Effectiveness of new generation fabrics for reinforcement of non-tensile resistant materials

Composite Structures 227 (2019) 111315

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Effectiveness of new generation fabrics for reinforcement of non-tensile resistant materials Emanuela Speranzini

T

⁎

Department of Engineering, University of Perugia, Perugia, Italy

ARTICLE INFO

ABSTRACT

Keywords: Glass fiber fabrics Effectiveness Non-tensile resistant material Masonry FEM analysis

The use of new generation fabrics for structural purposes to reinforce non-tensile resistant materials has become very attractive in recent times. This is due to their particular characteristics such as the high strength, the ability to be corrosion resistant, the ease of application and the negligible influence on the increase in structural mass. Due to the variability of the materials and the different construction techniques, there are no reinforcements that are equally effective for all structural types. Thus it is clear that for these systems it is important to evaluate their overall effectiveness with regard to the material and the support structure. In this article a method was developed for evaluating the effectiveness of these reinforcement systems on the shear strength of wall panels that are unreinforced or reinforced with grout injections. For these evaluations, seventy-two 3D finite element models were constructed of structures obtained by varying the type of masonry, the wall thickness and the reinforcement, and they were calibrated by referring to a database of results from previous experimental shear tests on masonry panels. This analysis made it possible to formulate a mathematical relation to evaluate the effectiveness resulting from the application of fabrics onto masonry structures.

1. Introduction The search for materials alternative to traditional ones is not easy, given the risk of losing the effectiveness of the work being done, especially when it is aimed at increasing certain mechanical properties such as the strength of materials not having tensile strength, such as masonry. For these it is proposed to find innovative solutions that make it possible to strengthen existing buildings effectively, but in a reversible and minimally invasive way [1]. Fiber fabrics have long been used for this purpose because they are easy to apply and, above all, they have the advantage of providing considerable tensile strength without increasing the weight of the original structure. The use of these ranges from production sectors where it is necessary to meet the needs of low weight and high mechanical characteristics [2,3], to the aeronautical, naval, automotive, aerospace and war industries, to the plant engineering sector for making pipes [4] and tanks. They are also used for making sports devices, in medicine for prostheses and, lastly, they serve as the basis for the preparation of smart materials. These fabrics can be unidirectional when the reinforcing fibers are all parallel to each other and oriented in a given direction [5,6], or bidirectional or balanced when the fibers are arranged so as to form a 90° angle or with 3D-crimped fibers influencing the longitudinal ⁎

Young’s modulus [7]. The fibers are continuous and are available in various materials: glass, carbon, aramid, and high-strength steel [8] (galvanized or stainless steel). An interest in vegetable fibers has emerged recently; they are of greatly varied origin, as they can come not only from different plants but also from different parts of the plant: from the stem (flax, hemp [9], jute [10,11], broom, bamboo, common reed, wheat straw); from the leaf (sisal, banana [12], pineapple); from the leaf sheaths (Manila hemp); and from the seed (cotton). Natural fibers are valued for their biodegradability because special technologies are not needed for their disposal when they have reached the end of their life; however, it is impossible to use them in poorly controlled environments. The fabrics are bonded to the support to be reinforced by means of the matrix, which also acts as a link between the fibers, i.e. it keeps the fibers stably in position and in their geometry, which is important when we want to give a preferential direction to the mechanical properties. The matrix also serves to protect the fibers from the surrounding environment (corrosive or oxidizing environments), keeping them from deteriorating. Epoxy resins (organic thermosetting) are the most widespread matrices, because they allow rapid installation and high adhesion. On the other hand, inorganic matrices, made with lime- or cement-based binders, are preferable in applications on existing

Address: Department of Engineering, University of Perugia, via G. Duranti, 93, 06125 Perugia, Italy. E-mail address: [email protected].

https://doi.org/10.1016/j.compstruct.2019.111315 Received 15 July 2019; Accepted 14 August 2019 Available online 16 August 2019 0263-8223/ © 2019 Elsevier Ltd. All rights reserved.

