Shear performance of unreinforced masonry walls with door and window openings strengthened using welded steel mesh

Abstract

Unreinforced masonry (URM) walls often exhibit poor seismic performance, particularly when openings interrupt the load path and create stress concentrations that significantly reduce in-plane shear capacity. This study investigates welded steel mesh (WSM) as a practical and economical strengthening solution for URM walls with openings. Eleven masonry panels—including solid walls and walls with central openings—were tested under diagonal compression (ASTM E519), examining various WSM configurations such as orthogonal, diagonal, partial, and full layouts. The strengthened walls showed marked improvements in ultimate load, stiffness, and energy absorption, with the full diagonal mesh providing the highest enhancement. Although openings reduced shear capacity by 49%, WSM reinforcement helped redistribute stresses and delay crack initiation. A validated finite element model supported a parametric study, which identified an optimal WSM ratio of 0.08% and showed that large openings significantly reduce strength. The results confirm WSM as an effective retrofit for improving URM seismic performance.

Introduction

In recent years, the assessment of engineering structures and the materials used in them using laboratory testing, analytical models, and numerical simulations has emerged as a key area of research^1–5. Within this context, brick masonry walls stand out as one of the most significant structural elements in engineering practice. In many countries, brick masonry has long been favored in construction for its affordability, widespread availability, good thermal insulation, and minimal reliance on skilled labor or complex engineering^6–8. Despite these advantages, unreinforced masonry (URM) structures are particularly prone to earthquake damage due to their high weight and limited ductility. Many were erected with little regard for seismic safety, rendering them ineffective in energy dissipation during seismic events. Past earthquakes consistently reveal that URM buildings experience the most severe damage and highest casualty rates among all structural systems forces⁹. Additionally, incorporating openings in brick walls alters their ability to carry loads and affects how cracks develop under operational loading. Consequently, it is vital to strengthen these structures to ensure their stability and safety.

Under seismic activity, URM walls may experience failure in either the in-plane or out-of-plane direction. The most prevalent among these is in-plane shear failure¹⁰, which leads to distinctive diagonal cracking. The crack path usually follows the mortar joints when they are weaker than the masonry units or penetrates through the units when the units themselves are weaker. As shown in Fig. 1, URM walls experience several characteristic in-plane failure mechanisms during seismic actions, which are detailed below^11,12:

Fig. 1.

Typical in-plane failure modes observed in unreinforced brick masonry walls¹³. (a) Shear failure. (b) Sliding failure. (c) Rocking failure, (d) Toe crushing failure.

1. Shear failure: It is a common failure mode in masonry walls during earthquakes, occurring when the principal tensile stresses—arising from combined vertical and lateral loads—surpass the masonry’s tensile strength.

2. Sliding failure: Under low axial load and weak mortar conditions, earthquake forces often result in horizontal sliding along a mortar bed joint, causing the top section of the wall to shift.

3. Rocking and toe-crushing failure: A wall subjected to a high moment-to-shear ratio or improved resistance to shear may undergo rocking or experience toe crushing, influenced by the level of axial force acting on it.

To delay collapse and improve the seismic resilience of existing URM buildings, various retrofitting techniques were used, including shotcrete, steel bars, stitching, grout/epoxy injection, bamboo reinforcement, post-tensioning, confinement, center coring, and wire mesh¹⁴. Moreover, glass fiber reinforced polymer (GFRP) has been utilized by several researchers as a strengthening technique to enhance the ductile behavior of masonry structures^15,16. In a comparative analysis¹⁷, GFRP showed the highest shear strength enhancement among the tested unidirectional fibers—carbon, glass, and polyvinyl-alcohol. The study also revealed that diagonally reinforced walls performed better than those strengthened using a square grid arrangement. Another study¹⁸ showed that fully wrapping half-scale clay brick walls with GFRP enhanced their shear strength by 332% compared to unreinforced masonry, demonstrating significant strengthening effectiveness.

To evaluate in-plane behavior, NSM carbon FRP strips were applied in various orientations—horizontal, vertical, combined, and diagonal^19,20. Results indicated that shear strength improved significantly, with diagonal and combined configurations achieving the highest gains, ranging from 1.3 to 2.6 times over unreinforced walls²⁰. Moreover, failure mechanisms were largely attributed to diagonal shear, wall displacement through sliding, and the loss of adhesion between the FRP and masonry substrate¹⁹. A similar strengthening pattern using cost-effective geotextile was examined in¹³. Diagonal compression tests on solid clay brick walls showed that geotextile reinforcement enhanced crushing strength by 71% compared to unreinforced masonry, demonstrating its potential as an economical solution for wall strengthening. The application of GFRP has also proven effective in enhancing the flexural strength of masonry walls²¹. According to²², the failure moment of retrofitted walls increased by 794% compared to URM specimens. Another study²³, which conducted four-point bending tests on carbon FRP-strengthened masonry, reported a load capacity increase of over 780% relative to unreinforced counterparts. Carbon FRP anchorage was applied to hollow clay brick masonry, increasing strength and stiffness by over 15% and 32%, respectively²⁴. A recent study using basalt fiber reinforced cement mortar (BFRCM) to improve out-of-plane behavior showed strength and ductility enhancements exceeding fourfold and 29-fold, respectively²⁵. Additionally, fiber reinforced cementitious matrix (FRCM) was employed to enhance both shear and flexural performance, resulting in over twice the in-plane and out-of-plane strengths compared to unreinforced masonry walls^26–28.

Recently, low-cost materials like polypropylene (PP) bands and welded wire mesh have gained popularity for wall strengthening due to their high tensile resistance, significantly improving strength and ductility^14,29–35. In Padalu et al³⁶. conducted an experimental study on URM wallettes strengthened with welded wire mesh under out-of-plane loading. Wallettes retrofitted with welded wire mesh exhibited significant enhancements—up to 9.4 times in strength, 61 times in deformation capacity, and 1024 times in energy dissipation. Kadam et al²⁹. conducted diagonal compression tests on six unreinforced and twelve WWM and micro-concrete strengthened masonry panels. Results revealed that ferrocement strengthening significantly improved shear strength, ductility, rigidity, and drift capacity, enhancing the in-plane behavior of URM walls. Banerjee et al³⁷. conducted an experimental study on 32 masonry wall specimens—both unreinforced and strengthened with polypropylene bands and steel wire mesh—to evaluate out-of-plane flexural performance. The results demonstrated that both techniques effectively delayed collapse and significantly improved flexural strength and ductility. In another study, Banerjee et al³⁸. investigated the enhancement of shear and flexural behavior of URM wallets using various steel wire mesh layouts. Diagonal compression and four-point bending tests assessed in-plane and out-of-plane responses. Strength, ductility, and cost-effectiveness of the strengthening methods were evaluated. Furthermore, Nayak and Dutta³³ investigated the seismic performance of scaled-down masonry walls with openings. The results showed that such openings significantly affect crack development and damage patterns. Strengthening with polypropylene bands and steel wire mesh effectively mitigated these effects, offering cost-effective solutions for retrofitting masonry structures with openings.

Despite the extensive body of research on strengthening unreinforced masonry walls using fiber-reinforced polymers, cementitious composites, polypropylene bands, and welded wire mesh, existing studies have primarily focused on solid wall panels or on global strengthening schemes without explicitly addressing the presence of openings. Openings such as doors and windows, which are unavoidable in practical construction, significantly alter stress distribution and crack propagation mechanisms, leading to a pronounced reduction in in-plane shear capacity. Moreover, while welded steel mesh has been shown to be a cost-effective and practical retrofitting solution, there remains a lack of systematic experimental and numerical investigations that compare different WSM configurations, orientations, and coverage areas for masonry walls with openings under diagonal compression loading. This knowledge gap limits the development of rational design recommendations for strengthening URM walls with openings. Accordingly, the present study aims to experimentally and numerically evaluate the effectiveness of various WSM configurations in enhancing the in-plane shear performance of URM walls with openings, with particular emphasis on strength, stiffness, energy absorption, and failure mechanisms. To bridge the identified research gap, this study experimentally investigates unreinforced brick masonry panels with openings, retrofitted using welded steel mesh. A total of 11 panels were constructed: one without an opening and the remaining ten with openings. All specimens were tested under diagonal compression in accordance with ASTM E519³⁹ to simulate in-plane shear failure.

