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Recent earthquakes have highlighted the vulnerability of unreinforced masonry (URM) walls particularly those constructed with stone to lateral loads, underscoring the need for effective strengthening against shear failure. In this context, fiber-reinforced polymer (FRP) and carbon fiber mesh (CFM) have been explored as innovative alternatives to traditional reinforcement techniques. This study investigated unreinforced stone masonry walls, a common type of URM, strengthened using FRP and CFM materials in different configurations, focusing on the walls’ in-plane shear behavior under diagonal compression testing. A reference specimen, labeled URM-1, was constructed without reinforcement. FRP materials were applied to two specimens either horizontally or diagonally on both wall surfaces. Similarly, two specimens were strengthened on both surfaces using CFM, applied with either epoxy or repair mortar. Based on experimental and analytical results, the URM-5 specimen (CFM with epoxy) was identified as the most effective strengthening method. It significantly increased maximum load capacity, shear stress, ductility, and elastic stiffness. Additionally, the URM-5 specimen reduced wall fragility and maintained structural integrity during fracture. Visit for more information CFM Exam Questions online

Masonry structures have been known and built throughout human history and are still used today. Magnificent examples of historical masonry structures—built thousands of years ago—can still be seen intact in many places around the world. Although masonry structures have certain advantages, they are generally not considered earthquake-resistant due to their considerable weight and limited resistance to dynamic and horizontal loads such as earthquakes1,2,3,4,5,6.

In order for masonry structures to withstand seismic effects, their behavior during earthquakes must be understood, and their resistance must be improved7. –8. Historic stone masonry walls are particularly vulnerable to earthquake forces due to their low tensile strength, limited flexibility, and brittle nature. Common forms of damage include diagonal cracking, slippage of mortar joints, and out-of-plane collapse9. For these reasons, such walls are among the most vulnerable and high-risk elements in masonry structures during earthquakes.

Under seismic loading, in-plane shear damage in masonry walls is generally more critical than out-of-plane collapse, as it directly reduces the wall’s lateral load-carrying capacity. While out-of-plane failures often result from inadequate anchorage, in-plane shear damage tends to govern the overall structural stability of the walls10. Therefore, strengthening efforts aimed at improving seismic performance should primarily focus on mitigating in-plane damage.

Fiber-reinforced polymers (FRP), fabric-reinforced cementitious matrices (FRCM), and carbon fiber mesh (CFM) are commonly used to reinforce masonry walls. These materials increase strength and ductility while maintaining compatibility with the existing structure11. In the repair and strengthening of masonry structures, composites such as FRP and FRCM/CFM have been shown to effectively improve the in-plane behavior of masonry walls by increasing both strength and displacement capacity8.

FRP, in particular, has been shown to successfully enhance the strength of masonry walls due to its high tensile strength, light weight, ease of application, and resistance to corrosion12,13,14. Masonry structures are highly susceptible to both in-plane and out-of-plane collapse caused by lateral loads15,16,17,18. In previous experimental and numerical studies on the in-plane shear behavior of masonry walls, it was found that FRP reinforcement increased shear strength, ultimate load, stiffness, displacement, and ductility19,20,21,22,23,24,25,26,27,28,29. Numerous studies have confirmed that FRP significantly increases the load-carrying capacity of masonry walls27,28,29,30,31,32,33,34,35,36.

Although numerous studies have investigated the shear behavior of masonry walls, research focusing specifically on stone masonry and the use of historically compatible materials remains limited. This study introduces the novel application of traditional Khorasan mortar for strengthening stone masonry walls, an approach that has not been extensively explored in the literature. The in-plane shear behavior of these walls was investigated through a combination of experimental testing and numerical analysis. Additionally, the study offers a systematic comparison of different reinforcement techniques, providing valuable insights for the repair and seismic retrofitting of stone masonry structures, particularly in earthquake-prone regions. These contributions address a significant gap in the existing knowledge and offer practical guidance for the preservation and strengthening of historic masonry buildings.