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structures for their excellent compatibility with the substrate, sustainability and breathability [13]. Many experimental researches investigated the effect of polymeric nets on the mechanical behavior of masonry panels, and more specifically on their seismic resistant capacity [14]; or studied the use of fabrics in the reinforcement of arch structures [15]; or evaluated the shear strengthening of unreinforced concrete masonry walls with a fabric-reinforced cementitious matrix [16]; or numerical modeled fabric reinforced cementitious matrix [17]. Following the damage to existing structures caused by seismic events over the last twenty years, bidirectional fabrics have been used extensively for the repair and seismic improvement of historical buildings. In these fabrics, the interactions between fiber and mortarmatrix improve through the mechanical interlock, brought about by the development of an effective compound action in the mesh of the fabric, the extent of which depends on various factors and, above all, on the support material [18]. In recent years special attention has been given to the durability of the materials used to make fabrics [19] and to their compatibility with the matrix, such as steel, which over time may be subject to corrosion [20,21,22]. For this reason it is preferred to use non-metallic or at most stainless steel materials when the value of the structure justifies the higher costs. It should be pointed out that it is not possible to propose repair methods and seismic improvements valid for all existing building structures due to the variability of materials and techniques used in their construction. Indeed, various types of wall construction can be found in relation to the size and shape of the building components (rough stone, erratic stone, cobblestone, etc.), their origin, the type of stone (sandstone, limestone, tuff, etc.) and to the quality of the mortar. Consequently the reinforcement techniques that are proposed should be investigated with reference to the different types of structures to which they are applied, to understand and evaluate their effectiveness [23]. There are many studies devoted to experimental campaigns on full scale masonry walls that were strengthened with external fabric reinforcements [24,25,26], and to evaluating the role of the inorganic matrix in determining the effectiveness of fabric-reinforced cementitious matrix (FRCM) confinement [27]. Little research is available in the literature on the effectiveness of consolidation/improvement techniques that are adequate for resisting seismic action. Some of these studies are dedicated to cases of European historic buildings, such as the repair and upgrading of brick or stone masonry structures [28,29,30], the choice of adequate materials for reconstruction [31,32,33], and the seismic performance of historic churches [34]. There is indeed an imminent need for further research that studies the adequacy and effectiveness of the most commonly used retrofitting techniques, because part of the European historical heritage is made up of buildings with high seismic vulnerability, as was seen from the consequences of the earthquakes [35] that occurred in various regions of Europe in recent decades. In this work, the efficacy of new generation fabrics used in the reinforcement of non-tensile resistant materials is evaluated, analyzing the results obtained from diagonal compression tests on masonry panels reinforced with fabrics. This analysis was integrated with simulations performed using the finite element method (FEM) based on the smeared-crack approach. Furthermore, this study made it possible to formulate an expression that can accurately and reliably assess the effectiveness of the strengthening methods as the result of the applied fabric.

2.1. Materials and specimens The masonry panels prepared for experimentation were all squares with 1160 mm sides, but of differing thicknesses: 250 mm for solid brick panels and 400 mm for rubble-stone and cobble-stone panels. All the panels were reinforced on both sides with the same type of bi-axial glass square grid fabric with a 66 × 66 mm mesh, which is not very sensitive to environmental conditions and therefore it is also suitable for aggressive environments. L-connectors of GFRP were also applied on both sides in order to increase the adhesion of the fabric. A layer of mortar was also applied with the function of bonding the fabric to the substrate, impregnating the fibers and protecting them from external agents. Three types of mortar were used: hydraulic lime mortar, pozzolan mortar and mixed cement-lime mortar. Another advantage of glass fiber fabric is that it offers the possibility of using mortars with lime and pozzolan binders, making the reinforcement compatible with the masonry materials. The application of these fabrics has the purpose of increasing the ductility and shear strength in the plane and avoiding the separation of leaves of masonry wall as a result of out-of-plane actions. If one wants to increase the strength of the panel, grout injection into the masonry can be done in addition to the application of the fabric. Grout injection serves to fill the empty spaces inside the masonry, repairing the cracks and providing better continuity, and thus strengthening the masonry to which the fabric is applied [37,38]. This technique also has the function of improving the connection between various leaves of masonry wall in the cases in which these are only next to each other, i.e. without being transversally connected. 2.2. Test layout All the tests were performed according to the ASTM E-519 standard. Each specimen was loaded in compression using a hydraulic jack (950 kN) at opposite corners of the panel (Fig. 1). The two faces of the panel were equipped with two Linear Variable Displacement Transducers (LVDT) applied along the two diagonals of each face, so that during the test the load and displacement values were recorded at the same time [39]. After being appropriately processed, these values allowed us to obtain deformations on each diagonal of the two faces as well as the angular deformation of the panel under load. The tests were performed under controlled force following a sequence of loading-unloading cycles until collapse, which was identified on the basis of the shear stiffness degradation.

2. Storing experimental data For the purposes of this research, the results were collected of many diagonal compression tests carried out in the laboratory on fabric-reinforced masonry panels. This is a typical test for evaluating the shear strength of masonry panels that is able to reproduce real wall conditions [36].