Experimental program

To evaluate the structural performance of URM walls, the experimental program proceeded in two stages. The initial phase involved characterization of materials using standardized tests. The second phase focused on assessing the in-plane shear resistance through diagonal compression tests. Comprehensive details regarding materials, specimen preparation, and testing techniques are described subsequently.

Specimen details

The masonry wall specimens were constructed at a geometric scale of 1:4 relative to typical full-scale unreinforced masonry walls. This scaling ratio was selected to accommodate laboratory space and loading capacity constraints while enabling the investigation of multiple welded steel mesh strengthening configurations within a consistent experimental framework. The scaling approach preserved geometric similarity, reinforcement ratios, and material composition to the extent possible, ensuring that the dominant mechanisms governing in-plane shear behavior were adequately represented. Furthermore, the tested specimens were designed to model the critical portion of a masonry wall containing an opening, where stress concentrations and crack initiation are most severe, rather than the entire wall height and length. Eleven masonry panels, each measuring 560 mm × 550 mm × 90 mm, were constructed under controlled laboratory conditions. One specimen was built without an opening, while the remaining ten specimens incorporated an opening measuring 200 mm × 180 mm, topped with a lintel beam measuring 90 mm × 50 mm and 360 mm in length. The thickness of both the mortar bed joints and head joints was maintained at 10 mm. All panels were cured for a minimum of 28 days before the application of the WSM layers. The presence of a sill band can contribute to mitigating shear cracks originating from window and door openings by providing horizontal continuity and reducing stress concentration at opening corners. Sill bands facilitate load redistribution across the opening and can delay the initiation of diagonal cracking under in-plane shear. In the present study, sill bands were intentionally excluded to isolate the structural contribution of welded steel mesh strengthening. However, the combined use of sill bands and WSM strengthening is expected to offer complementary benefits and represents a promising direction for future investigation.

To better understand the impact of various strengthening techniques, the experimental program is systematically divided into five groups (G1 to G5), each designed to investigate the structural behavior of wall specimens with or without openings under different welded steel mesh configurations, as shown in Table 1. The primary aim is to assess the influence of steel mesh arrangement, orientation, distribution, and coverage area on the performance of strengthened walls. Each group isolates a specific variable to better understand its impact on strength, ductility, and overall integrity of the wall systems.

Table 1.

Test matrix.

Group.	Wall`s ID	Arrangement of welded steel mesh	Size of welded steel mesh	Objective	Details
G1	O*	---------	---------	Master walls with/without opening	Figure 2-a
	O	---------	---------		Figure 2-b
	S	---------	---------		Figure 2-c
G2	O	---------	---------	Impact of divided and wide orthogonal welded steel mesh
	O-DOSM	Orthogonal	Distributed		Figure 3-a
	O-WOSM		Wide		Figure 3-b
G3	O	---------	---------	Impact of divided and wide diagonal welded steel mesh
	O-DDSM	Diagonal	Distributed		Figure 4-a
	O-WDSM		Wide		Figure 4-b
G4	O	---------	---------	Impact of covering area of welded steel mesh
	O-PSM	Covering	Partial		Figure 5-a
	O-FSM	Covering	Full		Figure 5-b
G5	O	---------	---------	Impact of divided welded steel mesh with different configuration
	O-ODSM	orthogonal and diagonal	Distributed		Figure 6-a
	O-OCSM	orthogonal and cross	Distributed		Figure 6-b

O*: Open wall without covering layer; O: Open wall with covering layer; S: Solid wall with covering layer; DOSM: Distributed orthogonal steel mesh; WOSM: Wide orthogonal steel mesh; DDSM: Distributed diagonal steel mesh; WDSM: Wide diagonal steel mesh; PSM: Partial steel mesh; FSM: Full steel mesh; ODSM: orthogonal and diagonal steel mesh; OCSM: orthogonal and cross steel mesh.

Group G1 serves as the control group to establish baseline performance data (Fig. 2). It includes three wall types: an open wall without a covering layer (O*) (Fig. 2a), an open wall covered with a traditional mortar layer (O) (Fig. 2b), and a solid wall without an opening but with a covering layer (S) (Fig. 2c). These specimens are essential for benchmarking the effects of both the wall opening and the presence of a protective covering layer. The comparison between specimens O and O* allows for evaluating the effectiveness of the covering layer, while specimen S represents a fully intact wall, providing insight into how the presence of an opening affects structural integrity.

Fig. 2.

Geometric and strengthening details of G1 masonry walls: (a) O, (b) O*, and (c) S. (Units: mm).

Group G2 focuses on understanding the role of orthogonal welded steel mesh in open walls (Fig. 3). It includes two specimens: O-DOSM and O-WOSM. The O-DOSM specimen was strengthened with distributed orthogonal steel mesh consisting of four strips arranged orthogonally around the opening in both the longitudinal and transverse directions. Each strip was 50 mm wide, with a center-to-center spacing of 130 mm in both directions (Fig. 3a). In contrast, the O-WOSM specimen was strengthened with wide orthogonal steel mesh composed of two strips arranged orthogonally around the opening in both directions (Fig. 3b). Each strip was 100 mm wide, with a center-to-center spacing of 410 mm. This group is designed to investigate whether the distribution pattern or the width of the orthogonal mesh enhances the wall’s resistance to applied loads. The distributed mesh is expected to offer uniform stress distribution, while the wide mesh may contribute to higher confinement and improved load transfer capacity.

Fig. 3.

Geometric and strengthening details of G2 masonry walls: (a) O-DOSM and (b) O-WOSM. (Units: mm).

Group G3 is structured similarly to G2 but utilizes diagonal welded steel mesh (Fig. 4). It contains two wall specimens: one strengthened with distributed diagonal steel mesh (O-DDSM) (Fig. 4a) and another with wide diagonal steel mesh (O-WDSM) (Fig. 4b). Diagonal reinforcement is often associated with improved shear resistance and enhanced crack control. This group aims to evaluate whether diagonal mesh outperforms orthogonal mesh in resisting the diagonal tension forces typically encountered around openings. Additionally, it provides a comparison between distributed and wide mesh configurations.

Fig. 4.

Geometric and strengthening details of G3 masonry walls: (a) O-DDSM and (b) O-WDSM. (Units: mm).

In Group G4, the focus shifts to evaluating the impact of the welded steel mesh coverage area (Fig. 5). This group includes two specimens: one strengthened with diagonal partial steel mesh coverage (O-PSM) around the opening, measuring 380 mm × 380 mm (Fig. 5a), and another specimen strengthened with full steel mesh coverage (O-FSM) around the opening (Fig. 5b). The primary goal is to understand whether increasing the welded steel mesh coverage area enhances wall performance. The partial coverage may simulate practical constraints or cost-saving strategies, while full coverage represents the optimal reinforcement scenario. This comparison will reveal the trade-offs between reinforcement efficiency and material use.

Fig. 5.

Geometric and strengthening details of G4 masonry walls: (a) O-PSM and (b) O-FSM. (Units: mm).

