Design approach of shear strengthened masonry: welded wire meshes, Reticulatus and cementitious plastering methods

Masonry often requires strengthening to withstand against extreme actions such as earthquakes, cyclones and flooding. Recently, new methods have been developed to strengthen masonry, such as fabric reinforced cementitious matrixes and fibre reinforced polymers. However, other strengthening systems such as welded wire meshing (WWM), reticulatus and plastering with cementitious matrixes/mortar (CP) have been also practiced to reinforce masonry, conversely no systematic design guidelines are available for these methods. In this study, an attempt has been made to establish rational design approaches to predict the shear resistance of WWM, reticulatus and CP methods. Three sets of experimental database have been developed for design verification. The effectiveness of these strengthening methods was appraised by comparing their structural performances. The available formulations to predict the shear resistance of unreinforced masonry (URM) and CP strengthened masonry were assessed against the established database, and suitable modifications were proposed to effectively account the contribution of cementitious matrix. A unified approach to estimate the shear strength was proposed based on the contribution of URM, CP and reinforcements. The design approach is shown to conservatively predict the shear strength of strengthened masonry.


Introduction
Masonry constitutes a major portion of the world building stock and heritage buildings are often built with different masonry assemblages. Despite masonry being preferred in construction, it exhibits low tensile strength and deformation capacity. This makes masonry vulnerable to high intensity actions such as earthquakes, cyclones and flooding. Structural analysis and vulnerability assessment are important to study the performances of masonry structures and to define appropriate retrofitting interventions (Valluzzi et al 2005;Ramos et al. 2010;Roca et al. 2010;Thamboo and Dhanasekar 2020).
Depending on the masonry quality and building configuration, walls in the upper floors are often susceptible to fail under out-of-plane mechanism, while those at lower levels often fail in shear. Various strengthening solutions have been developed and assessed in the past to strengthen masonry against in-plane and out-of-plane loading. These included the application of Fibre reinforced polymeric (FRP) sheets and bars (Prota et al. 2008;Martinelli et al. 2016;Monaco et al. 2017), Fabric reinforced cementitious matrixes (FRCM) (Dong et al. 2021;Castori et al. 2021), Composite Reinforced Mortar (CRM) (Faella et al. 1 3 for irregular stone masonry (Borri et al. 2011a, b;Corradi et al. 2016), when the fair-face aspect needs to be preserved. In addition, there are applications of using only high strength cementitious mortars/plasters/matrixes (CP) on masonry surface to strengthen against shear effects Najafgholipour et al 2018;Longo et al. 2021).
In this paper, an attempt was made to analyse the effectiveness of three different strengthening methods. An experimental database has been established using available literature studies. The experimental database consists of three strengthening solutions, namely (1) WWM (2) Reticulatus and (3) CP. Thereafter, the applicability of the available provisions to design such strengthening solutions under in-plane shear loading was assessed using the experimental database and a unified design approach to predict the shear resistance of these strengthened masonry assemblages was calibrated and proposed in Sect. 3. Finally, key conclusions are outlined in Sect. 4.

Experimental database
In order to study the effectiveness of above mentioned (WWM, Reticulatus and CP) strengthening methods, a database has been developed from the experimental campaigns reported in the scientific literature. These strengthening systems are shown in Fig. 1. The experimental results reported in journals articles, conference papers, master theses and scientific reports were retrieved to establish the database.
In total, 75, 18, and 48 shear tests were considered for WWM, Reticulatus and CP methods, respectively. The database established for these three retrofitting methods are further classified according to the type of masonry, strengthening types/methods and their load resisting mechanisms. It has to be mentioned, although a quite large amount of data was found, in-depth quantitative comparisons among the key parameters were not possible, due to the intrinsic limitations for the large number of variables. The following appraisal was mainly carried out to compare and qualitatively evaluate the influence of masonry typologies, strengthening methods on the overall shear performance of strengthened masonry subject to diagonal compression test.  (Sandoval et al. 2021), Reticulatus (Corradi et al. 2017) and CP (Corradi and Borri 2018) strengthened masonry panels 1 3

