Experimental behaviour of damaged masonry arches strengthened with steel fiber reinforced mortar (SFRM)

Composites Part B 177 (2019) 107386

Contents lists available at ScienceDirect

Composites Part B journal homepage: www.elsevier.com/locate/compositesb

Experimental behaviour of damaged masonry arches strengthened with steel fiber reinforced mortar (SFRM) � Simoncello, Paolo Zampieri *, Jaime Gonzalez-Libreros, Carlo Pellegrino Nicolo Department of Civil, Environmental and Architectural Engineering, University of Padua, Via Marzolo 9, 35131, Padua, Italy

A R T I C L E I N F O

A B S T R A C T

Keywords: Steel fiber reinforced mortar (SFRM) Masonry arches Strengthening Damage Experimental test Composite materials Analytical formulation

In this paper, the results of an experimental campaign aimed to study the behavior of damaged solid clay brick masonry arches strengthened with steel fiber reinforced mortar (SFRM) are presented. Conditions of damage studied included preloading, horizontal displacement of one of the supports, or a combination of both. After damage was produced, the arches were strengthened with one layer of SFRM at the intrados and retested. The performance of the strengthened arches is discussed in terms of failure mode, and variation in the load carrying capacity, ductility and stiffnesses with respect to unstrengthened undamaged condition. The results show that the SFRM strengthening was able to increase significantly the strength and stiffness of the arches, although in some cases such increase was accompanied by a reduction in the specimens’ ductility. In addition, an analytical formulation for the design and assessment of the capacity of masonry arches strengthened with SFRM was developed. Comparison between predicted and experimental values show good agreement, which allowed validating the analytical method.

1. Introduction Masonry arches are an architectural and structural element used since ancient times for the construction of buildings, bridges and via­ ducts [1]. Their structural behavior is characterized mainly by the development of compressive stresses developed in the cross section. However, this structural feature is only guaranteed if the supports are appropriately resistant and rigid to counteract the horizontal reaction forces applied at the arch’s springing. When this condition is not satis­ fied, such horizontal reaction forces, caused by a seismic event [2,3], for instance, are transferred from the arches to the supports and/or a poor foundation system and may induce horizontal displacements or settle­ ment of the arch supports. This phenomenon can cause damage to the masonry arch, a decrease in its load carrying capacity and, if measures to preclude its further development are not taken in time, lead to the collapse of the structure. In general, the behavior of masonry structures can be studied by means of on site or full scale laboratory experimental tests [4–8], or through numerical simulations as micromechanical analysis [9], limit analysis [10], multiscale strategy [11], using fibre beam elements [12], discrete macro-elements [13], nonlinear modeling [14], and numerical procedures based on the thrust line [15–17]. Unfortunately, theoretical

or experimental evidence regarding how the structural response and failure mode of masonry arches is modified by the presence of settlement or displacement of supports is still scarce [18–21]. In addition, after the cause of the settlement/displacement of the structure is individuated and effectively intervened and depending on the extension of the dam­ age, further measures will be required in order to restore the structure’s original carrying capacity and guarantee an adequate safety level in the structure. For the case of masonry structures, the use of fiber reinforced poly­ mer (FRP) composites has become a widely popular strengthening technique due to their advantages such as low specific weight, corrosion immunity, high tensile strength, adaptability to curved surfaces and ease of application [22]. Furthermore, experimental results have shown that the FRP system is able to provide satisfactory increase in strength and ductility on irregular masonry walls [23], masonry arches strengthened at the extrados [24,25] or intrados [26], or numerically modeled by means of limit analysis [27,28], and to concrete elements [29,30]. However, some disadvantages of the FRP composites, usually associated with the use of the resins, have been pointed out [31]: poor behavior at temperatures above the glass transition temperature, inability to apply FRP on wet surfaces or at low temperatures;

* Corresponding author. E-mail address: [email protected] (P. Zampieri). https://doi.org/10.1016/j.compositesb.2019.107386 Received 30 May 2019; Received in revised form 18 July 2019; Accepted 26 August 2019 Available online 27 August 2019 1359-8368/© 2019 Elsevier Ltd. All rights reserved.

N. Simoncello et al.

Composites Part B 177 (2019) 107386

Nomenclature ASFRM bi d dFmax DIC Em ESFRM F f fb fk fm fm,c Fmax Fmax_C fSFRM,t i ji K k Ke L ME MRd

NE ni Nm,c NRd NSFRM,t P s SFRM sR SRd w wR x ySFRM

SFRM area of the layer Bricks numbering Arch crown displacement Displacement corresponding to maximum load Digital image correlation Masonry elastic modulus SFRM elastic modulus Applied arch load Arch rise Bricks compressive strength Masonry compressive strength Mortar compressive strength Ultimate masonry compressive strength Maximum load Peak load value of the control specimen SFRM tensile strength Index of numbering Mortar joint numbering Coefficient of masonry compressive strength Coefficient of reduction for masonry compressive strenght Coefficient masonry elastic modulus Span length Bending moment related to the P considered Resisting bending moment

ε εFmax εm,u εSFRM,u εSFRM,y εt,1 εt,2 μ σ SFRM,t φ

χ

lack of vapor permeability, incompatibility of epoxy resins and substrate materials, among others.

Axial force related to the P considered Numbering of hinges location Masonry compressive force Resisting axial force SFRM tensile force Mid-span concentrated load considered Arch thickness Steel fiber reinforced mortar SFRM thickness Shear capacity Arch width SFRM width Neutral axis depth Depth of the SFRM tensile force from the bottom of the section Longitudinal strain Longitudinal strain at peak load Ultimate masonry compressive strain Ultimate SFRM strain Yield SFRM strain Strain at SFRM - masonry interface Strain at the bottom of the section Ductility SFRM tensile stress Friction coefficient Curvature

on the development of analytical formulation for the modelling of composite strengthening systems [41–44]. Recently, the use of a material comprised of short fibers and high strength mortars, known as fiber reinforced mortars (FRM) for the strengthening of concrete structures has caught the attention of re­ searchers [45,46]. The addition of fibers in the mortar has proven to increase the tensile and flexural strength, abrasion resistance, perme­ ability, toughness and ductility of the material [47]. Among the ad­ vantages of FRM for the strengthening of masonry arches, it is possible to find its ease of application as it only requires the use of traditional formwork, and the possibility of filling pre-existing cracks in the ma­ sonry members due to the flowable consistency of the FRM at the time of the strengthening. In this paper, the use of steel fiber reinforced mortars (SFRM) as an alternative to other available strengthening techniques such as FRP or FRCM composites for the strengthening of damaged masonry arches is studied. With this aim, solid clay bricks masonry arches were subjected to pre-damage caused by preloading, horizontal displacement of one of

In addition, for the case of historical constructions, they do not guarantee that the original structure characteristics and aesthetic are preserved. Newly developed techniques, such as fiber reinforced cementitious matrix (FRCM) composites, have been studied with the aim of overcoming some of these disadvantages [32–35]. They have been applied for the strengthening of masonry arches at the intrados [36], or extrados [37], or both [38,39]. In this case, resins are replaced by mortars that allow an intervention more compatible with masonry ma­ terial. In addition, the system is reversible and allows its removal when required (for instance, for a post-earthquake inspection) [31]. However, results have shown that the increase in strength is significantly lower than that achieved by means of FRP composites. The different response and failure modes between FRP and FRCM composites has been sum­ marized in Zampieri et al. [40]. Additional research has been carried out

Fig. 1. Arch geometry, brick and mortar joint numbering, and instrumentation. 2

N. Simoncello et al.

Composites Part B 177 (2019) 107386

Table 1 Tests description.

