Construction and Building Materials 65 (2014) 243–253

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Construction and Building Materials

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Shear strengthening of un-reinforced concrete masonry wallswith fabric-reinforced-cementitious-matrix

http://dx.doi.org/10.1016/j.conbuildmat.2014.04.1160950-0618/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 732 298 4859.E-mail addresses: s.babaeidarabad@umiami.edu (S. Babaeidarabad), d.arboleda@

umiami.edu (D. Arboleda), giovanni.loreto.gl@gmail.com (G. Loreto), nanni@miami.edu(A. Nanni).

Saman Babaeidarabad ⇑, Diana Arboleda, Giovanni Loreto, Antonio NanniDepartment of Civil, Architectural, and Environmental Engineering, University of Miami, Miami, FL 33146, USA

h i g h l i g h t s

� The effectiveness of FRCM composite for strengthening of masonry walls was investigated.� A total of nine concrete masonry wall panels, 1.2 m � 1.2 m in size, were tested under diagonal compression.� FRCM and FRP strengthened walls were compared after normalizing the data.� The experimental results were also compared with analytical model predictions.

a r t i c l e i n f o

Article history:Received 13 November 2013Received in revised form 13 April 2014Accepted 23 April 2014

Keywords:Concrete URMFabric-reinforced-cementitious matrixRetrofittingShearStrengthening

a b s t r a c t

In this paper, the in-plane behavior of un-reinforced concrete masonry walls externally strengthenedwith a fabric-reinforced cementitious matrix (FRCM) system is investigated. The experimental programconsists of testing nine un-reinforced concrete masonry walls strengthened on both sides with twodifferent FRCM schemes (one and four reinforcement fabrics). The analytical model as per ACI 549-13is used to predict the shear capacity of the strengthened walls. The effects of design limitations in theapproach proposed by ACI 549-13 are also discussed. Finally, experimental data from other researchprograms using fiber-reinforced polymer (FRP) composites are presented to demonstrate that whennormalized shear capacity is related to a calibrated reinforcement ratio, the two overlay strengtheningtechnologies match well.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Masonry is one of the oldest construction materials.Un-reinforced masonry (URM) walls are a widespread constructionpractice around the world, but are not well-suited to withstandin-plane loading and may exhibit brittle failure followed byscattering of debris. Retrofitting masonry walls with techniquessuch as externally-bonded fiber reinforced polymer (FRP) and nearsurface mounted (NSM) FRP bars effectively enhances shear capac-ity and pseudo-ductility, and controls the scatter of fragmentswhich can be a threat to life [1–7]. Depending on the masonry’sphysical and mechanical properties, the failure modes of URMwalls subjected to in-plane loading as identified by tests [1–11],ACI 440-10 [12], and ASCE 41 [13], are: diagonal tensile cracking,joint sliding, and toe crushing. Diagonal tensile cracking typicallyoccurs with the formation of a single diagonal crack through

concrete masonry units. Shear sliding can form along a single mor-tar bed joint or along multi-bed and head joints in a step format.Toe crushing failure may occur at the compressed corners.

Grando et al. [1] and Tumialan [10] performed experiments byapplying diagonal compression to concrete masonry walls retrofit-ted with externally-bonded glass FRP (GFRP) laminates or GFRPNSM bars in the mortar joints. Results showed a remarkableenhancement in shear capacity. Likewise, Li et al. [2] carried outan experimental program on concrete masonry walls under diago-nal compression after strengthening them with different schemesof GFRP NSM bars or GFRP strips. Strengthened walls showed sig-nificantly improved in-plane behavior in terms of load carryingcapacity and pseudo-ductility. Yu et al. [11] tested under diagonalcompression concrete block walls strengthened externally withdifferent amounts of GFRP grid-reinforced polyurea. The resultsagain showed considerable improvements in shear capacity.

The popularity of FRP stems from its lightweight, simplicity ofapplication, and availability in different forms such as pre-curedlaminates, sheets, grids, and bars [12,14]. Despite improvement interms of strength and pseudo-ductility, the externally-bonded FRPtechnology has some limitations: inability to install FRP on damp

Nomenclature

Af area of mesh reinforcement by unit width, mm2/mm(in2/in)

Am interface loading area between steel shoe and wall,mm2 (in2)

An net area cross-sectional of masonry wall, mm2 (in2)E�f tensile modulus of elasticity of the un-cracked FRCM

specimen, GPa (ksi)Ef tensile modulus of elasticity of the cracked FRCM spec-

imen and other strengthening system, MPa (ksi)Em modulus of elasticity of masonry wall, MPa (ksi)fc compressive strength of mortar, MPa (psi)fft transition stress corresponding to the transition point,