WWM strengthening
The dataset obtained of WWM strengthened masonry panels includes 75 test results. General purpose cement mortars, ferrocement, fine graded granular concrete and lime based mortars were used as matrixes for the WWM strengthening. It is worth noting that there is a clear difference between the FRCM and WWM strengthening methods. FRCM consists in an initial application of a mortar coating and subsequently the composite mesh is installed. Finally, the wall is plastered again with the same mortar to cover up the mesh. The WWM application is normally started by connecting or anchoring the WWM to the masonry and subsequently plastered to required thickness to develop adequate bonding between the WWM and masonry substrate. Another difference is the reinforcement, where in FRCM is made of flexible bonded open fabrics (composite mesh), while in WWM system this is made of conventional welded open steel bars or wires. The load resisting and transferring mechanisms of these two systems are clearly different, therefore have to be treated separately. Banerjee et al. (2020a, b) investigated the influence of steel WWM strengthening for brickwork (f u = 2.0 MPa) and concrete block (f u = 15.0 MPa) masonry. Masonry made of clay bricks has shown relatively smaller gain in shear strength (1.4 to 3.2 times) than the concrete masonry (3.2 to 4.6 times). Shermi and Dubey (2018) examined the influence of WWM dimensions (using square grids with spacing of 25 mm, 38 mm, and 50 mm) and WWM tensile strengths (873 MPa, 936 MPa, and 1005 MPa) to the shear behavior of strengthened masonry. No specific studies were found on the influence of the matrix types (e.g. depending on the matrix mechanical properties) on the shear characteristics of strengthened masonry systems. However, it can be presumed, as observed in FRCM matrixes, that the use of matrices with higher mechanical properties would lead to an improved structural response of WWM reinforced masonry. Moreover, different types of anchorages are typically used in WWM applications, such as bolting and sealed with epoxy and cement bond anchorages of the wire ends (Cheng et al. 2020; Bustos-García et al 2019; Kadam et al. 2014). However, no systematic studies have been dedicated so far to investigate the influence of the anchoring methods to the overall shear strength characteristics of WWM strengthened masonry. In addition, despite of several experimental studies and applications in the past, no systematic design approach was found in the scientific literature to analytically determine the in-plane shear resistance of WWM strengthened masonry.

Reticulatus method
The Reticulatus method consists of inserting flexible metallic or composite fiber wires into the masonry mortar joints. The wires are normally connected across the thickness of the walls via transverse anchors at an interval that depending on masonry type. Mortar joints have to be recessed about 50-60 mm (depending on the thickness of bed joints) prior to inserting the transverse anchors and wires, and then repointed with compatible mortar after inserting the wires. This type of strengthening is preferred to preserve fair-faced masonry, especially for stone masonry. In total, eighteen data were gathered from the past studies reported from testing of 29 wall panels. Borri et al. (2014) have investigated the characteristics of Reticulatus strengthened stone and clay brick masonry. Increments in the shear resistance of strengthened masonry in the range of 1.15 to 1.5 times were observed from their testing. Similar test results were recorded in other experimental campaigns conducted by the same research group (Borri et al. 2011a(Borri et al. , 2011bCorradi et al. 2016). Despite this system is quite well established, no design guidelines are available to evaluate the shear resistance of Reticulatus strengthened masonry.

CP strengthening
The dataset of 48 CP strengthened masonry panels tested under diagonal compression were gathered for the analyses. Mainly, clay brick (42 data), stone (4 data) and concrete block (2 data) masonry assemblages were strengthened with CP. The mechanical characteristics of the matrix vary across the studies considered: matrices were mostly made of mortars with high tensile/adhesive properties such as engineered cementitious composites (ECC) and fibre reinforced mortars (e.g. Polypropylene and glass fibre). However, conventional Portland cement and lime-based mortars were also recorded (De Felice et al. 2014). Nonetheless, the CP strengthening is a rather simple method compared to other strengthening solutions, where a high strength/adhesive cementitious matrix is directly applied to the masonry surface to improve the tensile strength of masonry. Cheng et al. (2020) evaluated the performance of clay brick masonry strengthened with conventional cement mortar (compressive strength f mat = 11.8 MPa) and ECC (compressive strength = 32 MPa) plastering. The results revealed that the ECC application increased shear resistance in the range of 90-125%, where the conventional cement plastering increased the shear resistance only up to 50-100%. Quite similar findings were reported from the study conducted by Bustos-Garcıa et al. (2019) using conventional Portland cement mortar and glass fibre reinforced mortar. No specific studies were conducted to compare the performances between the different masonry types. The CP plastering was generally applied to the entire face of the panels, either on one or both sides. However, the single sided CP reinforcement is less effective compared to the double sided method (Shabdin et al. 2018;Del Zoppo et al 2020;Shabdin et al. 2021). Similar to WWM and Reticulatus methods, no design formulations exist to estimate the shear resistance of CP strengthened masonry.