Table 2 Mechanical properties of the materials.

ARCH

TEST

DESCRIPTION

1

Unstrengthened (UN), no damage (ND) Unstrengthened (UN), pre-damage due to loading (LD) Strengthened (SFRM), pre-damage due to loading (LD)

2

UN.ND.01_00 UN.LD.01_00 SFRM. LD.01_00 UN.SD.02_10

3

SFRM. SLD.02_10 UN.SD.03_10

4

SFRM. SD.03_10 UN.SD.04_20 SFRM. SLD.04_20

Material

Brick Mortar SFRM

Unstrengthened (UN), pre-damage due to 10 mm horizontal displacement (SD) Strengthened (SFRM), pre-damage due to loading and 10 mm horizontal displacement (SLD) Unstrengthened (UN), damage due to 10 horizontal displacement without loading (SD) Strengthened (SFRM), pre-damage due to 10 mm horizontal displacement without preloading (SD) Unstrengthened (UN), pre-damage due to 20 mm horizontal displacement (SD) Strengthened (SFRM), pre-damage due to loading and 20 mm horizontal displacement (SLD)

the supports, or a combination of both and then strengthened with a layer of SFRM applied on the arch intrados. The tests were carried out by applying an increasing monotonic load at the arch keystone and the response of the arches was evaluated in terms of failure mode, and variation in the load carrying capacity and ductility of the specimens. In addition, digital image correlation (DIC) was used to study the evolution of the strains in the SFRM layer. Finally, with the aim of providing a calculation method for evaluating the increase in the load capacity provided by the SFRM, an analytical prediction formulation was developed.

Density

Compressive strength

Flexural strength

Elastic Modulus

[kg/m3]

[MPa]

CoV

[MPa]

CoV

[MPa]

CoV

1744 1807 2402

>18.8 7.22 91.02

– 9.88 1.59

– 2.22 15.43

– 4.61 11.98

>9024 3706 24040

– 16.33 22.01

Fig. 2. Steel fiber reinforced mortar (SFRM): steel fibers and mortar.

2. Experimental program

reported by the producer, are shown in Table 2. A cement-based mortar (Class M5 according to UNI EN 998–2_2016 [48]) was used for the masonry joints. Average values of density, compressive and flexural strength, and elastic modulus of the mortar evaluated by means of 40 � 40 � 160 mm prisms according to UNI EN 1015-11-2007 [49] and EN 13412:2006 [50] are presented in Table 2. The masonry compressive strength (fk) and elastic modulus (Em) were calculated using the equations provided by Eurocode 6 [51]:

A total of four brick masonry arches (arches 1, 2, 3 and 4) were built using 29 solid clay bricks and 10 mm thick joint mortars (see Fig. 1) and tested under monotonic load (F) applied at the arch crown. Bricks and mortar joints were numbered according to the convention bi and ji, respectively, where i ranges from 1 to 29 for the bricks and from 1 to 30 for the joints. All the arches had an arch rise (f), span length (L), thickness (s) and width (w) equal to 610 mm, 1430 mm, 110 mm, and 245 mm, respectively. In order to investigate the effect of the SFRM strengthening on damaged arches, the arches were subjected to a specified damage con­ dition due to pre-loading, horizontal displacement of one of the supports or combination of both (see Section 2.3) and then strengthened with a layer of SFRM applied at the arch intrados. Arch 1 was tested before strengthening (test UN.ND.01_00) and works as control specimen. After the test, the specimen was retested in order to evaluate the residual strength after damage (test UN.LD.01_00). Then, arch 1 was strength­ ened and retested (SFRM.LD.01_00). Arch 2 and 4 were subjected to horizontal displacements at one of the supports equal to 10 mm and 20 mm, respectively, and tested (tests UN.SD.02_10 and UN.SD.04_20). Subsequently, these arches were strengthened and retested (tests SFRM. SLD.02_10 and SFRM.SLD_20). Finally, a horizontal displacement equal to 10 mm was applied to arch 3 but additional damage due to loading was not applied. It was strengthened and then tested (test SFRM. SD.03_10). Table 1 summarizes the designation and description of the tests performed in each arch.

fk ¼ K⋅fb

0:7

⋅fm

0:3

Em ¼ Ke ⋅fk

(1) (2)

where the coefficient K, the brick compressive strength (fb) and the mortar compressive strength (fm) were assumed equal to 0.44, 18.8 MPa, and 7.22 MPa, respectively. Accordingly, the computed value of ma­ sonry compressive strength is equal to 6.21 MPa. From Eq. (2), taking Ke as 1000, the computed elastic modulus of the masonry is equal to 6210 MPa. 2.1.2. Steel fiber reinforced mortar (SFRM) Arches were strengthened with a 30 mm thick layer of SFRM. The SFRM is comprised of a high strength mortar fiber-reinforced with around 2% of hook end steel fibers in volume (see Fig. 2). The diameter and length of the steel fibers are equal to 0.5 mm, and 30 mm, respec­ tively. Based on the geometric characteristics of the arch, the minimum thickness of the SFRM layer recommended by the producer was chosen. For the material studied in this paper, such value must be equal to the length of the steel fibers, i.e., 30 mm. Experimental values of compres­ sive and flexural strength, and elastic modulus of the SFRM material, evaluated according to UNI EN 1015-2-2007 [49], are reported in Table 2.