Lastly, Group G5 investigates the effect of combining different mesh orientations (Fig. 6). It consists of one specimen strengthened with a combination of orthogonal and diagonal distributed mesh (O-ODSM) (Fig. 6a), and another combining orthogonal and cross distributed mesh (O-OCSM) (Fig. 6b). This group explores the potential synergy between various mesh orientations and aims to determine whether a hybrid approach can provide enhanced confinement, crack resistance, and ductility. Such configurations may reflect real-world practices where complex stress distributions necessitate multidirectional reinforcement.

Fig. 6.

Geometric and strengthening details of G5 masonry walls: (a) O-ODSM and (b) O-OCSM. (Units: mm).

It should be noted that the experimental program included a single specimen for each strengthening configuration, which limits the statistical significance of the results and does not allow direct assessment of experimental variability. This approach was adopted to enable a comprehensive comparison of a wide range of welded steel mesh configurations within practical laboratory constraints. Accordingly, the experimental findings should be interpreted primarily in a comparative and exploratory sense, with emphasis on identifying relative performance trends, dominant failure mechanisms, and the influence of mesh orientation and coverage. The consistency of observed behavioral patterns across different configurations, together with the close agreement between experimental results and validated finite element simulations, provides additional confidence in the reliability of the main conclusions, while acknowledging that further testing with multiple replicates would be beneficial for future studies.

Materials

Masonry material properties

Brick and mortar

For specimen fabrication, hollow clay bricks with approximate dimensions of 180 mm × 90 mm × 50 mm were selected as shown in Fig. 7a. Their mechanical and physical properties were evaluated in accordance with ASTM C67/C67M-20⁴⁰. The compressive strength of the bricks was found to be 11.07 MPa, with a coefficient of variation (CoV) of 13.2%, indicating moderate variability among the samples. The modulus of rupture, representing the flexural strength, averaged 2.90 MPa, with a CoV of 13%. The average density of the bricks was 1720 kg/m³, indicating a relatively lightweight unit suitable for applications where reduced dead load is beneficial. The CoV values, shown in parentheses, reflect the level of consistency and reliability in the measured properties across all tested specimens.

Fig. 7.

Materials tested for used bricks and mortar: (a) sample of used bricks, (b) compression test for blocks, (c) direct shear test for bricks.

Furthermore, a cement mortar with a mixed proportion of 1:5 (cement: sand) was adopted, and a proper quantity of water was used to ensure good workability of the mortar. The water-cement ratio was maintained at 0.45. To evaluate the mechanical and physical performance of the mortars, compressive strength, rupture modulus, and density were measured in accordance with ASTM C109/C109M-07⁴¹ and ASTM C78-09⁴². The mortar exhibited a compressive strength of 3.02 MPa with a coefficient of variation (CoV) of 4.1%. It also demonstrated a rupture modulus of 2.48 MPa (CoV = 7.8%) and the density measured at 2069 kg/m³.

In accordance with ASTM C1314-21⁴³ and BS EN 1052-3:2002⁴⁴, the compressive strength, elastic modulus, and shear bond strength of masonry prisms were assessed (Fig. 7b and c). Prisms comprising three brick units were used to determine compressive strength, while triple wallettes were used for bond shear testing. Mortar bed joints were consistently 10 mm thick. All specimens were cured under identical conditions as the mortar samples. result show that the masonry prisms showed a compressive strength of 6.38 MPa (CoV = 23.2%) and an elastic modulus of 1161 MPa (CoV = 3.67%). Its shear bond strength was 0.12 MPa (CoV = 19.6%).

Normal concrete

As recommended by a study conducted by Fayed et al⁴⁵., the concrete samples were cast using a consistent normal-strength concrete mix, the details of which are provided in Table 2. The constituents included natural sand, crushed basalt dolomite with a maximum aggregate size of 15 mm, Portland cement Grade 42.5, clean potable water, and Sikament-163 M as a high-range water-reducing admixture. The proportions were designed on a weight basis of 1 : 2.80 : 4.80 with a water–cement ratio of 0.50 to achieve the required workability and strength. Following the provisions of ECP 203/2018⁴⁶, standard 150 mm cube specimens were prepared to measure compressive strength, resulting in an average value of 20 MPa, while cylindrical specimens measuring 150 × 300 mm were also produced to assess the splitting tensile strength, which reached 1.8 MPa.

Table 2.

Compositions of normal concrete (kg/m³)⁴⁵.

Concrete mix type	Cement	Water	Fine aggregate	Coarse aggregate	Super plasticizer	Water/cement (%)
NC	250	150	700	1200	2.5	0.50

Steel reinforcement and steel mesh

In the experimental program, steel bars with an 8 mm diameter were installed as bottom reinforcement in the lintel beams. Tensile testing confirmed a yield strength of 281 MPa, ultimate strength of 438 MPa, modulus of elasticity of 200 GPa, and elongation at break of 11%. According to the manufacturer, the welded steel mesh exhibited an average yield strength of approximately 550 MPa and an ultimate tensile strength of about 600 MPa, with stable post-yield behavior. These characterized properties were used in the interpretation of the strengthening mechanism and were also adopted in the finite element modeling to ensure consistency between experimental observations and numerical simulations.

The welded steel mesh adopted in this study featured a diamond grid pattern. This configuration was selected due to its wide availability and ease of application in practical construction, as well as its mechanical suitability for resisting diagonal tensile stresses associated with in-plane shear loading. The inclined grid orientation promotes effective crack bridging and stress redistribution, while also enhancing mechanical interlock with the surrounding mortar layer.

Table 3.

Mechanical properties of welded steel mesh (from manufacturer’s datasheet).

Property	Value
Wire diameter	1.5 mm
Mesh spacing (center-to-center)	10 × 10 mm
Yield strength (fy)	550 MPa
Ultimate tensile strength (fu)	600 MPa
Elastic modulus (E)	200 GPa

Strengthening procedures

The strengthening of URM walls with openings followed a systematic multi-stage process, as illustrated in Fig. 8. This procedure was designed to ensure proper installation of the welded steel mesh (WSM) reinforcement and achieve consistent performance across specimens. The process began with placing lintel beams above the planned openings. These beams were cast in situ using normal concrete within wooden formworks (Fig. 8a). The lintel dimensions were 360 mm in length, 90 mm in depth, and 50 mm in thickness, providing structural support across the top of each opening.

Fig. 8.

Strengthening preparation. (a) Casting lintel beams. (b) Construction of URM wall. (c) Applying WSM around the opening, (d) Finishing the strengthening using a traditional mortar layer.

Following the installation of the lintel, unreinforced masonry walls were constructed using standard hollow clay bricks and mortar (Fig. 8b). Each wall measured 560 mm × 550 mm × 90 mm, with a centrally located opening measuring 200 mm × 180 mm—except for one specimen, which was constructed without an opening. Mortar joints were uniformly maintained at 10 mm for both bed and head joints, and each wall was built with nine courses to ensure dimensional consistency.

After the masonry walls had cured sufficiently, the welded steel mesh (WSM) was applied (Fig. 8c). The mesh was carefully cut and shaped to fit around the perimeter of the opening, following the specific configuration designated for each specimen group (e.g., orthogonal, diagonal, partial, or combined mesh types). This step was crucial to ensure that the mesh provided effective confinement and reinforcement, particularly in areas of high stress concentration around the edges of the opening. The strengthening process continued with surface preparations to ensure proper bonding between the wall and the final layer. This included cleaning the wall surface, aligning the mesh, and securing it in place to avoid displacement during plaster application. Finally, a traditional mortar layer was applied over the mesh to form the outer surface of the strengthened wall. This layer served both as mechanical protection for the mesh and as an additional confinement mechanism. The panels were then left to cure for 28 days under controlled conditions to ensure consistent hardening before testing.