Fig. 1. Diagonal compression test execution pattern. 2

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The interpretation of the diagonal cracking failure mode was performed in Turnšek and Čačovič’s model [40], where the limit stress domain of masonry is defined in a direct manner by evaluating experimentally the tensile strength which is calculated by assuming that the failure of masonry specimens derives from the reaching of the maximum principal stress at its center. It is possible to describe the stress using the two-dimensional graphical representation of Mohr’s circle and to observe that the main directions are inclined by 45° with respect to the reference axes (horizontal and vertical, respectively the base and height of the panel), according to experimental evidence that shows fissures characterized by this inclination. Alternative interpretations of the test results (various definitions of the stress field inside the square specimen) are found in the literature, such as Brignola et al. [41], Frocht [42]. In the database of this research, the masonry shear strength τ0d was evaluated using the following relationship: 0d

=

2 Fmax 3 A

the strength of the unreinforced masonry, the greater the increase in strength provided by the application of reinforcement fabrics. More specifically, the values of the strength increase coefficient are larger for cobblestone walls, which have the lowest strength of all the unreinforced panels tested. The size of the fabric mesh has only a slight influence on the increase in strength (Table 1). This was mainly due to the possible difficulty of having the mortar completely penetrate the meshes, leaving empty spaces where the reinforcing fabric fibers intersect. This incomplete impregnation of the fabric compromises the adhesion of the fibers and limits the tensile strength of the reinforcement. In general, it can be pointed out that even when the fabric’s contribution to the peak bearing capacity is limited, it becomes fundamental in the development of the diagonal cracking state. 3. FEM based simulations The FEM analysis, based on the smeared-crack approach and calibrated on the basis of the database of experimental results, was carried out with the aim of obtaining an accurate and reliable modeling tool for simulating the observed experimental behavior. To do this, three-dimensional FE models of the tested specimens were performed using the commercial software Ansys. The geometry of the masonry walls was first defined with CAD drawings; next, the volumes were imported and discretized using isoparametric brick elements (Solid 65), which are defined by eight nodes with three degrees of freedom each and isotropic material properties. Otherwise, both GFRP grids and GFRP connectors were discretized using 3-D uniaxial tension-compression elements (Link 180). The crosssection was discretized with a sufficient number of elements across the specimen thickness to overcome localization and shear locking effects without using extra shape functions. A sensitivity analysis was performed using different mesh sizes in order to evaluate the optimum mesh density in each FE model. As a result, it became apparent that a good choice was to divided masonry specimens along their depth into twenty elements, in such a way that the width-height ratio of the element was close to 1. More in detail, there are sixteen elements across the masonry panel and two elements across each mortar coating. In samples thus modeled, it was possible to capture the most critical details, at the same time avoiding distorted meshes. Fig. 2(a) shows the complete FE model: it consists of 70,661 elements and 110,012 nodes, with 304,695 degrees of freedom, while Fig. 2(b) gives the mesh of the glass fabric. A tension cut-off type material model was then assumed for describing the behavior of the masonry. This model is appropriate for cohesive-frictional materials and was used for concrete loaded both in

(1)

where α is a factor depending on the method used for the interpretation of the diagonal compression test (α = 0.707 according to RILEM standards interpretation [43], α = 0.500 according to [41]), Fmax is the value of the maximum diagonal load and A is the area of the horizontal cross-section of the panel. To facilitate the interpretation of the results, the panels tested have been grouped into three series which differ by type of masonry and to which the three codes have been assigned: Panel1 (solid brick masonry), Panel2 (rubble stone masonry), Panel3 and Panel4 (cobblestone masonry). These identify the unreinforced panels, and the results are taken as a reference to evaluate the advantages resulting from the application of the fabrics. The reinforced panel codes derive from the unreinforced panel codes, followed by characters which identify the mortar type: “La” and “Lb” the two types of hydraulic lime mortar, “CL” mixed cement-lime mortar and “PZ” pozzolan mortar. In reference to the aforesaid codes, Table 1 shows: the number of specimens by masonry type, the panel thickness, the type of reinforcement, and the value of the maximum load recorded at collapse for each series, as well as the value of the coefficient that expresses the increase in strength achieved following the application of reinforcement. The results of the diagonal-compression tests have confirmed that the reinforced panels have a ductility and a greater dissipative capacity than that of the unreinforced panels. Furthermore, the test results showed that the increase in strength of the masonry panel depends mainly on the type of masonry: the lower Table 1 Test specimen results. Panel Series