This study uniquely compares CFM applied with either epoxy resin or lime-based mortar, highlighting the trade-off between mechanical performance and material compatibility. While epoxy provides higher strength, lime mortar offers greater compatibility with historic masonry, aligning with recent findings in conservation research. This dual assessment contributes to the development of effective and sustainable strengthening methods for heritage stone structures.

High-strength andesite stone was used as the masonry unit, and Khorasan mortar served as the binding material in this study. The cut stones used in constructing the masonry walls measured 200 × 100 × 100 mm3 and 100 × 100 × 100 mm3, with an average joint thickness of 10 mm. The Khorasan mortar, applied between the stones, consisted of 40% lime, 20% sand, and 40% stone dust by weight. This composition makes the Khorasan mortar more durable and allows it to harden under water30. The masonry wall was built using cut stones in a staggered weave, with overall dimensions of approximately 540 × 540 × 100 mm3. After construction, the wall was cured for 28 days to allow it to gain strength.

Two different composite materials, FRP and CFM, were used in this study. The FRP consisted of high-strength, unidirectional carbon fiber fabric embedded in a two-component epoxy matrix. This configuration offers ease of application for reinforcements against bending and shear. The material exhibits high fatigue and a very low creep value. The FRP used in this study had a thickness of 0.166 mm, an ultimate tensile strength of 4950 MPa, and an elastic modulus of 227 GPa37. The CFM used in this study was a bi-directional carbon fiber mesh designed for structural reinforcement. It can be applied using either epoxy-based adhesives or cement/lime-based structural repair mortars. CFM increases the strength and ductility of masonry walls. The material had a thickness of 0.048 mm, an ultimate tensile strength of 2500 MPa, and an elastic modulus of 230 GPa37.

A diagonal shear test was conducted on the wall specimens using the setup illustrated in Fig. 1, following the ASTM E519/E519M-15 standard38,39. The test equipment included a hydraulic jack, load cell, displacement transducers, and data acquisition systems. A load-controlled monotonic shear loading procedure was applied to the masonry specimens. The load was applied using a hydraulic jack with a capacity of 500 kN. It was transferred to the specimens via a steel shoe positioned at the upper corner of the wall, and subsequently distributed to vertical steel shoes below, in accordance with ASTM E519/E519M-1538,39. The loading shoes featured a contact length of 152 mm along the specimen surface40.

Two linear variable differential transformers (LVDTs) were installed to measure horizontal and vertical displacements of the specimens (see Fig. 1). The vertical displacement transducer, LVDT-1, was positioned directly beneath the base of the wall specimen, aligned perpendicular to the vertical loading direction (y-axis) within the experimental coordinate system. This placement allowed precise measurement of vertical elongation or shortening during loading. The horizontal displacement transducer, LVDT-2, was installed on the lateral side of the specimen, aligned parallel to the horizontal axis (x-axis) to capture lateral displacements. The lengthening and shortening of the masonry wall were measured with the LVDT transducers. LVDTs generate a tension from the back-and-forth movement of the central shaft, allowing readings with a precision of 0.01 mm.

Experimental and numerical studies were conducted to examine the in-plane shear capacity of unreinforced walls with different reinforcement materials and configurations. Five wall specimens were subjected to diagonal shear tests under fixed-axis conditions. To evaluate the shear behavior under in-plane loading, the walls were constructed with a height-to-length ratio of 1:1 (540 mm x 540 mm).

This study investigated the repair and strengthening of masonry walls using different fiber polymer materials (FRP and CFM), shapes, and binders (Table 1). The unreinforced reference specimen was designated URM-1. In URM-2, 100 mm-wide FRP material with epoxy adhesive was applied to the bottom and top rows on both the front and back surfaces of the wall. For URM-3, 100 mm-wide FRP was applied crosswise to both wall surfaces using epoxy. The URM-4 specimen was reinforced with CFM applied on both surfaces using natural lime repair mortar. Finally, URM-5 was strengthened with CFM using epoxy adhesive on both the front and back surfaces of the wall.

In this study, the masonry wall specimens were constructed using andesite stone units and traditional Khorasan mortar to simulate typical unreinforced masonry walls. The specimen dimensions were standardized at 540 × 540 × 100 mm3 to ensure consistency throughout the experimental program.