2.1. Materials 2.1.1. Masonry Materials used for the construction of the arches were selected in order to replicate actual conditions of existing masonry arches. Clay solid bricks with nominal dimensions equal to 60 � 110 � 245 mm were used for the construction of the arches. Mean values of density, compressive and flexural strength, and elastic modulus of the bricks, as

2.2. Test procedure and instrumentation As shown in Fig. 3, the arches were tested under point monotonic 3

N. Simoncello et al.

Composites Part B 177 (2019) 107386

Fig. 3. Masonry arch experimental setup.

loading using a stiff steel reaction frame with a total capacity of 600 kN at the arch midspan. The load (F) was applied using a manually operated servo-hydraulic jack connected to a load cell with a maximum capacity of 100 kN. The load was cell was placed on the top of a 20 mm thick steel plate located on top of the arch in order to guarantee a better distribution of the force (see detail P1 in Fig. 3). Arches were mounted on top of a stiff HEA steel beam and the verticality of the specimens was verified before testing with the aim of avoiding any instability effects. In order to restrain the opening of the arches at the springing, two steel plates were located at each end of the arch and were connected through two threaded steel rods. For unstrengthened and strengthened specimens, a linear variable differential transducer (LVDT) was located below the arch in order to measure the vertical displacement at the arch crown, d, as shown in Fig. 1 (LVDT 4). Six additional LVDTs were used to measure horizontal (LVDTs l, 2, 6, and 7) and vertical (LVDTs 3 and 5) displacements in the strengthened specimens, according to the distribution shown in Fig. 1. Two DD1 strain transducers with a gauge length ¼ 50 mm were placed at the SFRM bottom surface, aligned parallelly to the arch axis and in correspondence with the location of the applied force. Digital Image Correlation (DIC) system was also used to monitor strain and displace­ ment fields using two monochrome cameras with 5 Megapixel CCD resolution and 12 mm focal length lenses. For DIC measurements, a white base layer was applied to the surface of the arch and the SFRM layer within the designated target area (see Fig. 1), and a random speckle pattern was then applied using a black marker.

Fig. 4. Repair procedure.

one of the arch supports. With this aim, during the construction of the arches, two steel plates were placed between brick b1 and the support (see detail P2 in Fig. 3). Before testing, one or both plates were removed in order to obtain the specified horizontal displacement depending on the studied damage condition. A detailed description of the tests per­ formed during the experimental campaign included in this paper is presented in Table 1. Tests on strengthened arches were stopped when an arch crown displacement of around 6 mm was reached in order to avoid the damage of the instrumentation. Then, all the instrumentation was removed, and the test continued until the collapse of the arches.

2.3. Definition of damage As discussed previously, two types of damage were investigated in this paper. The first one corresponds to damage due to preloading. For this case, unstrengthened specimens were loaded until 85% of the peak load in the post-peak branch and then unloaded. The second type of damage consisted in applying a 10 or 20 mm horizontal displacements in

2.4. Repair procedure The arches were strengthened with a SFRM layer with thickness (sR) 4

N. Simoncello et al.

Composites Part B 177 (2019) 107386

was superficially damped. The mortar was slowly poured through a hole left at the top of the formwork, under brick b15, until it filled the formwork. The formwork was removed one day after casting took place and the SFRM layer was left to cure under environmental conditions until the day of testing (30 days after casting).

Table 3 Summary of test results. TEST UN.ND.01_00 UN.LD.01_00 UN.SD.02_10 UN.SD.04_20 SFRM.LD.01_00 SFRM.SLD.02_10 SFRM.SD.03_10 SFRM.SLD.04_20 a

Fmax [kN] a

0.44 0.34 1.89 2.18 14.15 10.13 18.52 22.35

dFmax [mm]

Fmax/Fmax_C

μ

εFmax [%]

2.6 1.72 0.38 0.53 2.29 5.16 1.76 2.03

1.00 0.77 4.30 4.95 32.16 23.02 42.09 50.80

12.77 11.72 1.70 1.13 2.90 9.63 1.27 1.21

– – – – 0.240 0.303 0.683 0.782

3. Experimental results The maximum load Fmax, the arch crown displacement correspond­ ing to the maximum load (dFmax), and ductility factor of each test are summarized in Table 3. In this paper, the ductility (μ) is computed as the ratio between the ultimate displacement (the displacement at ultimate load, taken as 85% of the maximum load in the descending branch of the applied load vs. arch crown displacement curve) and the displacement at the end of the elastic branch [40]. For tests carried out on strengthened arches, Table 3 includes as well the increase in strength provided by the SFRM system with respect to the control specimen, computed as the ratio between the Fmax for a given test and that of test UN.ND.01_00 (Fmax/Fmax_C), and the longitudinal strain in the SFRM layer at peak load (εFmax).

Fmax_C corresponds to the value of peak load of test UN.ND.01_00.

3.1. Unreinforced masonry arches 3.1.1. Applied load versus arch crown displacement Fig. 5 shows the applied load F versus arch crown displacement d curves obtained during the tests performed on unstrengthened arches. When values of Fmax obtained during tests UN.ND.01_00 (unstrength­ ened and undamaged condition) and UN.LD.01_00 are compared, results in Table 3 and Fig. 5 show that the damage due to loading implies a reduction in the arch capacity of around 23% and a significant reduction of the initial stiffness of the specimen. The lower strength witnessed during test UN.LD.01_00 with respect to test UN.ND.01_00 is associated to the loss of contribution to the strength of the bond between the mortar and bricks due to the previous opening of the cracks at the hinge loca­ tions. For both tests, the curve is characterized by an initial linear elastic part followed by a nonlinear branch until maximum load is attained.

Fig. 5. Load F vs. arch crown displacement d for unstrengthened arches.

and width (wR) equal to 30 mm and 200 mm, respectively, applied at the arch intrados (see Fig. 4). Considering that the SFRM is flowable when fresh, a formwork comprised of two lateral rubber profiles with a height of 30 mm and a bottom flexible steel plate was attached under the arch, as shown in Fig. 4. Before applying the SFRM layer, the arch intrados

Fig. 6. Hinge mechanisms for: a) Test UN.LD.01_00; b) Test UN.SD.02_10; c) UN.SD.03_10; d) Test UN.SD.04_20. 5

N. Simoncello et al.

Composites Part B 177 (2019) 107386

and, subsequently, the geometry and the strength of the member are modified. In the latter case, when the concentrated load is applied the arch collapse configuration is made up of four hinges, three of which are those opened due to horizontal displacement of the support. This hinge configuration differs from that obtained applying the same concentrated load to an arch without any horizontal displacement. Therefore, considering the two theorems of the limit analysis, the load collapse multiplier is greater for an arch with horizontal displacement than for a member without horizontal displacement [52–54]. It is worth noting that the initial stiffness for tests UN.SD.02_10 and UN.SD.04_20 is the same, independently of pre-damage condition, i.e., magnitude of the horizontal displacement applied at the support. Due to the increase in stiffness, values of dFmax for these tests are significantly lower than those witnessed during test UN.SD.01_00. For tests UN. SD.02_10 and UN.SD.04_20, Fig. 5 also shows that until peak load is attained, the specimens showed a linear behavior followed by rapid reduction on the arch strength with the increase of the arch crown displacement. This behavior implies a significant reduction in the ductility of the specimens when compared to that witnessed during test UN.ND.01_00, as shown in Table 3.

Fig. 7. Load F vs. arch crown displacement d for strengthened arches.