Panel1 Panel1-Lb Panel1-CL

N. of spec.

Wall type

Wall thickness

Reinforcing system

[mm]

Matrix

Fabric

[kN]

Solid bricks

250

– Hydraulic lime Mixed cement-lime Pozzolan

– GFRP grid (66x66 mm)

191.85 359.30 324.15 345.30

1.80

7

Rubble stone

400

– Hydraulic lime Mixed cement-lime Pozzolan

– GFRP grid (66x66 mm)

238.60 438.65 461.10

– 1.84 1.94

438.20

1.84

8

Cobblestone

400

– – Mixed cement-lime Hydraulic lime

– – GFRP grid (66x66 mm)

118.20 48.25 375.50

– – 3.18

218.30

4.52

Panel2-PZ Panel3 Panel4 Panel3-Lb Panel4-La

Strength increase coefficient

7

Panel1-PZ Panel2 Panel2-Lb Panel2-CL

Max load (Fmax)

3

– 1.87 1.69

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Fig. 2. Finite element model discretization.

compression and tension, and then taking into account both crushing and cracking failure modes through a smeared model. In particular, the brittle behavior of masonry was defined in this research by two material parameters: uniaxial compressive strength “fc” and uniaxial tensile strength “ft”. Otherwise, the composite materials were modeled with a linear elastic material law [44] without damage: the material properties were taken from the manufacturer’s technical information. Unilateral contact interfaces were also used for simulating the contacts between loading plates and the masonry wall in order to reach the highest level of reliability of the numerical model [45]. The modeling of the contacts requires the use of specific flexible/flexible contact elements. A specific unilateral contact law was applied in the tangential direction of each interface, indicating that sliding may or may not occur, by using the Coulomb friction law. The results of the FE analysis are given in Fig. 3(a), which shows the distribution of the maximum tensile stress in a specimen, and in Fig. 3(b), where the corresponding cracking pattern on the test specimens confirms the panel behavior. The maximum load-capacity values obtained from the FEM model are then compared with the experimental results in Table 2. This comparison shows a good agreement between experimental data and estimated theoretical results for the in-plane load capacity, evidencing how the FEA results are always on the safe side. A single exception was in the case of the Panel2-Lb series, where a higher shear strength was numerically observed. More specifically, the evaluations are very good for unreinforced masonry panels where the error of the model was less than 5%. As regards the reinforced masonry panels, the accuracy of the assessments is slightly lower: the error percentage

Table 2 Experimental versus predicted ultimate load capacities. Panel Series

Panel1 Panel1-Lb Panel1-CL Panel1-PZ Panel2 Panel2-Lb Panel2-CL Panel2-PZ Panel3 Panel4 Panel3-Lb Panel4-La

Wall type

Solid bricks

Rubble stone

Cobblestone

Experimental loadcapacity (Fmax,ex) [kN]

Maximum loadcapacity FEM model (Fmax,th) [kN]

[%]

191.85 359.30 324.15 345.30

192.06 333.53 315.62 308.04

+0.11 −7.17 −2.63 −10.79

238.60 438.65 461.10 438.20

227.27 455.63 436.77 406.90

−4.75 +3.87 −5.28 −7.14

118.20 48.25 375.50 218.30

114.06 44.58 292.40 173.29

−3.50 −7.60 −22.13 −20.62

Error of the model

ranged between 3% and 10% for solid bricks and rubble stone masonry walls, while an average error of 20% was found for cobblestone specimens. 4. Design by testing The quality of a process, organism or product improves if integrative design methods are used, such as design by testing, which is one of the approaches at the system level. In line with this way of thinking, this paragraph is aimed at calibrating a formulation that allows one to

Fig. 3. Distribution of the maximum tensile stress and the corresponding cracking pattern. 4

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(caption on next page) 5

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Fig. 4. Values of mechanical δRP and δRP+GI coefficients as a function of the wall thickness values for the different coating thicknesses: a) 25 mm; b) 40 mm; c) 60 mm.