Among the specimens prepared, the URM-1 stone masonry wall was designated as the reference specimen. For URM-2 and URM-3, a two-component epoxy adhesive was carefully mixed and uniformly applied to the cleaned masonry surfaces using a roller. Next, 100 mm-wide FRP strips were positioned and mechanically pressed onto the epoxy-coated surfaces with a roller to ensure full contact and effective bonding.

In URM-4, a natural lime-based repair mortar was first applied to the prepared masonry surface to promote adequate bonding. CFM reinforcement was then placed, followed by an additional layer of repair mortar to fully encapsulate and secure the mesh. For URM-5, a two-component epoxy resin was uniformly applied to the cleaned wall surface using a roller. The CFM was then positioned on the epoxy-coated surface and mechanically pressed with a roller to ensure optimal adhesion. All reinforcements were applied to both the front and back surfaces of the wall specimens. The procedures for specimen preparation are illustrated in detail in Fig. 2.

The shear stress of the wall was calculated using Eqs. 1 and 2 from the ASTM E519/E519M-1538,39 standard for diagonal shear testing of masonry walls. In Eq. 1, \(\:{\uptau\:}\) is the shear stress (MPa), \(\:{P}_{\:max}\) is the applied ultimate load (kN), and \(\:{A}_{n\:\:}\)is the net cross-sectional area of the wall (mm2). In Eq. 2, \(\:L\) is the specimen height (mm), H is the specimen width (mm), and t is the specimen thickness (mm).

The structural ductility factor (µ) is defined as the ratio of the displacement of the structure to the displacement at yield. Determining the structural behavior of masonry walls is challenging due to their highly nonlinear response. To address this, Tomzazevic40 introduced a bilinear approximation of the force–displacement curve to provide a more realistic calculation of the structural ductility factor for masonry walls (Fig. 3)6,41.

In the graph above, the first region represents the elastic behavior. The ultimate load, Pcr, is defined as 70% of the maximum load and calculated as Pcr = 0.7 × Pmax. The displacement corresponding to this ultimate load, dcr, is taken as the elastic displacement value. In the second region, the displacement corresponding to the maximum load Pmax is denoted as dPmax.

The yield load, Pu, is calculated as 80% of the maximum load, defined by Pu = 0.8 × Pmax, representing the point at which the load drops to 80% of its peak value. The displacement corresponding to the yield load is denoted as du39,43,44. Structural ductility is then calculated using the equation \(\:{\mu\:=d}_{u}\:/{\:d}_{cr}\).

For the elastic region of the idealized bilinear force–displacement curve, the stiffness is defined as the effective stiffness at the point where the masonry wall first cracks, denoted as Ke40,41,42. The effective stiffness is calculated \(\:{K}_{e}=\left({P}_{c}\:/{\:d}_{cr}\right)\). The idealized elastic limit displacement, de, is then evaluated as\(\:{\:d}_{e}=\left({P}_{u}\:/{K}_{e}\right)\:\)42.

A diagonal shear test was conducted on the wall specimens. The results are summarized in Table 2; Fig. 3. The parameters listed in Table 2—Pmax, τ, dcr, du, µ, Ke, and de—represent the maximum load carried by the specimens, maximum shear stress, elastic displacement, displacement at yield, ductility factor, effective stiffness, and idealized elastic limit, respectively.

The unreinforced masonry wall specimen was labeled URM-1. According to the diagonal compression test results, URM-1 sustained a maximum load of 20.82 kN, corresponding to a maximum shear stress of 0.27 MPa. At peak load, the wall exhibited a vertical displacement of 6.60 mm and a horizontal displacement of 1.51 mm. As shown in Fig. 4, the load–displacement curve increased linearly up to 20.82 kN, after which it dropped sharply, indicating sudden failure. No visible cracks were observed before reaching the ultimate load. However, upon reaching peak load, an instantaneous brittle failure occurred. Post-test inspection revealed no cracking in the masonry units themselves, but separation was observed along the horizontal and vertical mortar joints, particularly along the vertical axis of the wall.