Afterwards, both curves show a descending branch until the test is stopped. The behavior of arches subjected to horizontal displacement shows a significant increase in the values of Fmax and initial stiffness when compared to test UN.ND.01_00. The increase in the load carrying ca­ pacity can be explained as a combination of two different conditions: a) arch subjected only to horizontal displacement, and b) arch subjected to horizontal displacement and additional vertical loading. For the former case, an increase in the displacement implies a reduction in the arch rise

3.1.2. Hinge mechanism Fig. 6 shows the numbering and location of the hinges (with respect to mortar joint, bi) developed for unstrengthened arches. During test UN. ND.01_00, a typical four hinge mechanism formed (see hinges LD in Fig. 6a). After unloading, and retesting (test UN.ND.01_00) the location of the hinges remained the same. It is observed that the position of hinges n2 and n4 is not symmetric, probably due to geometric

Fig. 8. Failure mode: a) detachment of the SFRM layer; b) Peeling-off of the masonry substrate; c) SFRM cracking; d) Brick crashing, sliding, and SFRM cracking and detachment; e) Hinge at the support at failure; f) SFRM cracking at failure. 6

N. Simoncello et al.

Composites Part B 177 (2019) 107386

Fig. 9. Hinge mechanisms for tests: a) SFRM.LD.01_00; b) SFRM.SLD.02_10; c) SFRM.SD.03_10; d) SFRM.SLD.04_20.

imperfections of the specimen [55]. Arches subjected to horizontal displacement showed a three-hinge mechanism (see hinges SD, in Fig. 6b, c, and 6d), independently of the value of horizontal displacement. The position of the hinges n1 and n3 (j6 and j27, respectively) is the same for arches subjected to 10 mm horizontal displacement while the position of hinge n2 varied. The hinge mechanism observed during test UN.SD.04_20 is similar to that of tests UN.SD.02_10 and UN.SD.03_10 but there is a slight variation in the position of the hinges, as shown in Fig. 6d. However, it is worth noting that the second hinge appears two mortar joints before or after the brick b15 which means symmetric configuration that could be caused by irregular geometry [55–57]. On arches that were subjected to horizontal displacement and then preloaded before strengthening, the formation of a fourth hinge was observed (hinge LD n4 in Fig. 6b and 6d).

respect to both unstrengthened undamaged and damaged conditions. However, the effectiveness of the SFRM system for increasing the arch strength is more limited when unstrengthened damaged and strength­ ened damaged conditions due to horizontal settlement are compared. In addition to the increase in the arch strength, Fig. 7 shows that the SFRM significantly increases the initial stiffness of the strengthened arches with respect to the unstrengthened conditions. Fig. 7 shows that two distinct trends on the load F versus arch crown displacement d curves can be identified, although the initial stiffness is similar for the four tests. The curves for tests SFRM.LD.01_00 and SFRM. SLD.02_10 resemble those obtained during tests UN.ND.01_00 and UN. LD.01_00, with a long plateau after peak load is attained. Diversely, the curves for tests SFRM.SD.03_10 and SFRM.SLD.04_20 followed a linear behavior up to peak load followed by a rapid decrease in the applied load, as observed during tests UN.SD.02_10 and UN.SD.04_20. As shown in Table 3, the ductility of the strengthened specimens is significantly lower than those obtained during test UN.ND.01_00. However, as seen in Fig. 7, the strengthened arches can withstand high values of load for large values of displacement, which is an indication of the satisfactory ductility of the system (see Fig. 7). A similar behavior was reported by Carozzi et al. [25] for masonry arches strengthened with steel reinforced grouts (SRG).

3.2. Repaired arches 3.2.1. Applied force versus arch crown displacement Fig. 7 shows the load F versus arch crown displacement d curves obtained during the tests performed on strengthened arches. Results in Fig. 7 and Table 3 show that the SFRM strengthening can provide an increase in the arch strength with respect to test UN.ND.01_00 that ranges from 23.02 to 50.80 times, depending on the pre-damaged con­ dition. However, it is worth noting that values of increase in strength for strengthened specimens with respect to their corresponding predamaged unstrengthened condition are different from those reported in Table 3. For instance, the SFRM is able to increase the arch strength 32.80 times when compared to the undamaged condition (tests UN. ND.01_00 and SFRM.LD.01_00) or 41.6 times when compared to the damage condition (tests UN.LD.01_00 and SFRM.LD.01_00). On the other hand, specimens subjected to horizontal displacement on the springing showed an increase in the strength before strengthening, as seen in Fig. 5 and Table 3. Therefore, the increase in the arch strength provided by the SFRM given by the ratio Fmax/Fmax_C is higher than that obtained when unstrengthened and strengthened damaged conditions are compared. For instance, the ratio of values of peak load for tests UN. SD.04_20 and SFRM.SLD.04_20 is equal to 10.25 while the ratio Fmax/ Fmax_C for test SFRM.SLD.04_20 shown in Table 3 is 50.8. These results suggest that the SFRM system can increase the arch capacity with

3.2.2. Failure mode The failure mode of the strengthened specimens was characterized by the detachment of the SFRM layer from the masonry substrate, as shown in Fig. 8a. An inspection of the SFRM layer after the end of the test showed that the detachment was accompanied by peeling-off of the masonry substrate (see Fig. 8b). Before failure, the development of cracks on the SFRM surface, running perpendicular to the arch longi­ tudinal axis, was also observed (see Fig. 8c). Such cracks were located mainly below the point of application of the load and started appearing for values of load lower than the maximum load. In addition, some specimens showed crushing of bricks located around the point of application of the load (see Fig. 8d). The hinge mechanism was char­ acterized by the formation of four hinges after the load was applied (see Fig. 8e), as reported for unstrengthened specimens. As the displacement increased, cracks developed in earlier load stages continued to increase their width as shown in Fig. 8f for failure condition of arch SFRM. 7