Testing procedure

The in-plane diagonal shear strength of both unretrofitted and retrofitted masonry panels was evaluated in accordance with ASTM E519/E519M-10⁴⁷. Diagonal compression was applied at opposing corners using a 250-ton capacity universal testing machine. As shown in Fig. 9, the test setup included steel shoes to transfer displacement-controlled loads through the top and bottom edges of the specimens. A loading rate of 0.1 mm/min was used for unreinforced panels, while retrofitted panels were tested at 0.3 mm/min, allowing each test to be completed in approximately 2 min⁴⁷. Specimens were transferred to the testing frame using the laboratory’s overhead crane, with measures in place to prevent structural damage—particularly to the URM panels, which are susceptible to failure due to their limited tensile capacity. To maintain stability and prevent out-of-plane deformations, all specimens were transported in a vertical orientation. Diagonal displacement was measured at the center of the panel using two linear variable differential transducers (LVDTs) positioned diagonally. The transducers were mounted using screw-and-clamp mechanisms and connected to the same data acquisition system used for load monitoring, enabling synchronized measurement of both load and deformation.

Fig. 9.

Test set-up and details of the instrumentations: (a) schematic of tested wall and (b) image of the wall during the test. (Units in mm).

Results of tests and discussion

This section presents the performance results of the tested walls, focusing on crack and failure patterns, ultimate load, displacement behavior, stiffness, shear response, and energy absorption. Table 3 summarizes the ultimate load (P), deflection (δ), absorbed energy (E) from the load-deflection curve, and initial stiffness (K) derived from the elastic slope of the response.

Table 4.

Test results.

Group	Wall`s ID	Cracking Stage		Ultimate Stage			Elastic stiffness index (K)	K/Ko	Absorbed energy (E)	E/Eo
		P cr (kN)	P cr /P cro	P u (kN)	P u /P uo	Δ Pu (mm)
G1	O*	15.21	0.77	22.34	0.69	2.18	12.27	0.59	33.74	0.58
	O	19.64	1.00	32.23	1.00	1.98	20.67	1.00	58.06	1.00
	S	34.98	1.78	62.69	1.95	2.93	34.29	1.66	164.06	2.83
G2	O	19.64	1.00	32.23	1.00	1.98	20.67	1.00	58.06	1.00
	O-DOSM	20.20	1.03	34.84	1.08	1.91	29.97	1.45	70.5	1.21
	O-WOSM	21.40	1.09	36.85	1.14	1.76	31.15	1.51	70.99	1.22
G3	O	19.64	1.00	32.23	1.00	1.98	20.67	1.00	58.06	1.00
	O-DDSM	20.43	1.04	35.27	1.09	2.12	26.49	1.28	68.45	1.18
	O-WDSM	22.00	1.12	37.63	1.17	1.79	40.37	1.95	71.19	1.23
G4	O	19.64	1.00	32.23	1.00	1.98	20.67	1.00	58.06	1.00
	O-PSM	22.78	1.16	39.13	1.21	2.44	27.88	1.35	74.71	1.29
	O-FSM	24.16	1.23	41.37	1.28	2.25	42.66	2.06	91.37	1.57
G5	O	19.64	1.00	32.23	1.00	1.98	20.67	1.00	58.06	1.00
	O-OCSM	20.82	1.06	35.85	1.11	1.96	25.58	1.24	71.35	1.23
	O-ODSM	22.40	1.14	38.34	1.19	1.96	36.85	1.78	80.85	1.39

Failure mode

Cracks and failure modes were documented at each load increment as the walls were progressively loaded to failure. Figures 10, 11, 12, 13 and 14 illustrate the cracking and failure patterns observed in Groups G1 through G5 during the testing process.

Fig. 10.

Failure mode of Group G1: (a) O*, (b) O, and (c) S.

Fig. 11.

Failure mode of Group G2: (a) O-DOSM and (b) O-WOSM.

Fig. 12.

Failure mode of Group G3: (a) O-DDSM and (b) O-WDSM.

Fig. 13.

Failure mode of Group G4: (a) O-PSM and (b) O-FSM.

Fig. 14.

Failure mode of Group G5: (a) O-ODSM and (b) O-OCSM.

In Group G1, as shown in Fig. 10, the failure modes differed significantly depending on the presence of an opening and the application of a covering layer. Wall O*—an open wall without a covering layer—highlighted the importance of surface confinement. This wall experienced severe damage, with wide and prominent cracks forming at the corners of the opening, leading to significant separation between the bricks and the lintel beam (Fig. 10a). The absence of a covering layer accelerated crack development and weakened the connections between structural components, ultimately compromising load transfer and stability. In contrast, the behavior of wall O, representing an open wall with a covering layer, was notably more stable. It exhibited minor tensile cracks localized at the corners of the opening, with a delayed onset of initial cracking (Fig. 10b). The first visible crack appeared at a load of 19.64 kN, marking a 29% improvement compared to wall O*. These cracks were fine and well-distributed, indicating that the covering layer effectively limited crack propagation. As a result, the structural integrity of the wall was preserved under loading, with no major separation or detachment observed. On the other hand, wall S, a solid wall with a covering layer and no opening, demonstrated a different failure mode. It developed wide diagonal cracks extending across the wall body, accompanied by splitting and internal fracturing of the masonry (Fig. 10c). Although the covering layer provided some degree of confinement, the absence of an opening allowed shear forces to concentrate within the wall body, resulting in a typical diagonal shear failure commonly observed in unreinforced masonry walls subjected to in-plane loading.

In Group G2, wall O-DOSM, an open wall strengthened with distributed orthogonal steel mesh, exhibited a failure mode resembling that of wall O. Fine tensile cracks emerged at the corners of the opening due to localized stress concentrations. The WSM effectively restrained their growth, enhancing surface confinement, delaying crack initiation, and preserving structural integrity (Fig. 11a). The first visible crack occurred at 20.20 kN, indicating a 3% improvement over wall O. Similarly, wall O-WOSM, incorporating wide orthogonal steel mesh, developed narrow, evenly distributed cracks in the same regions (Fig. 11b). The broader coverage facilitated more uniform stress distribution, improving ductility and delaying cracking, which first appeared at 21.40 kN—a 9% increase over wall O. In both walls, no significant separation or failure was observed, underscoring the beneficial role of orthogonal steel mesh in enhancing the performance of walls with openings.

Similarly, the URM walls in Group 3 (Fig. 12), strengthened with diagonal welded steel mesh, exhibited a failure pattern comparable to those in Group 2, characterized by tensile cracks concentrated at the corners of the openings due to localized stress concentrations. This strengthening technique effectively delayed the onset of initial cracking compared to the Group 2 walls. The first visible crack in wall O-DDSM appeared at a load of 20.43 kN, marking a 4% increase over wall O, while in wall O-WDSM, it occurred at 22.00 kN, indicating a 12% improvement.

On the other hand, the URM walls in Group 4 (Fig. 13), which evaluated the effect of welded steel mesh coverage area, exhibited a failure pattern similar to those in Groups 2 and 3. However, they outperformed all other tested techniques by further delaying the onset of initial cracking and promoting a more favorable distribution of diagonal cracks. The first visible crack in wall O-PSM — strengthened with diagonal partial steel mesh coverage — appeared at a load of 22.78 kN, representing a 16% increase over wall O. In wall O-FSM — strengthened with diagonal full steel mesh coverage — the first crack occurred at 24.16 kN, reflecting a 23% improvement, making it the best-performing wall in terms of delaying the onset of initial cracking among all the strengthened walls.

In contrast, the URM walls in Group G5 (Fig. 14), strengthened with a combination of different mesh orientations around openings, showed lower performance in delaying the onset of initial cracking and in crack distribution compared to the strengthened walls in Group 4. The first visible crack in wall O-OCSM — strengthened with a combination of orthogonal and diagonal distributed mesh — appeared at a load of 20.82 kN, representing a 6% increase over wall O. In wall O-ODSM — strengthened with a combination of orthogonal and cross distributed mesh — the first crack occurred at 22.40 kN, reflecting a 14% improvement.