Analytical prediction of shear resistance
Although the experimental assessment of the characteristics of strengthened masonry is very useful, the analytical approaches are critical to routinely design such retrofit interventions. It is worth noting that, well developed design guidelines for FRCM and FRP strengthened masonry (ACI 440.2R-17; ACI 549.4R-13 CNR-DT-200; CNR-DT-215) exist and these can represent an useful starting point to explore suitable design approaches for WWM, Reticulatus and CP methods. Particularly, the shear resistance of these strengthened masonry assemblages is the interest of this study. Although, masonry walls are not always subjected to pure-shear stress state, the design verification is conventionally carried out at component levels (i.e. different stress-states) according to the most probable failure scenarios and corresponding shear resistance. Therefore, a separate formulation to predict the shear resistance of masonry assemblage is necessary, as generally provided in the design standards (e.g. ACI 440.2R-17; ACI 549.4R-13 CNR-DT-200; CNR-DT-215).
The generalised analytical approach to predict the shear resistance (V s ) of strengthened masonry is given in Eq. (1), where, V URM and V RM are the contributions of masonry and strengthening system, respectively: This implies that the prediction of shear resistance of strengthened masonry relies on the shear resistance of URM and strengthening system. Several studies have been dedicated to assess the shear resistance of unreinforced masonry (URM), and this depends on the failure modes under in-plane action, such as sliding, shear friction, diagonal tension and toe crushing (Siano et al. 2019;Zahra et al. 2018). The formulations to predict the URM resistance against these possible failure modes are given in Table 1. The parameters associated with these formulations are explained in the remarks column. In order verify the applicability of the formulations outlined, their accuracy has to be assessed. In Sect. 3.1, the applicability of the given formulations to predict the URM shear resistance will be discussed and verified.

Prediction of shear resistance of URM
In order to validate the literature formulations, the established database was used to verify the applicability of these formulations to predict the shear resistance of the URM. The masonry constitutive and geometric properties acquired in the database from the relevant studies were used to compute the V URM values. The minimum of resistance value, out of four possible failure modes of URM masonry [i.e. minimum of V ss , V sf , V dt , and V tc (Table1)] is recommended to be considered. The computed shear resistance corresponds to those four failure modes for each data are provided in Appendix A to C for the three strengthening systems. It has to be mentioned that not all studies in the database have provided the complete masonry constitutive properties required to compute the shear resistance of URM. Therefore, in the absence of these data, certain assumptions had to be made to appropriately calculate corresponding resistance values. Table 2 provides the details of URM constitutive characteristics taken from the existing literature. The initial shear bond strength (τ 0 ) was taken from the values recommended in EN 1996-1-1 (2005). However, the characteristic shear bond strength values were converted to mean values, by considering COV (Coefficient of Variation) of 15% and a normal distribution of the data. It has to be noted that a range of values were used, and this depended on the mortar strength used in the masonry assemblages (i.e. in EN 1996-1-1, τ 0 is varied based on the mortar strength grade). For an example, for tuff block masonry, τ 0 was taken from Augenti and Parisi (2011). Moreover, the coefficient of shear friction (μ) was taken from several studies for different masonry typologies as given in Table 2. Most of these investigations have reported the masonry compressive strength (f m ). However, in the absence of this, the f m value was computed using the equation given in EN 1996-1-1 (2005) based on the normalised unit and mortar strengths gathered in the database (Zahra et al. 2021a, b). The tensile strength (f t ) of the masonry was estimated from the equation given in Silva et al. (2008). Consequently, the material constitutive parameters provided in Table 2 and the formulations outlined in Table 1 were used to predict the shear strength of the URM. Figure 2 shows the experimental and predicted shear strengths of URM. Since the database was purposely divided into three strengthening systems, the corresponding predictions of URM shear strengths are also separately computed. However, in Fig. 2d, all the URM data were grouped to show the overall comparison of URM shear strengths against the experimental values in the database. It can be noted that the minimum resistance values for the four possible failure modes are smaller compared to the corresponding experimental values, and the used provision seems to be conservative in estimating the shear strength of URM.
The derived statistical parameters are given in Table 3 for comparison purpose. The model error (ME) (i.e. experimental value divided by predicted strength value) was computed for each case to evaluate the accuracy of predictions. Although in some cases, the minimum ME values are close to 1, this happened only in four cases out of 127 data gathered. Given the different masonry typologies considered in the database, existing  Silva et al. (2008) formulations to evaluate the shear resistance of URM have shown to be quite conservative predictions.