N. Simoncello et al.

Composites Part B 177 (2019) 107386

from j13 to j15, respectively. 3.2.3. Strain development on the SFRM layer Values of longitudinal strain on the SFRM layer (ε) were acquired using the DIC system. With this aim, a horizontal virtual strain gauge, labelled as SG_DIC, was located at the bottom of the SFRM layer, un­ derneath the point of application of the load, as shown in Fig. 10. The initial gauge length was set equal to 25 mm. Values of strain at peak load (εFmax) presented in Table 3 show that, with exception of test SFRM.SD.02_10, higher values of strain at peak load are associated with higher values of peak load. As expressed pre­ viously, the early brick shear sliding observed during test SFRM. SD.02_10 might have influenced significantly the values of peak load and strain witnessed for this specimen. Fig. 11 shows the F/Fmax and ε/εFmax versus arch crown displacement d curves for all tests. For test SFRM.LD.01_00 (Fig. 11a), results show that before peak load there is a fast increase in the SFRM strains. For a displacement of around 1.5 mm, values of strain stabilize, and the curve is almost constant up to peak load. After peak load, values of strain start to decrease slowly, reaching a minimum value of ε/εFmax ¼ 0.75 for a displacement of 6.0 mm. It is interesting to note that for this case, the curves for F/Fmax and ε/εFmax, follow the same trend, which might be an indication of a linear relationship between the load and the SFRM strain. For tests SFRM.SD.03_10 and SFRM.SLD.04_20 (Fig. 11c and d, respec­ tively), the behavior up to peak load of parameter F/Fmax and ε/εFmax is similar to that described for test SFRM.LD.01_00. After peak load, however, values of F/Fmax for both tests show a higher decrease than that observed during test SFRM.LD.01_00. Regarding ε/εFmax, the curves show a similar behavior for the three tests. In fact, for d ¼ 6.0 mm, values of ε/εFmax observed during tests SFRM.LD.01_00, SFRM.SD.03_10, and SFRM.SLD.04_20 are almost the same (around 0.80). The behavior of the F/Fmax and ε/εFmax versus arch crown displace­ ment d curves for test SFRM.SLD.02_10 (Fig. 11b) differs from that described for the remaining three tests. In fact, for this specimen, values

Fig. 10. Location of the virtual strain gauge SG_DIC.

SD.03_10. During test SFRM.SLD.02_10, early local debonding of the SFRM layer without peeling-off of the substrate around the arch crown was observed (see Fig. 8a). As a result, shear sliding of the bricks around the point of application of the load was witnessed. The lower value of the maximum peak load attained for this specimen is attributed to this phenomenon. The hinge mechanisms for the strengthened specimens are shown in Fig. 9. When compared to unstrengthened specimens, it can be seen that it is mainly the same for all the specimens. However, the formation of a fourth hinge during test SFRM.SD.03_10 at the support (see Fig. 9c) was witnessed. In addition, for arch SFRM.SLD.04_20, location of hinges n1 and n2 varied from joint j5 in the unstrengthened configuration to j9,and

Fig. 11. Load and SFRM strain evolution for tests: a) SFRM.LD.01_00, b) SFRM.SLD.02_10, c) SFRM.SD.03_10, c) SFRM.SLD.04_20. 8

N. Simoncello et al.

Composites Part B 177 (2019) 107386

Fig. 12. Stress-strain diagrams: a) Compressive stress-strain of masonry, b) SFRM elasto-plastic tensile stress-strain; c) SFRM rigid-plastic tensile stress-strain.

Fig. 13. Strain distribution of a SFRM strengthened masonry arch cross-section subjected to axial force and a) negative bending moment, b) positive bending moment.

of F/Fmax continue increasing after the end of the elastic branch (d ¼ 0.8 mm) which was not observed during the other tests. In contrast with the other three tests, values of ε/εFmax for test SFRM.SLD.02_10 do

not show a linear relationship with F/Fmax during the initial elastic branch. It shows a rapid increase at the beginning of the test and sta­ bilize for a value of d ¼ 2.0 mm. After this point, values of ε/εFmax remain

Fig. 14. Strain and stress distributions corresponding to points in the M 9

N interaction diagram (positive bending moment).

N. Simoncello et al.

Composites Part B 177 (2019) 107386

Fig. 14. (continued).

almost constant, with a value of ε/εFmax for d ¼ 6.0 mm similar to those of the remaining tests. As explained before, such behavior can be explained by the atypical failure mode witnessed for this specimen which influenced significantly the maximum value of peak load and the overall performance of the arch.

The flexural capacity (in presence of axial force) is defined through an M N interaction curve while the shear capacity can be expressed in terms of the friction resistance between joints: SRd ¼ φ⋅NE

(3)

where φ is the friction coefficient. The internal forces (bending moment ME, shear force SE and axial force NE) were computed for a curved beam with homogenous section and then compared with the resisting ones. A M N interaction diagram for a masonry arch strengthened with a layer of SFRM can be computed based on the generic strain distribution shown in Fig. 13 and the stress-strain relationships of the masonry (Fig. 12a) and the SFRM material displayed in Fig. 12b.

4. Analytical prediction In this section, a simplified analytical procedure to check the ca­ pacity of an SFRM-strengthened arch is presented. In this procedure, the resisting forces were computed considering the hypothesis of perfect bond between SFRM and the substrate, and the constitutive law of the materials shown in Fig. 12. 10

N. Simoncello et al.

Fig. 15. M

Composites Part B 177 (2019) 107386

N diagram for unstrengthened and strengthened cross-sections.

When a negative bending moment is applied to the arch section, the top fibers are stretched and the layer of SFRM remains in compression (Fig. 13a). Considering a masonry section with thickness (s) and width (w) and an SFRM layer of thickness (sR), the resisting bending moment (MRd) and axial force (NRd) are given by Eq. (4): 8 NRd ¼ k⋅fm;c ⋅½ðx sR Þ⋅w þ ðwR ⋅sR Þ� > < � � (4) x þ sR s2R > : MRd ¼ k⋅fm;c ⋅ ðx sR Þ⋅w⋅ þ ⋅wR 2 2 where k⋅fm,c is the reduced ultimate masonry strength and x is the neutral axis depth (k ¼ 0.85, fm,c ¼ 6.21 MPa). In Fig. 12, values of εm,u, εSFRM,y and εSFRM,u are equal 0.35%, 0.04%, and 0.21%, respectively. When the positive bending moment is applied, the bottom fibers of the section are stretched, and the reinforcement is generally in tension (see Fig. 13b). For this case, six strain limit states (shown in Fig. 14) can be used to evaluate the corresponding points in the M N diagram: 8 NRd ¼ k⋅fm;c ⋅x⋅w þ NSFRM;t < � � � � (5) : MRd ¼ k⋅fm;c ⋅x⋅w s sR x þ NSFRM;t s 2 2 where NSFRM,t is the integral of tensile stresses σSFRM,t in the reinforce­ ment area (ASFRM), considering fSFRM,t ¼ 1.58 MPa: Z NSFRM;t ¼ σSFRM;t ⋅dASFRM (6) In general, the distribution of SFRM tensile stress change if the strain

Fig. 16. Elastic solution for curved beam. Axial load N(x), bending moment M (x), curvature χ (x), and S/N(x) diagrams.