Load-displacement behavior

Figure 15 graphically presents the load–displacement (P–Δ) behavior of all tested URM walls, illustrating their performance under progressively increasing loads. The x-axis represents displacement measurements obtained from linear vertical displacement transducers (LVDTs), while the y-axis shows the applied load values. The load-displacement response generally progresses through three phases. The first is the elastic phase, starting with load application and continuing until the first visible cracks appear, characterized by a linear relationship and showing the effect of strengthening techniques in delaying crack initiation. Next is the nonlinear or plastic phase, which begins at crack onset and continues until the load peaks, marked by progressive stiffness degradation due to crack propagation that reduces the wall’s strength and deformation capacity. Finally, the failure phase follows the peak load and features a sharp drop in load-bearing capacity caused by excessive cracking and structural instability.

Fig. 15.

Load-vertical displacement relationships for all tested walls: (a) Group G1, (b) Group G2, (c) Group G3, (d) Group G4, and (e) Group G5.

To provide further insight into the behavior of the tested URM walls, Fig. 15a illustrates the P–Δ curves for the master URM walls, revealing a notable improvement in the performance of wall O compared to wall O*. Wall O demonstrated the highest ultimate load capacity () and elastic stiffness, as indicated by the steeper slope of its P–Δ curve, and reached the greatest ultimate displacement () of 2.18 mm, reflecting a 10% increase over wall O*. This highlights the beneficial role of the covering layer in enhancing the load–displacement response of URM walls. In contrast, wall O showed a significant reduction in P–Δ performance compared to wall S. Wall S achieved a higher , greater stiffness, and a larger , with a 48% improvement over wall O. This emphasizes the adverse impact of openings on the structural behavior of URM walls.

Furthermore, Fig. 15b demonstrates a notably improved P–Δ response for the Group G2 walls compared to wall O, emphasizing the effectiveness of orthogonal WSM strengthening in enhancing shear performance. Among the G2 specimens, wall O-WOSM exhibited the most pronounced improvement, with the steepest P–Δ curve, reflecting higher elastic stiffness and ultimate load capacity (). Likewise, wall O-DOSM showed a superior P–Δ response relative to wall O, further validating the positive impact of orthogonal WSM reinforcement. Similarly, the walls in Groups 3, 4, and 5 showed a marked enhancement in the P–Δ response, reflected in improved elastic stiffness, greater energy absorption, and higher ultimate load capacity compared to wall O. These results confirm the effectiveness of all proposed strengthening techniques in enhancing the shear resistance of URM walls with openings. Among the tested specimens, wall O-FSM—reinforced with full WSM coverage around the opening—exhibited the most superior load–displacement performance.

Ultimate strength

Table 3 displays the ultimate load () recorded for each tested URM wall, highlighting the influence of various strengthening methods on structural performance. Overall, using WSM as a strengthening techniques enhances the ultimate shear capacity of strengthened walls.

A closer analysis of the Group G1 walls—the baseline group—shows ultimate load capacities of 22.34 kN for wall O*, 32.23 kN for wall O, and 62.69 kN for wall S, as presented in Table 3. These results indicate that the application of a covering layer increased the ultimate shear capacity by approximately 44%. Conversely, the presence of an opening led to a 49% reduction in ultimate shear capacity. The observed increase in ultimate shear capacity by 44% due to the applied covering layer can be attributed to its ability to enhance the confinement of the masonry, improve cohesion between units, and delay the initiation and propagation of cracks. This additional layer contributes to a more uniform stress distribution, increased stiffness, and improved load-bearing capacity. In contrast, the 49% reduction in shear capacity caused by the presence of an opening is due to the interruption in the load path, which concentrates stress around the edges of the opening and reduces the effective area resisting shear. This discontinuity leads to earlier cracking, decreased lateral stiffness, and compromised energy dissipation, all of which weaken the wall’s structural performance under shear loads.

In Group G2, walls were tested to assess the effect of orthogonal WSM strips on the shear performance of URM walls. As shown in Table 3, the ultimate loads () for walls O-DOSM and O-WOSM were 34.84 kN and 36.85 kN, representing increases of 8% and 14%, respectively, compared to wall O. These findings indicate that applying orthogonal WSM strips around openings significantly enhances the shear resistance of URM walls, with the most notable improvement observed in wall O-WOSM, which was strengthened using wide orthogonal WSM strips. This enhancement is attributed to the ability of the orthogonal WSM strips to effectively confine the masonry around the openings, limiting crack propagation and distributing stresses more uniformly under shear loading. The wider strips in wall O-WOSM provide greater confinement and anchorage, thereby increasing both the wall’s stiffness and its capacity to resist shear forces.

Similarly, the URM walls in Group G3 exhibited a notable improvement compared to those in Group G2. This group investigated the effect of employing diagonal WSM strips around the openings, as opposed to the orthogonal strips used in Group G2, on the shear performance of URM walls. The results showed that wall O-DDSM recorded a of 35.27 kN, while wall O-WDSM achieved a of 37.63 kN, reflecting increases of 9% and 17%, respectively, compared to wall O. These findings indicate that the application of diagonal WSM strips around openings significantly enhances the shear resistance of URM walls, with the most notable improvement observed in wall O-WDSM, which was strengthened using wide diagonal WSM strips. The enhanced performance of walls strengthened with diagonal WSM strips can be attributed to their ability to intercept and resist diagonal shear cracks more effectively than orthogonal strips. Diagonal reinforcement aligns more closely with the natural crack propagation paths under lateral loading, thereby improving crack control, enhancing energy dissipation, and increasing both stiffness and shear capacity. This alignment allows the diagonal strips to contribute directly to resisting shear forces, resulting in a more efficient strengthening mechanism around the openings.

Regarding the URM walls in Group G4, which focused on evaluating the impact of WSM coverage area on shear resistance, wall O-FSM—strengthened with full WSM coverage around the opening—demonstrated the best performance among all tested walls. It recorded a peak load () of 41.37 kN, representing a 28% increase compared to wall O. Wall O-PSM ranked second, achieving a of 39.13 kN, corresponding to a 21% increase relative to wall O. These findings indicate that this strengthening method—particularly full coverage—is the most effective among the evaluated techniques for enhancing the shear performance of URM walls. The superior performance of wall O-FSM can be attributed to the full distribution of WSM reinforcement over the entire wall surface, which ensures more uniform stress transfer and improved confinement around the opening. This comprehensive coverage helps restrain crack initiation and propagation, thereby enhancing both the load-carrying capacity and ductility of the wall. In contrast, wall O-PSM, which used partial WSM coverage, provided localized reinforcement, resulting in moderate improvement. These outcomes confirm that greater reinforcement coverage leads to better structural integrity and higher shear resistance in URM walls.

In contrast, the URM walls in Group G5, strengthened with a combination of different mesh orientations around the openings, exhibited lower performance than those in Group G4, but still outperformed the walls in Groups 2 and 3. Wall O-OCSM, reinforced with a combination of orthogonal and diagonal distributed mesh, achieved a of 35.85 kN—an 11% increase over wall O. Wall O-ODSM, strengthened with orthogonal and cross distributed mesh, recorded a of 38.34 kN, showing a 19% improvement. This relatively lower performance in Group G5 may be attributed to the interaction between different mesh orientations, which could lead to stress incompatibility or uneven distribution of forces around the openings. Such interactions may have limited the overall strengthening efficiency, unlike the more uniform mesh patterns used in Group G4, which likely provided better confinement and crack control.