In the URM-2 specimen, FRP reinforcement was applied using epoxy resin in horizontal strips on both the front and back surfaces of the wall. The test results indicated a maximum load capacity of 25.09 kN and a corresponding maximum shear stress of 0.33 MPa. At peak load, the vertical displacement was 5.44 mm and the horizontal displacement 1.83 mm. According to the load–displacement graph (Fig. 4), the load increased linearly up to 23.76 kN and 1.03 mm displacement, transitioning into the plastic phase thereafter. The load then increased by an additional 1.33 kN, reaching a final displacement of 5.46 mm. Despite the FRP reinforcement, the URM-2 specimen exhibited brittle behavior, with a calculated ductility factor of 1.0. Post-test inspection revealed shear cracks in the unreinforced central region of the wall, primarily along the horizontal mortar joints. Notably, no damage was observed in the FRP-strengthened areas, and no cracking occurred in the masonry units themselves.

In the URM-3 specimen, diagonal FRP reinforcement was applied to both the front and back surfaces of the masonry wall using epoxy resin (Table 1). The specimen exhibited a maximum shear stress of 0.53 MPa. The load–displacement curve showed a linear increase, with the plastic phase beginning at 37.31 kN and a displacement of 13.01 mm. The ultimate load capacity was 40.73 kN, with a vertical displacement of 13.93 mm and a horizontal displacement of 1.09 mm. URM-3 displayed brittle behavior, with a calculated ductility factor of 1.03. Post-test inspection revealed that the horizontal FRP strips detached near the wall edges, followed by detachment of the vertical strips. Tearing of the FRP was observed near the bottom center and right side of the wall. The specimen exhibited both vertical and horizontal separations, along with partial collapse of the lower wall section. Small cracks were also observed in the masonry units.

The URM-4 specimen was reinforced on both the front and back surfaces using CFM embedded in repair mortar. The test results showed a maximum load capacity of 35.25 kN and a maximum shear stress of 0.46 MPa. The load–displacement curve exhibited a first peak at 23.91 kN, followed by a drop to 8.74 kN. As diagonal loading continued, the load rose again, reaching a second peak of 35.25 kN, at which point the specimen underwent plastic deformation and reached its displacement capacity. At maximum load, the vertical and horizontal displacements were 11.85 mm and 27.24 mm, respectively. The specimen exhibited brittle behavior, with a calculated ductility factor of 1.06. Cracking initiated at the lower corner of the wall and propagated diagonally toward the upper right. Initial cracks were capillary in nature and widened with increasing shear load, forming symmetrically on both the front and back surfaces. Significant openings developed in the lower and right portions of the wall, leading to spalling of the repair mortar. Shear cracks were accompanied by visible deformation in the CFM reinforcement, while no cracking was observed in the masonry units themselves.

The URM-5 specimen was reinforced on both the front and back surfaces using CFM embedded in an epoxy-based repair material. The test results indicated a maximum load capacity of 114.24 kN and a corresponding maximum shear stress of 1.50 MPa. The load–displacement curve showed an initial increase to 75.89 kN, marking the first peak and the onset of plastic behavior, followed by a sudden drop to 54.02 kN. The load then rose again, reaching a second peak at 112.96 kN. The vertical displacement at maximum load was 4.86 mm. Compared to the other specimens, URM-5 exhibited more ductile behavior, with a calculated ductility factor of 1.38. Post-text inspection revealed an opening along the horizontal mortar joint in the bottom row. The CFM repair material detached first, followed by separation of the mortar joint, leading to shear cracks that formed symmetrically on both the front and back surfaces. No cracks were observed in the masonry units. These results highlight the significant influence of mortar joints on the shear behavior of masonry walls. Since joints are the most affected by manual workmanship, overall wall performance depends not only on the quality of the masonry units and mortar, but also on construction and curing practices. As a result, the bond strength at the block–mortar interface often emerges as the weakest link governing shear strength.

The interaction between the epoxy and CFM in the URM-5 specimen created a highly effective composite reinforcement system that enhanced load transfer, improved crack resistance, and delivered superior mechanical performance compared to other methods, which explains the significantly improved results observed in the tests.