design the reinforcement of a masonry wall with fiberglass fabrics alone or also of a wall previously strengthened with lime grout injections. To do this, in order to estimate the increase in strength due to the proposed strengthening method, it was decided to carryout FEM simulations varying some significant design parameters. Thus six types of masonry (irregular/pebble stone, barely cut stone, properly dressed, soft stone, perfectly cut and solid brick), four masonry wall thicknesses (300, 400, 500, and 600 mm) and three coating thicknesses (25, 40 and 60 mm) were considered. As a result of combining these parameters, the behavior of 72 types of reinforced masonry panels was investigated using the finite element method. In this program, the effectiveness of the glass fabric reinforcement system alone “δRP” or combined with the grout injection technique “δRP+GI” was thus numerically and analytically assessed for each of these models. The grout injections in the FEM analysis were simply modeled as the change of the mechanical properties (Young modulus and tensile strength) without a significant effect on the unit weight. The values of the δRP and δRP+GI coefficients as a function of the wall thickness for the different coating thicknesses are plotted in Fig. 4. The δRP and δRP+GI values are represented respectively in the right and left parts of each graph. These curves highlight that it is not possible to assess the strength increase of reinforced masonry panels as a function of a single numerical value. Observing the results, it can be seen that the δRP and δRP+GI coefficients assume a linear trend (Fig. 5) as a function of the ratio between the thickness of the mortar coating (scoat) and the thickness of the masonry wall (swall) according to the following equations: RP

S = m coat + q Swall

RP + GI

=m

Scoat +q Swall

Table 3 Factor η provided by NTC Code for reinforcement interventions. Masonry types

Reinforced plaster ηRP

Reinforced plaster + grout injection ηRP+GI

Irregular/Pebble Stone Barely Cut Stone Properly Dressed Stone Soft Stone Perfectly Cut Stone Solid Bricks

2.50 2.00 1.50 2.00 1.20 1.50

5.00 3.40 2.25 3.40 1.44 2.25

referring to six different types of masonry. From the design stage, Eqs (2) and (3) allow one to define the increase in masonry strength, having chosen the ratio (scoat/swall). Vice versa, setting the value of the δRP and δRP+GI coefficients, one can know the value that the ratio must assume in order to obtain the desired masonry strength increase. Therefore, the effectiveness of the proposed strengthening methods is affected by and dependent on the ratio between coating and panel thickness (scoat/swall). More specifically, the use of grout injections makes it possible to increase the structural properties of the masonry wall: the lower the thickness ratio (i.e. the greater the thickness of masonry wall), the lower the ratio between the effectiveness of the glass fabric reinforcement system alone (δRP) and the effectiveness of this reinforcement system in conjunction with grout injections (δRP+GI). 4.1. Comparison of the results The results of the procedure used can be compared with other data provided by the technical literature or with construction regulations (for example, EC8 [46], ACI 549 [47] and NTC [48,49]) for assessing the reliability of a masonry structure subject to expected seismic action. In this section, reference was made to the coefficients indicated by the NTC code [48]. Specifically, this code provides factor η (Table 3) that allows one to estimate the increase in shear strength in the masonry panel plane following the application of a new generation fabric (also called reinforced plaster) alone or in combination with the grout

(2) (3)

where the slopes (m and m*) and intercepts (q and q*) vary with the type of masonry wall. In Table 4, Eqs (2) and (3) are shown in the full form included the values of m, m* and q, q* (second and third column of the Table 4)

Fig. 5. Trends of the δRP and δRP+GI coefficients as a function of the scoat/swall ratio. 6

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Table 4 Comparison between the analytical and the theoretical predictions. Masonry typology

FEM analysis δRP

δRP + GI

Irregular/Pebble Stone

RP

= 11.85

Barely Cut Stone

RP

=

Properly Dressed Stone

RP

=

Soft Stone

RP

=

Perfectly Cut Stone

RP

=

Solid Bricks

RP

=

NTC

scoat + 0.89 s wall scoat 8.67 + 0.94 s wall s 6.34 coat + 0.97 s wall s 9.74 coat + 0.92 s wall s 4.14 coat + 0.99 s wall s 7.26 coat + 0.96 s wall

scoat + 1.89 s wall scoat + 1.66 RP + GI = 9.03 s wall scoat + 1.39 RP + GI = 6.82 s wall scoat + 1.65 RP + GI = 10.19 s wall scoat + 1.22 RP + GI = 4.29 s wall scoat + 1.46 IRP + GI = 7.48 s wall RP + GI

= 12.54

injection technique. The coefficients η are derived from the ratio between the shear strength of the reinforced and unreinforced panel and are expressed by RP