Diagonal welded steel mesh arrangements exhibited superior performance compared to orthogonal patterns because their orientation is closely aligned with the principal tensile stress directions associated with diagonal shear cracking. This alignment enables more effective crack bridging, earlier activation of tensile resistance in the mesh, and improved stress redistribution around openings. Orthogonal mesh arrangements, while still beneficial, are less efficiently oriented to resist diagonal tensile stresses and therefore provide comparatively lower strengthening effectiveness.

Elastic stiffness and absorbed energy

Table 3 presents the structural rigidity and energy absorption capacities of the tested walls. The stiffness parameter (K) represents the initial elastic response, while the energy dissipation capacity (E) reflects the wall’s ability to resist collapse under cyclic loading. All retrofitting methods significantly enhanced these properties in the structurally deficient specimens, as shown in Figs. 16 and 17. In Group G1, calculations revealed that applying a covering layer to the URM wall (wall O) resulted in a 68% increase in elastic stiffness and a 72% increase in energy absorption compared to the unstrengthened wall O*. This improvement is attributed to the confinement effect and enhanced surface integrity provided by the retrofitting layer, which helped distribute stresses more evenly and delay the onset of cracking. In contrast, the presence of an opening in wall O caused a sharp reduction in elastic stiffness and energy absorption by 40% and 65%, respectively. This decline is due to stress concentration and disruption of the load path around the opening, which significantly compromised the wall’s ability to resist deformation and dissipate energy during loading.

Fig. 16.

The elastic index for all tested walls (kN/mm).

Fig. 17.

The absorbed energy for all walls (kN.mm).

For specimens in test series G2, computational results indicated that the elastic stiffness of walls strengthened with orthogonal WSM strips increased by 45% and 51% for O-DOSM and O-WOSM, respectively, compared to the defective wall O. Additionally, the absorbed energy improved by 21% and 22% for the same walls. Building upon these results, Group G3 demonstrated further enhancements, as the elastic stiffness of beams reinforced with diagonal WSM strips around the openings increased by 28% and 95% for O-DDSM and O-WDSM, respectively. Correspondingly, their absorbed energy increased significantly by 18% and 23%.

For specimens in group G2, the computational results revealed that strengthening with orthogonal WSM strips significantly enhanced performance. The elastic stiffness increased by 45% for wall O-DOSM and 106% for wall O-WOSM compared to the unstrengthened wall O, while energy absorption improved by 21% and 22%, respectively. Building on these results, Group G3—focused on the effect of diagonal WSM strips around the openings—demonstrated further performance gains. The elastic stiffness increased by 28% for wall O-DDSM and 95% for wall O-WDSM, accompanied by corresponding increases in energy absorption of 18% and 23%, respectively.

Extending this trend, Group G4 demonstrated the most significant enhancements. Walls strengthened with partial diagonal (O-PSM) and full WSM coverage (O-FSM) around the opening exhibited increases in elastic stiffness by 35% and 106%, respectively, compared to wall O. Likewise, energy absorption improved notably, with gains of 29% for O-PSM and 57% for O-FSM. In contrast, the URM walls in Group G5—strengthened using combinations of different mesh orientations around the openings—showed slightly lower performance than those in Group G4, yet still outperformed the walls in Groups G2 and G3. Wall O-OCSM, reinforced with a combination of orthogonal and diagonally distributed mesh, showed a 24% increase in elastic stiffness relative to wall O. Meanwhile, wall O-ODSM, strengthened with orthogonal and cross-distributed mesh, achieved a 78% improvement in elastic stiffness. Correspondingly, energy absorption was enhanced by 23% for O-OCSM and 39% for O-ODSM.

Among the strengthening techniques evaluated, the wall strengthened with full WSM coverage around the opening (wall O-FSM) proved to be the most effective in enhancing structural performance. Specifically, it exhibited a 28% increase in ultimate load capacity, a 106% increase in elastic stiffness, and a 57% increase in energy absorption compared to the unstrengthened wall O. These improvements can be attributed to the continuous confinement and uniform stress distribution provided by the full WSM coverage, which effectively restrained crack propagation, improved load transfer mechanisms around the opening, and enhanced the overall integrity and ductility of the wall under shear loading. In descending order of effectiveness, walls O-ODSM and O-WDSM exhibited progressively lower levels of improvement. In contrast, wall O-DDSM, strengthened with distributed diagonal steel mesh, showed the least enhancement.

The energy absorption values reported in this study were derived from monotonic load–displacement responses obtained from diagonal compression tests. Accordingly, these values represent the monotonic deformation capacity of the strengthened masonry walls and should not be interpreted as measures of cyclic or hysteretic seismic energy dissipation. Nevertheless, the monotonic energy absorption provides a useful comparative indicator of ductility and post-cracking load-carrying capacity among the investigated welded steel mesh configurations.

Behaviour between welded steel mesh and mortar layer

The effectiveness of the WSM strengthening system is strongly governed by the bond behavior between the steel mesh and the surrounding mortar layer, as this interface controls stress transfer and composite action. During experimental testing, visual inspection of all strengthened specimens revealed no premature debonding, mesh slippage, or separation of the mortar layer from the masonry substrate prior to reaching peak load. Instead, cracking was primarily observed in the masonry units and mortar joints around the openings, while the mortar layer embedding the WSM remained well-adhered, indicating effective bond performance. This strong bond allowed tensile forces induced by diagonal shear cracking to be efficiently transferred from the masonry to the steel mesh, enabling the mesh to restrain crack opening, redistribute stresses, and enhance confinement around the opening edges. The integrity of the WSM–mortar bond was particularly evident in specimens with diagonal and full mesh coverage, where crack widths were smaller and more uniformly distributed. These observations confirm that the strengthening mechanism relies on effective composite action between the WSM and mortar layer, a behavior that was also reflected in the finite element model through the adoption of fully bonded embedded constraints.

Practical considerations for implementation of WSM strengthening systems

Beyond structural performance, the practical implementation of WSM strengthening systems requires consideration of constructability, cost, and durability. From a construction standpoint, orthogonal mesh configurations are generally simpler to install, as they involve straight mesh strips aligned with the wall geometry and require minimal cutting and on-site adjustment. Diagonal and combined mesh layouts, while structurally more effective, involve increased cutting, precise alignment around openings, and more careful placement, which may increase labor time and workmanship sensitivity. Full mesh coverage offers superior structural performance but entails higher material consumption and installation effort compared to partial or localized strengthening schemes.

In terms of cost implications, the primary contributors are mesh quantity, mortar usage, and labor. Distributed or partial mesh configurations may provide a favorable balance between performance improvement and material economy, whereas full coverage systems represent a higher initial cost but yield the greatest enhancement in strength, stiffness, and energy absorption. Therefore, the choice of configuration should be guided by the required performance level, available budget, and the severity of seismic demand.

Durability is another critical aspect, particularly with respect to corrosion protection of steel mesh. During installation, cut edges of the mesh may be susceptible to corrosion if left unprotected, especially in aggressive or humid environments. In the present study, the mesh was fully embedded within the mortar layer, which provides a basic level of protection. However, for long-term durability in practical applications, additional measures such as adequate mortar cover thickness, the use of corrosion-resistant coatings or galvanized mesh, and proper surface finishing are recommended. These considerations are essential to ensure sustained performance of WSM-strengthened masonry walls and to translate the observed experimental benefits into durable field applications.

FE modelling

To replicate the nonlinear response of masonry in three dimensions, simulations accounting for both geometric and material nonlinearity were carried out using ABAQUS. Systematic validation against test outcomes verified the numerical solution’s accuracy^48–50.