Prediction of shear resistance of strengthened masonry
Although the strengthening systems considered are very different, all of them have shown to improve the masonry shear resistance. In the Reticulatus method, the additional shear resistance (V R ) is generated by the reinforcement embedded in the repointed mortar joints. It can be postulated that the contribution of the repointing mortar is negligible. In the CP system, the matrix contributes to the shear resistance (V M ) and no additional reinforcement It can noted that the shear resistance of the strengthening system depends on the shear resistance of individual contributions from matrix (V M ) and reinforcement (V R ). In the following sections, the methods to evaluate the contribution of matrix and reinforcement will be considered.

Contribution of matrix strength
Cementitious matrix is commonly used in FRCM, WWM and CP strengthening systems. Specifically, the CP system only use cementitious matrix to plaster on the masonry surface. Primarily, it is accepted that the matrix cracks and de-bonds, once its tensile resistance or interface shear bond resistance is attained under diagonal compression loading. Few different formulations have been used in the past to account the contribution of matrix in the diagonal shear resistance of masonry assemblages. Determining the direct tensile strength of the matrix is a quite difficult task, however, most of the experimental studies invariably report the compressive strength of matrix along with the diagonal compression testing data. Therefore, the matrix tensile strength has to be derived from the corresponding compressive strength values. The formulation given in EN 1992-1-1 (2004) to determine the direct tensile strength of concrete from the compressive strength was used in this study. This formulation (see Eq. (3)) is recommended for concrete strength grades less than 50 MPa, therefore it could be also applicable to most of the cementitious matrixes used in masonry strengthening.
In order to assess the contribution of matrix to the strengthened masonry, the established database was used in this study. Especially, the CP database comprised only the assemblages strengthened with mortar matrixes, and it was used to verify the applicability of available design provisions in the literature. It has to be mentioned that, if the CP strengthening is applied only to one side of the masonry (single-sided reinforcement), the predicted resistance is reduced by factor of 0.7 as recommended in CNR- DT-200 (2013) and CNR-DT-215 (2018) for FRP and FRCM strengthened assemblages. The predictive formulations   Figure 3 shows the experimental and predicted shear resistances of the strengthened masonry assemblages (i.e. CP). It has to be mentioned that the experimental shear resistances (on the horizontal axis) are the overall strengths of the strengthened assemblages. The predicted resistance is given by the contribution of URM and matrix incorporated. This exercise was implemented to verify the contribution from the matrix to the overall strength of strengthened masonry. In general, it can be noted that the formulations conservatively predicted the contribution of the matrix to the shear resistance of strengthened masonry. The basic statistical parameters, derived in the analyses, are given in Table 5 for comparison. It can be noted that the formulation trilled by Almeida et al. (2015) (i.e. also used to predict the tensile resistance of URM assemblages) conservatively predicts the resistance compared to the formulation used by Donnini et al. (2021).