MPa (psi)ffu ultimate tensile strength of FRCM, MPa (ksi)ffv design tensile strength of FRCM shear reinforcement,

MPa (ksi)f 0m compressive strength of masonry, MPa (psi)f 0t tensile strength of masonry, MPa (psi)G shear modulus of rigidity of masonry wall, GPa (ksi)h concrete block height, mm (in)H wall height, mm (in)L wall length in the direction of the shear force, mm (in)n number of fabric layersP applied load (geometrically 1.414 times the shear force

in a square wall, kN (kip)t wall thickness, mm (in)Vc masonry wall shear capacity due to compression failure,

kN (kip)Vdt masonry wall shear capacity due to diagonal tension

failure, kN (kip)Vf contribution of FRCM to nominal shear strength of the

wall, kN (kip)

Vm contribution of masonry to nominal shear strength ofthe wall, kN (kip)

Vn nominal shear strength, kN (kip)Vsf masonry wall shear friction capacity, kN (kip)Vss masonry wall shear sliding capacity, kN (kip)w length of concrete block, mm (in)h inclined angle between horizontal and main diagonal of

wall, degl pseudo-ductility of masonry walll0 coefficient of internal shear friction in mortar jointlm modified coefficient of internal shear friction in mortar

jointccr shear strain at cracking, mm/mm (in/in)cu shear strain of the masonry at ultimate, mm/mm (in/in)eft transition strain corresponding to the transition point,

mm/mm (in/in)efu ultimate tensile strain of the FRCM, mm/mm (in/in)efv design tensile strain of FRCM shear reinforcement, mm/

mm (in/in)rc principal compression stress at the center of wall in-

duced by diagonal forces, MPa (psi)rt principal tension stress at the center of wall induced by

diagonal forces, MPa (psi)s0 shear bond strength in mortar joint, MPa (psi)s0,m modified shear bond strength in mortar joint, MPa (psi)scr shear stress at cracking, MPa (psi)su shear stress of the masonry at ultimate, MPa (psi)Uv strength reduction factor for shearxf calibrated reinforcement ratioq the ratio between area of FRCM/FRP reinforcement and

net area of URM walls

244 S. Babaeidarabad et al. / Construction and Building Materials 65 (2014) 243–253

substrate; poor behavior of the resin at temperatures above its glasstransition temperature; and, lack of vapor permeability, which maycause damage to the substrate [14–17]. An opportunity exists tocomplement FRP systems with an alternative that replaces theorganic binder (e.g., epoxy) with an inorganic one (e.g., cementitiousmortar) [15–17]. Accordingly, fabric-reinforced cementitiousmatrix (FRCM) has emerged as an innovative external retrofit tech-nology. FRCM was introduced in previous studies [16–21] for bothnew construction and repair (the topical area of interest in thispaper) under various terms, namely: textile reinforced mortar(TRM), textile reinforced concrete (TRC), cementitious matrix-grid(CMG), or inorganic matrix-grid (IMG) composite.

Parisi et al. [3] and Prota et al. [21] performed comprehensiveexperimental studies on tuff masonry under diagonal compressionafter externally strengthening with FRCM. Their experimentalresults showed that retrofitted walls achieved higher shearstrength and pseudo-ductility. Papanicolaou et al. [16,17] studiedthe effectiveness of FRCM to retrofit perforated clay brick/solidstone block walls subjected to in-plane and out-of-plane cyclicloading. Results showed again that FRCM provided substantialenhancements in terms of shear capacity and pseudo-ductility,proportionally to the number of reinforcement layers. Babaeidara-bad et al. [22–24] tested clay brick masonry walls strengthenedwith carbon-FRCM reinforcement under diagonal compressionand out-of-plane loading. Retrofitted walls showed significantenhancements in terms of strength and pseudo-ductility.

This paper presents an experimental program whereun-reinforced concrete masonry walls were externally retrofittedon both sides with carbon-FRCM and subjected to diagonalcompression. FRCM consists of a sequence of one or four layers

of carbon fabric applied to the wall surface through a mortar rein-forced with short fibers. The mortar is made of combinations ofPortland cement, silica fume and fly ash acting as the inorganicbinder plus silica sand. The fabric consists of primary directionand secondary direction strands where polymeric coatings areapplied to the fibers only to enhance the long-term durabilityand to prevent problems associated with handling and installation[15]. Results of this project are compared with the existing exper-imental database obtained on concrete masonry walls strength-ened with FRP under the same test setup configuration showingthat the two overlay strengthening technologies are comparableand provide similar results. Following ACI 549-13 [25] provisions,shear capacity is calculated for both prediction and design.