Model development

Building upon the experimental observations, a detailed computational model of wall O-ODSM was developed, as shown in Fig. 18. The model utilized 4-node linear tetrahedral elements (C3D4) for the masonry wall, lintel beam, loading steel cap, and mortar layer. The welded steel mesh was represented using three-node triangular shell elements (S3), while the bottom reinforcement of the lintel beam was modeled using T3D2 truss elements.

Fig. 18.

The numerical model, elements, materials, and interactions for wall O-ODSM.

To accurately capture the interaction between different materials within the model, additional constraint definitions were applied. Full bond embedded region constraints^51,52 were implemented to model perfect adhesion between the bottom reinforcement and lintel beam, as well as between the steel mesh and mortar layer, by coupling their degrees of freedom. The structural behaviour of masonry along bed and head joints was captured using a surface-based cohesive model, as described in⁵³. The interaction between the loading steel cap and the mortar layer was modeled using surface-to-surface contact. Normal behavior employed a hard contact model to avoid penetration, and tangential behavior captured frictional effects, enabling the transfer of shear and normal forces across the interface. Friction was represented by the penalty method with a coefficient of 0.3 to enhancing simulation reliability. Additionally, a cohesive surface model with damage evolution simulated the mortar layer - URM wall interface, adopting validated parameters^54–61. The three-stage interaction (Fig. 19) includes: linear stiffness (), peak stress (), and fracture energy (). Initial stiffness is derived from Eq. (1) following Guo and Cao’s methodology Guo, Cao⁶².

1

Fig. 19.

Cohesive-damage interaction behaviour.

In this context, denotes the thickness of the resin, represents the thickness of the concrete, and and symbolize the shear moduli of the adhesive and concrete materials respectively.

Furthermore, a mesh sensitivity study was carried out to refine the discretization of the URM wall model. Among the mesh sizes ranging from 5 mm to 20 mm, the 10 mm mesh was selected as it yielded accurate results with reasonable computational demand, corroborated by experimental validation in Fig. 18. Regarding boundary conditions, all translational degrees of freedom at the base plate’s reference point were restrained. Axial loading was applied by incrementally displacing the loading reference point, allowing for realistic simulation of load transfer into the URM wall. The complete set of numerical representations appears in Fig. 20.

Fig. 20.

The simulation for the tested walls. (a) O, (b) O*, (c) S, (d) O-WOSM, (e) O-DOSM, (f) O-DDSM, (g) O-WDSM, (h) O-PSM, (i) O-FSM, (j) O-ODSM, (k) O-OCSM.

Materials

Masonry wall

The compressive behavior of masonry, including its nonlinear characteristics, is modeled using the Drucker–Prager plasticity approach. This model captures material hardening and softening under compression, enabling simulation of failure modes. The Drucker–Prager model, first introduced by Drucker and Prager⁶³, generalizes the Mohr–Coulomb failure criterion for use with frictional materials like soils and rocks. Lubarda et al⁶⁴. later extended the model to capture yield behavior under hydrostatic compressive stress. In this study, a linear yield surface within the meridional (p–t) plane is applied, as shown in Fig. 21. The surface evolves with nonlinear deformation and is defined based on the masonry’s uniaxial compressive strength σ_c. Essential input parameters include the flow stress ratio R, dilation angle ω, and friction angle β, with the linear yield surface expressed as given in⁶⁵.

Fig. 21.

Linear yield surface of the DP model⁶⁵.

2

where

3

the hydrostatic pressure stress, p, is given by:

4

and the von Mises equivalent stress, q, is given by:

5

6

7

8

To capture the compressive hardening and softening behavior of masonry, the Drucker–Prager plasticity model was defined using compressive yield stress versus absolute plastic strain data, derived from expanded masonry units. These parameters were incorporated into the FE models to represent the compressive yield surface.

Normal concrete and steel bars

In this study, normal concrete was modeled in ABAQUS using the Concrete Damaged Plasticity (CDP) model, following the recommendations and parameter ranges reported in well-established previous studies to ensure realistic simulation of nonlinear behavior. The CDP parameters adopted for concrete included a dilation angle of 36°, eccentricity of 0.10, a ratio of biaxial to uniaxial compressive strength (fb₀/fc₀) of 1.16, a shape factor (Kc) of 0.667, and a viscosity parameter set to 0.0005 to aid numerical convergence, as recommended^66–70. The uniaxial compressive and tensile stress–strain relationships were defined based on the experimentally obtained material properties, with damage variables introduced to capture stiffness degradation under cracking and crushing. For the strengthening reinforcement steel, an elastic–plastic constitutive model with isotropic hardening was employed, assuming perfect bond between steel and concrete. The steel behavior was defined using a linear elastic response up to the yield stress, followed by a plastic branch based on the measured yield and ultimate strengths, with a Young’s modulus of 200 GPa and a Poisson’s ratio of 0.30, which are widely accepted values in the literature^71–73. This modeling strategy has been extensively validated in prior numerical investigations and was therefore considered appropriate for accurately reproducing the structural response of the strengthened reinforced concrete elements.

Computational results

The numerical results obtained from the ABAQUS simulations exhibited a strong agreement with the experimental findings, indicating that the developed finite element models were capable of accurately reproducing the actual structural behavior of the tested specimens. A detailed comparison of the failure modes revealed that the numerical models successfully captured the initiation and propagation of cracks, as well as the final collapse mechanisms observed during the laboratory tests. This close similarity in damage patterns and failure configurations between the numerical and experimental specimens is clearly illustrated in Figs. 22 and 23, where the predicted crack distributions and crushing zones correspond well with the experimentally observed damage. In addition to the qualitative comparison of failure modes, the numerical load–displacement curves showed a high degree of consistency with the experimental responses, particularly in terms of initial stiffness, load-carrying capacity, and post-peak softening behavior. Minor discrepancies observed at certain loading stages can be attributed to inherent material variability and experimental uncertainties, which are commonly reported in similar studies. To further quantify the level of agreement, the key performance indicators, including ultimate load and corresponding displacement, were extracted from both the experimental tests and numerical simulations and systematically compared in Table 4. The results presented in this table demonstrate that the numerical predictions closely matched the experimental values, confirming the robustness and accuracy of the adopted modeling assumptions and material constitutive laws. Overall, the strong correlation between numerical and experimental results validates the effectiveness of the ABAQUS modeling framework in simulating the structural response, crack evolution, and failure behavior of the investigated strengthened reinforced concrete elements.

Fig. 22.

Experimental and Numerical load-vertical displacement relationships for all tested walls: (a) G1, (b) G2, (c) G3, (d) G4, and (e) G5.

Fig. 23.

The numerical models of all tested walls. (a) O, (b) O*, (c) S, (d) O-WOSM, (e) O-DOSM, (f) O-DDSM, (g) O-WDSM, (h) O-PSM, (i) O-FSM, (j) O-ODSM, (k) O-OCSM.

Table 4.

Numerical and experimental results.

