Datils of specimens used for parametric study: (a) G1-FE and (b) G2-FE.
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Figure 16. Failure patterns for modeled walls in parametric study: (a) G1-FE and (b) G2-FE.
Figure 16. Failure patterns for modeled walls in parametric study: (a) G1-FE and (b) G2-FE.
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Figure 17. Effect of ratio of different sizes (aspect ratios) on numerical ultimate load capacity of walls.
Figure 17. Effect of ratio of different sizes (aspect ratios) on numerical ultimate load capacity of walls.
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Figure 18. Effect of slenderness ratio on numerical ultimate load capacity of walls.
Figure 18. Effect of slenderness ratio on numerical ultimate load capacity of walls.
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Table 1. Details of tested walls.
Table 1. Details of tested walls.
GroupWall NameAim of Tested GroupType of Strengthening MaterialRatio of Additional ReinforcementPlacing of StrengtheningSize of Strengthening Material
G1WMaster wall-----------------------------------
W-Gv4EBR using GSSsFour strips0.8%Horizontal placing1.00 mm thick of GSSs
W-Gv5Five strips1%
W-Gv7Seven strips1.4%
G2WMaster wall-----------------------------------
W-B2NSM using steel bars with/without GSSsTwo bars0.628%Vertical placing8 mm diameter of steel rebar
W-Gv4-B2Four sheets and two bars0.8% for GSSs
+
0.628% for bars		Horizontal and vertical placing for sheets and bars, respectively8 mm diameter
+
1.00 mm thick of GSSs
Table 2. Properties of steel elements.
Table 2. Properties of steel elements.
MaterialYieldUltimateE
(MPa)		Poisson Ratio
σy (MPa)εy (%)σu (MPa)εu (%)
Steel bar (8 mm diameter)2931.4545514.252010.30
Steel bar (12 mm diameter)3891.9560311.832000.30
Steel bar (16 mm diameter)4241.9763611.532120.30
GSS3421.9250111.261780.29
Table 3. Results from tested walls.
Table 3. Results from tested walls.
Specimens’
ID		Ultimate StageAbsorbed Energy
Measured Up to Ultimate Load (E)		E/EW
Pu
(kN)		Pu/PuWΔPu
(mm)
W6841.003.1814001.00
W6841.003.1814001.00
W-Gv47101.042.3617421.24
W-Gv57391.082.2819451.39
W-Gv77641.152.3722291.59
W6841.003.1814001.00
W-B27371.083.5621671.55
W-Gv4-B28241.224.2340542.90
Pu: ultimate load capacity; ΔPu: vertical displacement recorded at Pu; E: absorbed energy.
Table 4. Comparison between experimental (EXP) and FE results.
Table 4. Comparison between experimental (EXP) and FE results.
Specimens’
ID		Pu (kN)ΔPu (mm)
EXPFEEXP/FEEXPFEEXP/FE
W6847120.953.183.260.98
W-Gv47107380.962.362.410.98
W-Gv57397620.972.282.40.95
W-Gv77648000.962.372.520.94
W-B27377750.953.563.620.98
W-Gv4-B28248790.944.234.630.91
Average 0.95 0.95
Standard deviation (SD) 0.011 0.035
Coefficient of variation (COV) 0.002 0.006
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Hamoda, A.; Bahrami, A.; Abadel, A.A.; Ahmed, M.; Ghalla, M. Strengthening Reinforced Concrete Walls with Externally Bonded Galvanized Steel Sheets and Near-Surface Mounted Steel Bars. Buildings 2025, 15, 636. https://doi.org/10.3390/buildings15040636

AMA Style

Hamoda A, Bahrami A, Abadel AA, Ahmed M, Ghalla M. Strengthening Reinforced Concrete Walls with Externally Bonded Galvanized Steel Sheets and Near-Surface Mounted Steel Bars. Buildings. 2025; 15(4):636. https://doi.org/10.3390/buildings15040636

Chicago/Turabian Style

Hamoda, Ahmed, Alireza Bahrami, Aref A. Abadel, Mizan Ahmed, and Mohamed Ghalla. 2025. "Strengthening Reinforced Concrete Walls with Externally Bonded Galvanized Steel Sheets and Near-Surface Mounted Steel Bars" Buildings 15, no. 4: 636. https://doi.org/10.3390/buildings15040636

APA Style

Hamoda, A., Bahrami, A., Abadel, A. A., Ahmed, M., & Ghalla, M. (2025). Strengthening Reinforced Concrete Walls with Externally Bonded Galvanized Steel Sheets and Near-Surface Mounted Steel Bars. Buildings, 15(4), 636. https://doi.org/10.3390/buildings15040636

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