Contribution of the reinforcement
The contribution of the reinforcement to the shear resistance of strengthened masonry (WWM and Reticulatus) involves complex mechanisms. However, different rational approaches have been developed to account the contribution of fabric/fibre in the FRCM and FRP strengthened masonry assemblages. A similar method can be used to establish the contribution of reinforcement in WWM and Reticulatus techniques. However, unlike FRCM and FRP, the WWM and Reticulatus methods involve the use of steel meshes and wires, which are anchored  to the walls. For these strengthening methods, slippage mechanisms between the matrix and masonry substrate are relatively rare to occur compared to FRCM systems. Especially, due to the debonding mechanism in FRP, the term "effective/design tensile strain" and "effective/ design tensile stress" limits are considered in FRP systems to account for the fibre contribution to the shear resistance (Vaculik et al. 2018;Porta et al. 2008). Due to the slippage and debonding mechanisms in FRCM systems, commonly referred as "telescopic effect", a similar analogy is considered to deduce the "conventional/design tensile strain" and "conventional/ design tensile stress" limits (Thermou et al. 2021;Araya-Letelier et al. 2019). However, it can be hypothesized that such debonding and slippage would not be the governing failure modes in WWM and Reticulatus methods, as reinforcement bars/meshes are stiffer, and matrix cracking (due to failure of matrix/mortar under tensile stress) was more frequently recorded in the experimental studies. Further matrix impregnation in fabrics, and their debonding observed in FRCM, are not the mechanism observed in steel bars/wire in Reticulatus and WWM systems. Subsequently, the cracking of matrix in WWM could be due to the tensile failure of matrix, and not due to the relative slippage between reinforcement and matrix.
Since the WWM and Reticulatus systems involve the use of steel meshes, bars and wires, the design approach of Reinforced Masonry (RM), which is widely used in North America and Australasia for concrete block walls will be considered (Araya-Letelier et al. 2019;Zahra et al. 2021a, b), where the reinforcing steel bars are inserted in the vertical cores of the hollow blocks and additional bars are embedded in the horizontal bed joints. In RM, the reinforcement bars (horizontal and vertical) are placed mainly inside the walls (hollow cores), however in WWM and Reticulatus, the reinforcement is applied on the surface or near the surface (i.e. for Reticulatus). Figure 4 illustrates the reinforcement arrangement in the different systems considered. Therefore, a similar approach can be drawn from the design concepts provided for Near Surface Mounted (NSM) FRP bars in masonry . The available design formulations are given in Tables 6 and 7.
It can be noted that the formulations have similar form, where the contribution of reinforcement is accounted using the effective horizontal cross-sectional area of reinforcement and its yield strength. It is widely understood that the horizontal reinforcement provides resistance to the in-plane shear action, and the vertical reinforcement is primarily effective in resisting the in-plane flexural actions. Therefore, the generalized formulation to predict the contribution of reinforcement in resisting the shear action can be written: where A r and f r are the area and yield strength of reinforcement, respectively. s and d are the spacing of reinforcement and effective depth of shear resistance (it is equal to the width of the panels tested). C is a coefficient taken to account the contribution/efficiency of horizontal reinforcement in resisting shear. It is accepted that the horizontal reinforcement does not fully contribute to resisting the shear effects. It was highlighted, that the shear effect is initially carried by masonry, and the reinforcement is fairly unloaded. The horizontal reinforcement only starts contributing to resist shear, once the cracks appeared and opened in masonry. Therefore, the contribution of shear reinforcement is reduced to conservatively predict the shear resistance (Voon and Ingham 2007;Augenti et al. 2010) in RM assemblages. A similar analogy was used to verify the established methodology to predict the shear resistance of WWM and Reticulatus strengthened masonry.
Subsequently, using the formulations established to calculate the URM (Sect. 3.1), matrix (Sect. 3.2.1) and reinforcement contributions (Sect. 3.2.2), the shear resistance of strengthened masonry (WWM and Reticulatus) was predicted. The proposed formula is given in Eq. (5). Since the contribution of the URM and matrix have been already discussed in the previous sections, the accuracy of predicting the contribution of reinforcement in the shear resistance will be discussed in this section.
where V URM has to be determined from the set of formulations outlined in Sect. 3.1. θ,f t,mx and A mx are the inclination angle between horizontal and diagonal direction of the masonry wall panel, the tensile strength of matrix and cross sectional area of matrix, respectively. Moreover, A r and f r are the cross sectional area and yield strength of reinforcement, respectively. s and d are the spacing of reinforcement and effective depth of shear resistance. As mentioned, C is a constant incorporated to reduce the contribution of horizontal reinforcement to the shear resistance. The experimental database established for WWM and Reticulatus systems was utilised to verify the accuracy of the design approach. If the CP strengthening is applied only to one side of the masonry (WWM or Reticulatus), the predicted resistance is reduced by a 0.7 factor. Figure 5 shows the predicted and experimental shear capacity of WWM and Reticulatus strengthened masonry. In order to predict the shear capacity of strengthened masonry, and to account for the contribution of reinforcement, the constant C in the Eq. (5) was calibrated against the experimental database established. The value of C corresponds to the 95th percentile of ME and it was computed to achieve a relatively conservative prediction. C was initially assumed as unity, then calibrated to achieve the 95th percentile of the data. Successively, the C values for WWM and Reticulatus systems were 0.51 and 0.37, respectively. It can be concluded that the proposed unified approach can be used to predict the shear resistance of the strengthened masonry, where the minimum ME is closed to 1 and the 95th percentile ME is fairly higher (> 4).
Although the formulation developed has shown to predict the shear resistance of WWM, Reticulatus and CP strengthened masonry, the formula could be further calibrated with more data from future research studies. Because masonry types vary between regions and counties, the applicability of the examined strengthening methods and their contribution to the shear resistance need further experimental verification, also incorporating the variability in the constitutive properties, different masonry arrangements and strengthening types. Moreover, suitable numerical analysis methods have to be developed to effectively analyse the stress-state of strengthened masonry (WWM, Reticulatus and CP) under inplane shear loading, where the numerical analysis results would enable to validate certain assumptions (stresses in steel meshes/bars, stresses in interface between CP and masonry) made to establish the proposed design approach.