=

RP

RP + GI

=

RP + GI UNR

ηRP

ηRP + GI

RP

RP + GI

2.50

5.00

0.136

0.248

2.00

3.40

0,122

0,193

1.50

2.25

0.084

0.126

2.00

3.40

0.111

0.172

1.20

1.44

0.051

0.051

1.50

2.25

0.074

0.110

5. Conclusions There is an imminent need for further research that studies the adequacy and effectiveness of the most commonly used retrofitting techniques, because part of the European historical heritage is made up of buildings with high seismic vulnerability, as was seen from the consequences of the earthquakes in recent time. This article evaluated the efficacy provided by the application of fiber fabrics on non-tensile materials such as those of masonry structures. For this purpose, data from the results of diagonal compression tests on brick or stone masonry panels reinforced with glass-fiber fabrics and inorganic matrix were used. These results were also used to calibrate finite element models based on the smeared-crack approach, specifically constructed to describe the experimental behavior observed and with the aim of using them for simulations of various types of masonry. Therefore, main design parameters governing the in-plane response were first identified (masonry texture type, coating and masonry wall thickness); FE analyses were then performed (by combining the values of the aforementioned design parameters) to investigate the effectiveness of the reinforced plaster system alone “δRP” or combined with the grout injection technique “δRP+GI”. The results of these simulations, obtained by investigating the behavior of 72 types of reinforced masonry panels, have made it possible to establish mathematical relationships that can predict the efficacy provided by the application of the fabric. It was in fact observed that the effectiveness of the proposed strengthening methods may not be assessed as a function of a single parameter (e.g., factor η). Therefore, mathematical relationships were formulated (Eqs. (2) and (3)) in which the effectiveness of the glass fabric reinforcement system “δRP” and “δRP+GI“ are linear functions of the ratio between the mortar coating thickness (scoat) and the masonry wall thickness (swall). The procedure used gave good results when a comparison was made with data provided by the construction regulations, in which the effectiveness is assessed by a single parameter. Furthermore, it was shown that the analytical approach adopting can be used as lower bound performance assessment limits in the case of panels strengthened with the reinforced plaster system.

(4)

UNR

Scoat/Swall

(5)

in the case of reinforced plaster (ηRP) and reinforced plaster combined with grout injection (ηRP+GI), respectively. Table 3 shows the values of the coefficient η referring to six types of masonry. Each coefficient, multiplied by the strength of the respective unreinforced masonry, allows estimating the masonry strength after the application of the reinforced plaster. The values of the coefficient ηRP vary in the range 1.2 (perfectly cut stone) to 2.5 (irregular pebble stone), whereas the values of ηRP+GI vary in the range 1.44 ÷ 5.00 for perfectly cut stone and irregular/pebble stone, respectively. The comparison between the results of the FEM analysis and the theoretical predictions obtained by the NTC code (Table 4) highlights how this analytical approach can be used as the lower bound of performance assessment limits, since it provides mostly conservative estimations in the case of panels strengthened with the reinforced plaster system. The sixth and seventh columns of the Table 4 show the values of the ratio scoat/swall when the (δRP) and (δRP+GI) coefficients have the same values of (ηRP) and (ηRP+GI). Therefore, with reference to table 4, it can be observed for example: ηRP < δRP only when scoat/swall > 0.136, for irregular/pebble stone masonry, ηRP < δRP only when scoat/swall > 0.122, for barely cut stone, i.e. coefficient ηRP provides conservative values only when the ratio scoat/swall takes values greater than those calculated with the analytical method and provided in the Table 4. Lower values of the ratio scoat/swall give non-conservative results (i.e. these are not the safe side). Similar results are obtained when the reinforced plaster is used in conjunction with grout injections to strengthen specimens built with weaker masonry types: ηRP+GI < δRP+GI when, for example:

Acknowledgement

scoat/swall > 0.248 for irregular pebble stone, scoat/swall > 0.193 for barely cut stone and scoat/swall > 0.110 for solid bricks.

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sector. References

These observations confirm the validity of the analytical formulation (Eqs. (2) and (3)) and show that the code predictions, which use a single coefficient, are non-conservative in all cases.

[1] Foraboschi P. The central role played by structural design in enabling the construction of buildings that advanced and revolutionized architecture. Constr Build Mater 2016;114:956–76.