compression stress of the masonry depends only on the neutral axis position. In Fig. 15, the M N diagram is reported referring to SFRM.LD.01_00 arch and a comparison between the unreinforced and reinforced con­ ditions is shown. The reinforcement increases the resisting compressive axial force and gives an amount of tensile axial resistance. Moreover, the flexural capacity of the section is increased with a greater increment for a positive bending moment. Fig. 15 also shows that the system is able to provide an increase not only to the negative bending moment and tensile axial load capacities of the arch, as has been observed for FRP and FRCM strengthened arches [36,58], but also to the positive bending moment and compressive axial load strength. With the aim of simplifying the proposed analytical procedure, it is possible to adopt a tensile rigid-plastic behavior of the SFRM, as shown in Fig. 12c. Considering that the area of the reinforcement is small compared to that of the arch, this simplification should not imply a significant modification of the M N diagram shown in Fig. 15. In fact, a

comparison between the M N diagrams computed using an elasticplastic or a rigid-plastic constitutive law for the SFRM under tension showed a difference less than 1%. After the construction of the M N interaction diagram of the strengthened arch section, an elastic solution of the strengthened arch was performed with the aim to validate the analytical procedure through experimental evidence. The analysis was carried out considering a linear elastic curved beam with fixed supports, homogenized cross-section, a mid-span concentrated load (P) equal to 11 kN, and is reported in terms of internal forces (M and N) and curvature (χ) diagrams in Fig. 16. The value of the load P corresponds to the load at the end of the elastic branch on the applied load versus arch crown displacement curve wit­ nessed for the test SFRM.LD.01_00 (see Fig. 8). For the three sections of the curved beam shown in Fig. 16 (section 1 is at arch base, Section 2 where positive bending moment is maximum and Section 3 at the arch crown), it is possible to verify that the corre­ sponding bending moment and axial force (ME, NE) couples of each

εt,1 (i.e., strain at the top of the SFRM layer) is lower or reaches/exceeds the yield strain of the SFRM material (εSFRM,y ¼ 0.04%) while the

11

N. Simoncello et al.

Composites Part B 177 (2019) 107386

section are located inside the M N domain (see Fig. 15). For the analyzed condition, it is worth noting that for section 2, the corresponding bending moment and axial load couple is located near the N-M envelope which validates the analytical prediction. It is highlighted that in the analytical procedure here presented, partial safety factors were not considered. Otherwise, the procedure would have defined an ultimate point load lower than 11 kN. Fig. 16 shows that values of the ratio SE/NE at the arch base and arch crown are greater than 0.60, i.e, the friction coefficient commonly used for masonry structures. This result implies that failure of the arches due to shear sliding should have occurred at a value approximately 35% lower than the one obtained during the experimental test (11 kN). As pointed out by Ref. [59] for FRP strengthened arches, the presence of the SFRM layer in this case provides an addition contribution to the sliding resistance of the arch that diminishes the possibility of occurrence of failure due to shear sliding. However, it is worth noting that for arch SFRM.SLD.02_10, early shear sliding was witnessed, as described in Section 3.2.2. For this case, the contribution of the SFRM layer to the sliding resistance of the arch might have been compromised by a local decrease in the bond between the SFRM and the masonry substrate, due probably to issues related to the strengthening procedure of this arch.

early shear sliding of the bricks around the point of application of the load. � An analytical model aimed to obtain the M N interaction diagram for an SFRM strengthened arch was developed considering an elastoplastic tensile stress-strain behavior for the SFRM. When compared to a simplified approach using a rigid-plastic tensile constitutive law for the strengthening material, the difference between the M N diagrams developed by each approach were less than 1%. Results show that the SFRM layer is able to provide the capacity to resist tensile and compressive axial forces, and negative and bending moments. � In order to validate the model, values of moment, and axial load in the arch were obtained by idealizing the arch as a linear elastic curved beam with fixed supports, using the maximum applied load obtained for the arch subjected to damage by preloading. It was observed that the bending moment and axial force couples computed in this way fall inside the analytical M N domain which verifies the proposed analytical procedure. � Values of shear to axial ratio at the arch base and arch crown ob­ tained using the idealized curved beam are higher than that commonly used for masonry structures (i.e., 0.60). Based on the experimental results obtained for the strengthened arch subjected to damage due to pre-loading, this finding suggests that the increase in the shear sliding capacity of the arch due to the SFRM layer is around 35%.

5. Conclusions In this paper, steel fiber reinforced mortar (SFRM) was used to strengthen solid clay masonry bricks. Before strengthening, the arches were subjected to pre-damage conditions consisting in pre-loading, horizontal displacement of one of the supports, or a combination of both. Experimental results were analyzed in terms of failure mode and influence of the SFRM strengthening on the load carrying capacity and ductility of the strengthened arches with respect to the unstrengthened undamaged condition. In addition, an analytical design method for the design and assessment of arches strengthened with SFRM was developed and the results were compared to those obtained experimentally. The main conclusions of this study can be summarized as follows:

The above conclusions verify that the SFRM material is a valid technique for the strengthening of masonry arches, as it can provide a significant increase in terms of load-carrying capacity. However, further investigation is required in order to increase the knowledge regarding the behavior of masonry members strengthened with this material. Specifically, research efforts need to be made on the material charac­ terization and the study of the SFRM-masonry bond behavior, required for the development of more precise prediction models based on limit or non-liner numerical analysis. Acknowledgements

� Results show that the damage caused by preloading implied a reduction in the load carrying capacity of around 23% when compared to the undamaged test, due to the loss of bond between the mortar and bricks where hinges formed during the first loading. When a horizontal displacement in one of the supports was applied, the change in the arch rise to span length ratio and an imposed location of the hinges by the displacement caused a significant in­ crease on the load carrying capacity of the arch. However, such behavior was accompanied by an important reduction of the ductility of the arch with respect to the undamaged specimen, irrespectively of the magnitude of the horizontal displacement. � For the case of the arch subjected only to preloading, an increase in the load carrying capacity of SFRM strengthened arch of 32.16 times with respect to the undamaged unstrengthened condition was wit­ nessed. When the damaged included horizontal displacement, the maximum observed increase was equal to 50.80 times with respect to the undamaged unstrengthened condition or 10.25 times with respected to the corresponding damaged unstrengthened condition. � SFRM specimens showed a significant decrease in the ductility when compared to the undamaged unstrengthened counterpart, according to the criteria used in the paper to define the specimens’ ductility. However, it was witnessed that strengthened arches can withstand high values of load for large values of displacement, which is a valid indication of the satisfactory ductility of the system. � The hinge mechanism observed for the SFRM strengthened arches was comprised of four hinges and resembles that observed for unstrengthened specimens. At failure, detachment of the SFRM accompanied by peeling-off the masonry substrate was witnessed. Additional failure mode mechanisms include masonry crushing and