Specimen ID	Pcr (kN)			Δcr (mm)			Pu (kN)			ΔPu (mm)
	EXP.	FE	EXP/FE	EXP.	FE	EXP/FE	EXP	FE	EXP/FE	EXP	FE	EXP/FE
O*	15.21	16.32	0.93	1.24	1.28	0.97	22.34	24.26	0.92	2.18	2.26	0.96
O	19.64	20.11	0.98	0.95	1.02	0.93	32.23	34.46	0.94	1.98	2.18	0.91
S	34.98	36.25	0.96	1.02	1.09	0.94	62.69	66.13	0.95	2.93	3.16	0.93
O-DOSM	18.28	19.36	0.94	0.61	0.68	0.90	34.84	36.45	0.96	2.28	2.58	0.88
O-WOSM	20.05	21.01	0.95	0.47	0.52	0.90	36.85	39.64	0.93	2.54	2.69	0.94
O-DDSM	19.34	20.32	0.95	0.73	0.78	0.94	35.27	38.56	0.91	2.54	2.79	0.91
O-WDSM	19.78	20.58	0.96	0.49	0.53	0.92	37.63	40.31	0.93	2.32	2.72	0.85
O-PSM	20.07	21.85	0.92	0.72	0.75	0.96	39.13	41.76	0.94	2.92	3.11	0.94
O-FSM	25.23	26.22	0.96	0.81	0.85	0.95	41.37	43.36	0.95	3.19	3.09	1.03
O-OCSM	18.16	19.35	0.94	0.71	0.77	0.92	35.85	38.21	0.94	2.62	2.78	0.94
O-ODSM	19.16	20.18	0.95	0.52	0.53	0.98	38.34	41.26	0.93	2.54	2.82	0.90
Avg			0.95			0.94			0.94			0.93
SD			0.01645508			0.0261575			0.0128366			0.046757
COV			0.00164550			0.0026157			0.0012836			0.004676

EX: Experimental; FE: Finite Element Model; Avg: Average; SD: Standard deviation; CoV: Coefficient of variation.

Parameteric study

Using the validated FE model, a parametric study was carried out to investigate the effects of increasing the WSM reinforcement ratio, opening area, and wall aspect ratio on the ultimate load capacity of wall O-FSM.

Effect of WSM reinforcement ratio

The effect of increasing the WSM reinforcement ratio (λ) on the ultimate load capacity of wall O-FSM was investigated. This wall was strengthened with full WSM coverage around the opening. The parameter λ is defined as the average mesh thickness relative to the masonry wall thickness. The study evaluated λ values of 0%, 0.02%, 0.04%, 0.06%, 0.08%, 0.10%, and 0.12%. Each configuration was analyzed to determine the most effective ratio for enhancing shear capacity.

The results highlight the effectiveness of increasing the WSM reinforcement ratio in enhancing the shear strength of URM walls. The linear improvement in capacity up to λ = 0.08% suggests efficient utilization of the mesh within this range. The plateau beyond λ = 0.08% indicates a threshold, beyond which additional reinforcement offers diminishing returns. This behaviour may be attributed to the mesh reaching its full contribution to stress redistribution. Identifying λ = 0.08% as the optimal value is crucial for balancing performance and material economy in retrofitting applications.

Among the strengthening schemes investigated in this study, the welded steel mesh configuration with full surface coverage and a reinforcement ratio of λ = 0.08% exhibited the highest improvement in in-plane shear capacity, stiffness, and energy absorption relative to the reference unreinforced wall. It is emphasized that this configuration represents the best performance within the range of configurations, wall geometry, opening size, and loading conditions examined in the present experimental program, rather than a universally optimal solution. The observed performance trends highlight the potential effectiveness of increased mesh coverage and reinforcement ratio for URM walls with openings; however, further experimental investigations considering multiple specimens, different wall geometries, opening configurations, and reinforcement ratios are required to generalize these findings and establish broader design recommendations.

Effect of opening area

The effect of increasing the opening area percentage (χ) on the ultimate load capacity of wall O-FSM was investigated. This wall was strengthened with full WSM coverage. The parameter χ is defined as the ratio of the opening area to the total URM wall area. The study evaluated χ values of 0%, 5%, 10%, 20%, and 30%. The aspect ratio was kept constant at r = 1.00. Each configuration was analyzed in terms of its ultimate shear capacity.

The results demonstrate a clear inverse relationship between opening area percentage (χ) and the ultimate shear capacity of the URM wall, as shown in Fig. 24. As χ increased, the structural integrity weakened significantly. This is likely due to the increased disruption of load paths and the reduction in effective wall area resisting shear. The sharp 83% decrease in capacity at χ = 30% highlights the critical impact of large openings, even when full WSM coverage is provided. These findings emphasize the need to limit opening sizes in URM walls or adopt more robust strengthening methods when large openings are unavoidable.

Fig. 24.

The effect of increasing the opening area on the ultimate load of wall O-FSM (aspect ratio = 1).

Conclusion

This study presented an integrated experimental and numerical investigation on the in-plane shear behavior of unreinforced masonry walls with openings strengthened using welded steel mesh. A series of quarter-scale masonry wall specimens, representing the critical portion of walls containing openings, were tested under diagonal compression loading. Several welded steel mesh configurations were examined to assess their influence on cracking behavior, shear strength, stiffness, energy absorption, and failure mechanisms. A finite element model was developed and validated against experimental results to support interpretation and enable further parametric assessment. Based on the findings of this study, the following conclusions can be drawn:

1. Welded steel mesh strengthening significantly improved the in-plane shear performance of URM walls with openings, leading to noticeable increases in cracking load, ultimate shear capacity, stiffness, and post-cracking deformation capacity compared to the unstrengthened reference specimen.

2. The effectiveness of the strengthening system was strongly dependent on mesh configuration and orientation. Among the investigated cases, diagonal and full mesh coverage configurations exhibited the best performance within the tested parameters, owing to their favorable alignment with principal tensile stress paths associated with diagonal shear cracking.

3. The full-welded steel mesh coverage configuration achieved the greatest improvement among the tested cases, increasing the ultimate load capacity by 28%, elastic stiffness by 106%, and energy absorption by 57% compared to the unstrengthened wall, due to more effective stress redistribution and crack control around the opening.

4. Diagonal mesh arrangements showed superior performance compared to orthogonal configurations, as their orientation is better aligned with diagonal shear crack propagation, leading to more efficient crack bridging and tensile force mobilization.

5. The presence of openings resulted in a reduction of approximately 49% in the shear capacity of URM walls compared to the solid specimen, highlighting the increased vulnerability of masonry walls with openings under in-plane and seismic loading.

6. Strengthened specimens demonstrated improved crack control and more distributed cracking patterns, particularly around opening corners, indicating enhanced stress redistribution and confinement provided by the welded steel mesh–mortar composite action.

7. The experimental results, derived from single specimens per configuration, consistently revealed clear comparative performance trends among different WSM layouts; however, these results should be interpreted as indicative trends rather than statistically robust rankings.

8. The developed finite element model showed good agreement with experimental load–displacement responses, cracking mechanisms, and failure modes, confirming its reliability for qualitative mechanism validation and subsequent parametric studies, despite the use of idealized bond assumptions and literature-calibrated material parameters.

Limitations and recommendations

Although the diagonal compression test in accordance with ASTM E519 is a well-established method for evaluating the in-plane shear behavior of masonry panels, it represents a simplified and monotonic loading condition. For masonry walls with openings, the test does not fully reproduce the complex stress states, boundary conditions, and load redistribution mechanisms that occur in real structures under seismic excitation. In particular, the absence of cyclic loading, load reversals, and interaction with adjacent structural components limits the direct applicability of the measured shear strength and cracking load as predictors of seismic performance. Accordingly, the results presented in this study should be interpreted as comparative indicators of in-plane stiffness, strength, crack control, and failure mechanisms among different welded steel mesh strengthening configurations, rather than as direct measures of seismic capacity. Nevertheless, the diagonal compression test provides a consistent and rational basis for evaluating the relative effectiveness of strengthening techniques and for identifying performance trends relevant to seismic retrofitting applications.

Author contributions

Mohamed Ghalla (M.G.) designed the study, analyzed the data, and wrote the manuscript. Rabeea W. Bazuhair (R.W.B.) and Ehab A. Mlybari (E.A.M.) conducted the experiments and contributed to data interpretation. Arsalan Mahmoodzadeh (A.M.) and Galal Elsamak (G.E.) contributed to the statistical analysis and reviewed the manuscript. Saad A. Yehia (S.A.Y.) supervised the project, provided critical revisions, and reviewed the final manuscript. All authors reviewed and approved the manuscript.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.