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Mater 2015;88(7):94–104. [27] Cascardi Alessio, Micelli Francesco, Aiello Maria Antonietta. FRCM-confined masonry columns: experimental investigation on the effect of the inorganic matrix properties. Constr Build Mater 2018;186:811–25. [28] Modena C. Repair and upgrading techniques of unreinforced masonry structures utilized after the Friuli and Campania-Basilicata earthquake. Earthquake Spectra 1994;10(1):171–85. [29] Binda L, Modena C, Baronio G, Abbaneo S. Repair and investigation techniques for stone masonry walls. Constr Build Mater 1994;11(3):133–42. [30] Brencich A, Gambarotta L, Ghia A. History-based assessment of the dome of the Basilica of S. Maria of Carignano in Genoa. Int J Architect Heritage 2014;8(5):690–717. [31] Binda L, Baronio G, Tiraboschi C, Tedeschi C. Experimental research for the choice of adequate materials for the reconstruction of the Cathedral of Noto. Constr Build Mater 2003;17(8):629–39. [32] Corradi M, Borri A, Castori G, Speranzini E. Fully reversible reinforcement of softwood beams with unbonded composite plates. Compos Struct 2016;149:54–68. [33] Adnan M, Pinnick RA, Tang Z, Taylor LW, Pamulapati SS, Carfagni GR, et al. Bending behavior of CNT fibers and their scaling laws. Soft Matter 2018;14(41):8284–92. [34] Lourenço PB, Trujillo A, Mendes N, Ramos LF. Seismic performance of the St. George of the Latins church: lessons learned from studying masonry ruins. Eng Struct 2012;40:501–18. [35] Bianconi F, Catalucci S, Filippucci M, Marsili R, Moretti R, Rossi G, Speranzini E. Comparison between two non-contact techniques for art digitalization. J Phys 2017;882(1). https://doi.org/10.1088/1742-6596/882/1/012005. [36] Serena Chiara Calderini, Lagomarsino Cattari Sergio. The use of the diagonal compression test to identify the shear mechanical parameters of masonry. Constr Build Mater 2010;24(5):677–85. [37] Jorne F, Henriques FMA, Baltazar LG. Evaluation of consolidation of different porous media with hydraulic lime grout injection. J Cult Heritage 2015;16:438–51. [38] Tomazevic M, Api V. The strengthening of stone masonry walls by injecting the masonry-friendly grouts. Eur Earthquake Eng 1993;1(2):10–20. [39] Borri A, Castori G, Corradi M, Speranzini E. Shear behavior of unreinforced and reinforced masonry panels subjected to in situ diagonal compression tests. Constr Build Mater 2011;25(12):4394–402. [40] Turnsek V, Čačovič F. Some experimental result on the strength of brick masonry walls. In: West HWH, Speed KH, editors. Proc. 2nd Int. Brick Masonry Conf. British Ceramic Research Association; 1971. p. 149–56. Stoke-on-Trent. [41] Brignola A, Frumento S, Lagomarsino S, Podestà S. Identification of shear parameters of masonry panels through the in-situ diagonal compression test. Int J Architect Herit 2009;3(1):52–73. [42] Frocht MM. Recent advances in photoelasticity. ASME Trans 1931;55:135–53. [43] RILEM TC 76-LUM. Diagonal tensile strength tests of small wall specimens. RILEM, Recommendations for the Testing and Use of Constructions Materials. London: Taylor & Francis; 1994. p. 488–9. [44] Lanzoni L, Tarantino AM. A simple nonlinear model to simulate the localized necking and neck propagation. Int J Non Linear Mech 2016;84:94–104. [45] Savino V, Lanzoni L, Tarantino AM, Viviani M. Simple and effective models to predict the compressive and tensile strength of HPFRC as the steel fiber content and type changes. Compos B Eng 2018;137:153–62. [46] EN 1998-3: 2005-06: Eurocode 8: Design of structures for earthquake resistance. Part 3: Assessment and retrofitting of buildings. European Committee for Standardisation: Brussels June 2005. [47] ACI 549.4R: 2013: Guide to design and construction of externally bonded fabricreinforced cementitious matrix (FRCM) systems for repair and strengthening concrete and masonry structures. American Concrete Institute: Farmington Hills 2013. [48] NTC 2008: 2008-01: Technical Standard for the Construction (NTC 2008). Italian Official Bull 29. Directive of the Prime Minister: Rome January 2008 [in Italian]. [49] IMIT Circ. n. 617: 2009-02: Instruction for the application of the Technical Standard for the Construction (NTC 2008). Italian Ministry of Infrastructures and Transportation: Rome February 2009 [in Italian].