Conclusions
Masonry is weak in tension, often requiring strengthening to withstand lateral actions such as earthquakes, flooding and cyclonic actions. Various strengthening systems have been recently developed to enhance the lateral resistance of masonry. FRCMs sand FRPs are widely used as reinforcements and design guidelines are available for such systems. However, there are other interesting strengthening systems such as WWM, Reticulatus and CP, however no guidelines or instructions are available for design. In this study, a unified design approach was developed to predict the shear capacity of WWM, Reticulatus and CP strengthening systems. An experimental database of the shear strength characteristics comprising different masonry types has been developed. The applicability of the design approach was verified against the experimental shear resistance obtained from different masonry types. The following conclusions can be drawn from this study.
• The established experimental database revealed that WWM, Reticulatus and CP retrofitting methods invariably enhance the masonry shear resistance, where CP strengthening application is a fairly simple technique and Reticulatus strengthening system is preferred when fair-faced aspect of masonry needs to be preserved. WWM system is quite similar to FRCM strengthening system, nonetheless it uses conventional steel/wire mesh instead of composite fabrics. • The prediction of URM shear resistance for four possible failure modes (shear sliding, shear friction, diagonal tension, toe crushing) has shown to be conservative against the database established. • The formulations proposed to predict the matrix contribution to the shear resistance of CP and WWM strengthened masonry have demonstrated to be appropriate and quite conservative against the experimental results. A simplified equation has been proposed to predict the matrix tensile resistance from the compressive strength. • An approach similar to the one used to determine shear resistance of reinforced concrete block masonry (RM) was adopted to account for the contribution of reinforcement (WWM and Reticulatus). The formulation proposed was calibrated to compute the reduced contribution of reinforcement to the in-plane shear resistive mechanism of masonry. • A unified approach was also established to account the shear resistance of strengthened masonry, based on the contribution of URM, matrix and reinforcement used. WWM systems comprised of all three components, while Reticulatus only included URM and reinforcement contributions, and CP comprised of URM and matrix. The design approach has shown to conservatively predict the shear resistance, and it can be cautiously employed to predict the shear resistance of strengthened masonry.
It has to be recommended that the formulation developed here should be further verified against more experimental evidence, also including full scale shear testing results. It should be also highlighted that the Reticulatus methods was only verified with a limited number (18) of test results.