Eng. P. Napolitano and Mr. L. Martin are gratefully acknowledged for providing the SFRM composite material. Authors would like to thank master student Fabio Perusco for his help during the development of the experimental campaign. References [1] Brencich A, Morbiducci R. Masonry arches: historical rules and modern mechanics. Int. J. Archit. Herit. 2007;1(2):165–89. https://doi.org/10.1080/1558305070 1312926. [2] Giamundo V, Lignola GP, Maddaloni G, Balsamo A, Prota A, Manfredi G. Experimental investigation of the seismic performances of IMG reinforcement on curved masonry elements. Compos. B Eng. 2015;70:53–63. https://doi.org/ 10.1016/j.compositesb.2014.10.039. [3] Gattesco N, Boem I, Andretta V. Experimental behaviour of non-structural masonry vaults reinforced through fibre-reinforced mortar coating and subjected to cyclic horizontal loads. Eng. Struct. 2018;172:419–31. https://doi.org/10.1016/j. engstruct.2018.06.044. [4] Bertolesi E, Milani G, Carozzi FG, Poggi C. Ancient masonry arches and vaults strengthened with TRM , SRG and FRP composites : numerical analyses. Compos. Struct. 2018;187:385–402. https://doi.org/10.1016/j.compstruct.2017.12.021. [5] De Santis S. Bond behaviour of Steel Reinforced Grout for the extrados strengthening of masonry vaults. Constr. Build. Mater. 2017;150:367–82. https://doi.org/10.1016/j.conbuildmat.2017.06.010. [6] De Santis S, Roscini F, De Felice G. Full-scale tests on masonry vaults strengthened with steel reinforced grout. Compos. Part B 2018;141:20–36. https://doi.org/10 .1016/j.compositesb.2017.12.023. [7] Tao Y, Stratford TJ, Chen JF. Behaviour of a masonry arch bridge repaired using fibre-reinforced polymer composites. Eng. Struct. 2011;33:1594–606. https://doi. org/10.1016/j.engstruct.2011.01.029. [8] Galassi S. Analysis of masonry arches reinforced with FRP sheets: experimental results and numerical evaluations. MATEC Web Conf. 2018;207:01002. https:// doi.org/10.1051/matecconf/201820701002.

12

N. Simoncello et al.

Composites Part B 177 (2019) 107386 [34] Garmendia L, San-Jos�e JT, García D, Larrinaga P. Rehabilitation of masonry arches with compatible advanced composite material. Constr. Build. Mater. 2011;25: 4374–85. https://doi.org/10.1016/j.conbuildmat.2011.03.065. [35] Misseri G, Rovero L, Stipo G, Barducci S, Alecci V, De Stefano M. Experimental and analytical investigations on sustainable and innovative strengthening systems for masonry arches. Compos. Struct. 2019;210:526–37. https://doi.org/10.1016/j. compstruct.2018.11.054. [36] Alecci V, Focacci F, Rovero L, Stipo G, De Stefano M. Intrados strengthening of brick masonry arches with different FRCM composites: experimental and analytical investigations. Compos. Struct. 2017;176:898–909. https://doi.org/10.1016/j.com pstruct.2017.06.023. [37] Alecci V, Focacci F, Rovero L, Stipo G, De Stefano M. Extrados strengthening of brick masonry arches with PBO – FRCM composites : experimental and analytical investigations. Compos. Struct. 2016;149:184–96. https://doi.org/10.1016/j.com pstruct.2016.04.030. [38] Garmendia L, Marcos I, Garbin E, Valluzzi MR. Strengthening of masonry arches with Textile-Reinforced Mortar: experimental behaviour and analytical approaches. Mater. Struct. Constr. 2014;47:2067–80. https://doi.org/10.1617/ s11527-014-0339-y. [39] Alecci V, Misseri G, Rovero L, Stipo G, De Stefano M, Feo L, Luciano R. Experimental investigation on masonry arches strengthened with PBO-FRCM composite. Compos. B Eng 2016;100:228–39. https://doi.org/10.1016/j.compo sitesb.2016.05.063. [40] Zampieri P, Simoncello N, Tetougueni CD, Pellegrino C. A review of methods for strengthening of masonry arches with composite materials. Eng. Struct. 2018;154. 169–2, https://doi.org/10.1016/j.engstruct.2018.05.070. [41] Greco F, Leonetti L, Lonetti P. A novel approach based on ALE and delamination fracture mechanics for multilayered composite beams. Compos. B Eng. 2015;78: 447–58. [42] Bruno D, Greco F, Lonetti P. Dynamic mode I and mode II crack propagation in fiber reinforced composites. Mech. Adv. Mater. Struct. 2009;16(6):442–5. [43] Bruno D, Greco F, Lonetti P. Computation of energy release rate and mode separation in delaminated composite plates by using plate and interface variables. Mech. Adv. Mater. Struct. 2005;12(4):285–304. [44] Lonetti P. Dynamic propagation phenomena of multiple delaminations in composite structures. Comput. Mater .Sci. 2010;48(3):563–75. [45] Sevil T, Baran M, Bilir T, Canbay E. Use of steel fiber reinforced mortar for seismic strengthening. Constr. Build. Mater. 2011;25:892–9. https://doi.org/10.1016/j.co nbuildmat.2010.06.096. [46] Tsonos ADG. A new method for earthquake strengthening of old R/C structures without the use of conventional reinforcement. Struct. Eng. Mech. 2014;52: 391–403. https://doi.org/10.12989/sem.2014.52.2.391. [47] Altun F, Haktanir T, Ari K. Effects of steel fiber addition on mechanical properties of concrete and RC beams. Constr. Build. Mater. 2007;21:654–61. https://doi.org/ 10.1016/j.conbuildmat.2005.12.006. [48] UNI EN 998-2_2016. Specification for Mortar for Masonry - Part 2_ Masonry Mortar. [49] UNI-EN 1015-11. Methods of Test for Mortar for Masonry - Determination of Flexural and Compressive Strength of Hardened Mortar. [50] UNI EN 13412:2007. Products and Systems for the Protection and Repair of Concrete Structures - Test Methods - Determination of Modulus of Elasticity in Compression. [51] EN 1996-1 1 2005;1. Eurocode6. Structures G Rules for Reinforced and Unreinforced Masonry. [52] Stockdale GL, Sarhosis V, Milani G. Seismic capacity and multi mechanism analysis for dry stack masonry arches subjected to hinge control. Bull. Earthq. Eng. 2019: 1–52. https://doi.org/10.1007/s10518-019-00583-7. [53] Heyman J. The masonry arch. Ellis Horwood Ltd; 1982. [54] Heyman J. The stone skeleton. Int. J. Solids Struct 1966;2(Issue 2):249–79. ISSN 0020-7683, https://doi.org/10.1016/0020. [55] Cavalagli N, Gusella V, Severini L. The safety of masonry arches with uncertain geometry. Comput. Struct. 2017;188:17–31. https://doi.org/10.1016/j.co mpstruc.2017.04.003. [56] Cavalagli N, Gusella V, Severini L. Effect of geometric irregularities on the dynamic response of masonry arches. Procedia Eng. 2017;199:1140–5. https://doi.org/10 .1016/j.proeng.2017.09.242. [57] Zampieri P, Cavalagli N, Gusella V, Pellegrino C. Collapse displacements of masonry arch with geometrical uncertainties on spreading supports. Comput. Struct. 2018;208:118–29. https://doi.org/10.1016/j.compstruc.2018.07.001. [58] Caporale A, Feo L, Hui D, Luciano R. Debonding of FRP in multi-span masonry arch structures via limit analysis. Compos. Struct. 2014;108:856–65. https://doi. org/10.1016/j.compstruct.2013.10.006. [59] Valluzzi MR, Valdemarca M, Modena C. Behavior of brick masonry vaults strengthened by FRP laminates. J. Compos. Constr. 2001:163–9. https://doi. org/10.1061/(ASCE)1090-0268(2001)5:3(163).