[2] Bruckner A, Ortlepp R, Curbach M. Textile reinforced concrete for strengthening in bending and shear. Mater Struct 2016;39(8):741–8. [3] Falope FO, Lanzoni L, Tarantino AM. Modified hinged beam test on steel fabric reinforced cementitious matrix (SFRCM). Compos Part B Eng 2018;201:503–13. https://doi.org/10.1016/j.compositesb.2018.03.019. [4] Cicala G, Cristaldi G, Recca G, Ziegmann G, El-Sabbagh A, Dickert M. Properties and performances of various hybrid glass/natural fibre composites for curved pipes. Mater Des 2009;30:2538–42. [5] Rotunno T, Fagone M, Bertolesi E, Grande E, Milani G. Single lap shear tests of masonry curved pillars externally strengthened by CFRP strips. Compos Struct 2018;200:434–48. [6] Foraboschi P. Analytical model to predict the lifetime of concrete members externally reinforced with FRP. Theor Appl Fract Mech 2015;75(1):137–45. [7] Stig F, Hallström S. Influence of crimp on 3D-woven fibre reinforced composites. Compos Struct 2013;95:114–22. [8] Falope FO, Lanzono L, Tarantino AM. Double lap shear test on steel fabric reinforced cementitious matrix (SFRCM). Compos Struct 2018;201:503–13. [9] Borri A, Corradi M, Speranzini E. Reinforcement of wood with natural fibers. Compos B Eng 2013;53:1–8. https://doi.org/10.1016/j.compositesb.2013.04.039. [10] Ramnath BV, Kokan SJ, Raja RN, Sathyanarayanan R, Elanchezhian C, Prasad AR, et al. Evaluation of mechanical properties of abaca–jute–glass fibre reinforced epoxy composite. Mater Des 2013;51:357–66. [11] Fagone M, Loccarini F, Ranocchiai G. Strength evaluation of jute fabric for the reinforcement of rammed earth structures. Compos B Eng 2017;113:1–13. [12] Arthanarieswaran VP, Kumaravel A, Kathirselvam M. Evaluation of mechanical properties of banana and sisal fiber reinforced epoxy composites: influence of glass fiber hybridization. Mater Des 2014;64:194–202. [13] Papanicolaou CG, Triantafillou TC, Papathanasiou M, Karlos K. Textile reinforced mortar (TRM) versus FRP as strengthening material of URM walls: out-of-plane cyclic loading. Mater Struct 2008;41(1):143–57. [14] D’Ambrisi A, Mezzi M, Caporale A. Experimental investigation on polymeric netRCM reinforced masonry panels. Compos Struct 2013;105:207–15. [15] D’Ambrisi A, Focacci F, Caporale A. Strengthening of masonry-unreinforced concrete railway bridges with PBO-FRCM materials. Compos Struct 2013;102:193–204. [16] Babaeidarabad S, Arboleda D, Loreto G, Nanni A. Shear strengthening of un-reinforced concrete masonry walls with fabric-reinforced-cementitious-matrix. Constr Build Mater 2014;65(8):243–53. [17] Carozzi FG, Milani G, Poggi C. Mechanical properties and numerical modeling of Fabric Reinforced Cementitious Matrix (FRCM) systems for strengthening of masonry structures. Compos Struct 2014;107:711–25. [18] Smitha Gopinath, Iyer Nagesh R, Ravindra Gettu, Palani GS, Ramachandra Murthy A. Confinement effect of glass fabrics bonded with cementitious and organic binders. Proc Eng 2011;14:535–42. https://doi.org/10.1016/j.proeng.2011.07.067. [19] Nobili A, Signorini C. On the effect of curing time and environmental exposure on impregnated carbon fabric reinforced cementitious matrix (CFRCM) composite with design considerations. Compos Part B: Eng 2017;112:300–13. [20] Borri A, Castori G, Corradi M, Speranzini E. Durability analysis for FRP and SRG composites in civil applications. Key Eng Mater 2015;624:421–8. https://doi.org/ 10.4028/www.scientific.net/KEM.6X”.421. [21] Juhásová E, Sofronie R, Bairrão R. Stone masonry in historical buildings – ways to increase their resistance and durability. Eng Struct 2008;30(8):2194–205. [22] Savino V, Lanzoni L, Tarantino AM, Viviani M. Tensile Constitutive behaviour of high and ultra-high performance fibre-reinforced-concretes. Constr Build Mater 2018;186:525–36. [23] Peled A, Bentur A. Geometrical characteristics and efficiency of textile fabric for reinforcing composites. Cem Concr Res 2000;30:781–90. [24] Foraboschi P. Effectiveness of novel methods to increase the FRP-masonry bond capacity. Compos B Eng 2016;107:214–32. [25] Fagone M, Ranocchiai G. On the effectiveness of CFRP reinforcement of masonry panels loaded by out-of-plane actions. Proc Struct Integrity 2018;11:250–7. [26] Gattesco N, Boem I. Experimental and analytical study to evaluate the effectiveness of an in-plane reinforcement for masonry walls using GFRP meshes. Constr Build

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