This study has several limitations. The use of a single specimen for each strengthening method restricts the generalizability of the results. Additionally, the experiments were conducted under monotonic loading conditions, without accounting for dynamic or cyclic loads that more accurately simulate real earthquake conditions. Furthermore, due to idealizations in the numerical modeling, the heterogeneous nature of the materials could not be fully represented. Future research should involve testing a larger number of specimens, incorporating different loading scenarios, and employing more advanced numerical modeling techniques to improve the validity and applicability of the findings. Load–displacement graphs in both the horizontal and vertical directions, based on the experiment results, are presented in Fig. 4. Figure 5 demonstrates the effect of repair and reinforcement materials on the shear strength, ductility, elastic stiffness, and elastic displacement of the masonry wall.

The nonlinear behavior of stone masonry walls was simulated using a detailed micromodeling approach that incorporated the mechanical properties of masonry units, mortar, and reinforcement materials. A three-dimensional finite element model was developed using LUSAS software45, employing 10-node tetrahedral elements with three degrees of freedom per node to model the masonry units, mortar, and reinforcement layers. To capture the nonlinear behavior of the mortar and masonry units, the multi-crack concrete model originally proposed by Jefferson46 and available in LUSAS was utilized. For the repair and reinforcement materials, the Von Mises failure criterion was applied.

Material properties used in the numerical model were derived from experimental data11. The compressive strengths of the masonry units and Khorasan mortar were 18.59 MPa and 2.46 MPa, respectively, while their tensile strengths were 5.84 MPa and 0.55 MPa. The assigned elastic moduli were 1850 MPa for the masonry units, 4500 MPa for the mortar, 227,000 MPa for FRP, and 230,000 MPa for CFM. Poisson’s ratios were taken as 0.2 for the masonry units and mortar, and 0.3 for both FRP and CFM reinforcement materials.

In the numerical model, boundary conditions were applied by constraining the outer edges of the masonry wall in the vertical (y) direction, consistent with the experimental setup. The load was applied at the top of the wall, replicating the loading conditions used in the physical tests. To ensure numerical accuracy and convergence, a finite element mesh size of approximately 6 mm was adopted, which provided stable deformation results.

Failure assessment was based on the maximum plastic strain observed under increasing load levels. Numerical convergence was achieved by limiting the number of iterations to 10 per load step, ensuring model stability and reliable results. The close agreement between experimental and numerical outcomes confirms the adequacy of the convergence strategy and the predictive capability of the model. Figure 6 presents the experimental specimens alongside the numerical FEM analysis results. Figure 7 compares the experimental and numerical data.

The difference in initial stiffness between the numerical and experimental load–displacement curves arises from the heterogeneous nature of masonry and the inherent simplifications of the numerical model. Experimental results capture local phenomena such as microcracking and imperfect bonding, which are not fully represented in the idealized numerical model. Additionally, variations in boundary conditions contribute to this discrepancy. This behavior aligns with observations reported in prior masonry modeling studies (Fig. 7).

The in-plane shear behavior of unreinforced stone masonry walls was investigated using different carbon fiber materials in various configurations under diagonal compression testing. A total of five specimens were produced, including one unreinforced reference specimen (URM1). FRP material was applied horizontally (URM-2) and diagonally (URM-3) on both sides of the wall, while CFM material was applied to the entire surface on both sides using repair mortar (URM-4) and epoxy (URM-5). The key findings from the experimental and numerical results are summarized below.

In this study, the URM-5 specimen (CFM with epoxy) significantly improved the maximum load capacity, shear stress, ductility, and elastic stiffness. In addition, URM-5 reduced wall fragility and maintained structural integrity during fracture. URM-2 (horizontal FRP) was found to be an unsuitable system for the repair and strengthening of masonry walls.

The datasets generated and/or analysed during the current study are not publicly available due to legal and institutional restrictions associated with the protection of cultural heritage structures. However, the data are available from the corresponding author on reasonable request and subject to approval by the relevant heritage authorities.

T.C. Methodology, Investigation, Conceptualization, Supervision, Writing – original draft, Visualization, Writing – review & editing, Visualization.

The authors declare no competing interests.