[9] Caporale A, Luciano R, Sacco E. Micromechanical analysis of interfacial debonding in unidirectional fiber-reinforced composites. Comput. Struct. 2006;84:2200–11. https://doi.org/10.1016/j.compstruc.2006.08.023. [10] Caporale A, Luciano R, Rosati L. Limit analysis of masonry arches with externally bonded FRP reinforcements. Comput. Methods Appl. Mech. Eng. 2006;196: 247–60. https://doi.org/10.1016/j.cma.2006.03.003. [11] Greco F, Leonetti L, Luciano R, Nevone P. An adaptive multiscale strategy for the damage analysis of masonry modeled as a composite material. Compos. Struct. 2016;153:972–88. https://doi.org/10.1016/j.compstruct.2016.06.066. [12] De Felice G. Assessment of the load-carrying capacity of multi-span masonry arch bridges using fibre beam elements. Eng. Struct. 2009;31:1634–47. https://doi.org/ 10.1016/j.engstruct.2009.02.022. [13] Cannizzaro F, Pant� o B, Caddemi S, Cali� o I. A Discrete Macro-Element Method (DMEM) for the nonlinear structural assessment of masonry arches. Eng. Struct. 2018;168:243–56. https://doi.org/10.1016/j.engstruct.2012.02.039. [14] Pant� o B, Cannizzaro F, Caddemi S, Cali� o I, Ch� acara C, Lourenço PB. Nonlinear modelling of curved masonry structures after seismic retrofit through FRP reinforcing. Buildings 2017;7(3):79. https://doi.org/10.3390/buildings7030079. [15] Cavalagli N, Gusella V, Severini L. Lateral loads carrying capacity and minimum thickness of circular and pointed masonry arches. Int. J. Mech. Sci. 2016;115–116: 645–56. https://doi.org/10.1016/j.ijmecsci.2016.07.015. [16] Galassi S. A numerical procedure for failure mode detection of masonry arches reinforced with fiber reinforced polymeric materials. IOP Conf. Ser: Mater. Sci. Eng. 2018;369:012038. https://doi.org/10.1088/1757-899X/369/1/012038. [17] Tempesta G, Galassi S. Safety evaluation of masonry arches. A numerical procedure based on the thrust line closest to the geometrical axis. Int. J. Mech. Sci. 2019;155: 2016–221. https://doi.org/10.1016/j.ijmecsci.2019.02.036. [18] Coccia S, Di F, Zila C. Collapse displacements for a mechanism of spreadinginduced supports in a masonry arch. Int. J. Adv. Struct. Eng. 2015;7:307–20. htt ps://doi.org/10.1007/s40091-015-0101-x. [19] Zampieri P, Faleschini F, Zanini MA, Simoncello N. Collapse mechanisms of masonry arches with settled springing. Eng. Struct. 2018;156. https://doi.org/10 .1016/j.conbuildmat.2016.05.024. [20] Galassi S, Misseri G, Rovero L, Tempesta G. Failure modes prediction of masonry voussoir arches on moving supports. Eng. Struct. 2018;173:706–17. https://doi. org/10.1016/j.engstruct.2018.07.015. [21] Zampieri P, Simoncello N, Pellegrino C. Structural behaviour of masonry arch with no-horizontal springing settlement. Frat. Ed. Integrit� a. Strutt. 2018;12. https://doi. org/10.3221/IGF-ESIS.43.14. [22] Oliveira DV, Basilio I, Lourenço PB. Experimental behavior of FRP strengthened masonry arches. ASCE 2010;14:312–22. https://doi.org/10.1061/(ASCE)CC.19435614.0000086. [23] Feo L, Luciano R, Misseri G, Rovero L. Irregular stone masonries : analysis and strengthening with glass fibre reinforced composites. Compos. Part B 2016;92: 84–93. https://doi.org/10.1016/j.compositesb.2016.02.038. [24] Caporale A, Luciano R. Limit analysis of masonry arches with finite compressive strength and externally bonded reinforcement. Compos. Part B 2012;43:3131–45. https://doi.org/10.1016/j.compositesb.2012.04.015. [25] Carozzi FG, Poggi C, Bertolesi E, Milani G. Ancient masonry arches and vaults strengthened with TRM , SRG and FRP composites : experimental evaluation. Compos. Struct. 2018;187:466–80. https://doi.org/10.1016/j.compstruct.2017. 12.075. [26] Borri A, Castori G, Corradi M. Intrados strengthening of brick masonry arches with composite materials. Compos. Part B 2011;42:1164–72. https://doi.org/10.1016/j. compositesb.2011.03.005. [27] Caporale A, Feo L, Luciano R, Penna R. Numerical collapse load of multi-span masonry arch structures with FRP reinforcement. Compos. Part B 2013;54:71–84. https://doi.org/10.1016/j.compositesb.2013.04.042. [28] Caporale A, Feo L, Luciano R. Limit analysis of FRP strengthened masonry arches via nonlinear and linear programming. Compos. Part B 2012;43:439–46. http s://doi.org/10.1016/j.compositesb.2011.05.019. [29] Wang P, Chen H, Zhou J, Zhou Y, Wang B, Jiang M, Jin F, Fan H. Failure mechanisms of CFRP-wrapped protective concrete arches under static and blast loadings : experimental research. Compos. Struct. 2018;198:1–10. https://doi. org/10.1016/j.compstruct.2018.05.063. [30] Capani F, D’Ambrisi A, De Stefano M, Focacci F, Luciano R, Nudo R, Penna R. Experimental investigation on cyclic response of RC elements repaired by CFRP external reinforcing systems. Compos. Part B 2017;112:290–9. https://doi.org/10 .1016/j.compositesb.2016.12.053. [31] Triantafillou TC, Papanicolaou CG. Shear strengthening of reinforced concrete members with textile reinforced mortar (TRM) jackets. Mater. Struct. 2006: 93–103. https://doi.org/10.1617/s11527-005-9034-3. [32] Castori G, Borri A, Corradi M. Behavior of thin masonry arches repaired using composite materials. Compos. Part B 2016;87:311–21. https://doi.org/10.1016/j. compositesb.2015.09.008. [33] Greco F, Leonetti L, Luciano R, Trovalusci P. Multiscale failure analysis of periodic masonry structures with traditional and fi ber-reinforced mortar joints. Compos. Part B 2017;118:75–95. https://doi.org/10.1016/j.compositesb.2017.03.004.

13