2. Experimental program

2.1. Specimens

Nine un-reinforced concrete masonry walls, 1220 by 1220 by 92 mm (48 by 48by 3.63 in), were fabricated in a running bond pattern by a professional mason toensure compliance with good construction practices. Six walls were externallystrengthened with 1-ply and 4-ply FRCM covering both faces of the wall. In accor-dance to the requirements of AC434-13 [26], 1-ply and 4-ply were tested as thepossible extreme amounts of reinforcement. A 4-ply FRCM system was selectedas the highest level of reinforcement possible.

2.2. Material characterization

The nominal dimensions of the concrete blocks used in the construction of thewalls were 102 by 203 by 406 mm (4 by 8 by 16 in), with a net area of 24,322 mm2

(37.7 in2). Four prisms were built with three stacked concrete blocks match-curedwith the walls. Testing (ASTM C1314-12 [27]) resulted in an average net-area com-pressive strength of 19.5 MPa (2823 psi) and a coefficient of variation (C.O.V) of

Fig. 1. C-10 carbon fabric.

Table 1Mechanical properties of carbon FRCM coupons.

FRCM property (1) Symbol (2) Units (3) Mean (4) Standard deviation (5) C.O.V (6)

Modulus of elasticity (un-cracked) E�f GPa 813 212 26

Modulus of elasticity (cracked) Ef GPa 80 18 23Ultimate tensile strength ffu MPa 1031 54 5Ultimate tensile strain efu mm/mm 0.0100 0.0014 14Fiber area by unit width (One direction) Af mm2/mm 0.05 – –

Note: 1.0 GPa = 145.03 ksi; 1.0 MPa = 0.145 ksi; 1.0 mm/mm = 1.0 in/in; 1.0 mm2/mm = 0.039 in2/in.

S. Babaeidarabad et al. / Construction and Building Materials 65 (2014) 243–253 245

5.9%. A type M mortar was utilized to build the walls, having an average compres-sive strength of 22.0 MPa (3193 psi) and C.O.V of 5.2% when tested in accordancewith ASTM C109/C109M-12 [28]. FRCM was used for strengthening the walls ascomposed of a sequence of one or four carbon fabrics embedded in a cement-basedmatrix. The fabric consisted of a balanced network of dry carbon-fiber toes disposedalong two orthogonal directions at a nominal spacing of 10 mm (0.394 in) (seeFig. 1). The equivalent nominal fiber thickness was 0.048 mm (0.0019 in) in bothprimary and secondary directions.

Arboleda et al. [29] performed experimental tensile testing on carbon FRCMcoupons in order to identify the mechanical properties (see Table 1). Specimenswere tested by applying a monotonically-increasing uniaxial tensile load in accor-dance with AC434-13 [26]. Clevis-type grips were attached at both ends of the spec-imen allowing fiber slippage to control failure. Axial deformation was measured viaa clip-on extensometer with a 100-mm (4-in) gauge length attached at the speci-men mid-height (Fig. 2). Coupon test results are presented in Table 1, where Col-umns (1), (2), and (3) list the FRCM properties of relevance, symbol, and units,while Columns (4), (5), and (6) show mean, standard deviation, and C.O.V.,respectively.

The mechanical properties of the un-reinforced concrete masonry prisms andthe FRCM coupons were used as the basis of the analytical and design work.

2.3. Setup

The walls were loaded diagonally by means of two parallel jacks each withcapacity of 299 kN (67 kips) positioned at the top corner. The steel shoes, placedon diagonally-opposite corners of the wall, transferred the force to the wall

Fig. 2. FRCM coup

(Fig. 3). All walls were tested under load control. Two steel Dywidag rods pene-trated the shoes, creating a close-loop system. Two load cells were set on the bot-tom corner of the wall in order to measure the applied loads. Two linear variabledifferential transducers (LVDT’s) with gage length of 30 mm (1.2 in) were placedon both faces of the walls: one LVDT was oriented along the compression line tomeasure the wall shortening, while the other was perpendicular to the line of com-pression to record the wall elongation. Two strain gauges were attached at the cen-ter of the strengthened walls on each face. Also, two strain gauges were installed oneach Dywidag rod (front and back) to validate the load registered by the load cells.Walls were tested in three cycles of loading and unloading, where the last cycle wascontinued till failure. All data were gathered at a frequency of 10 Hz using aNational Instruments data acquisition system operating LabVIEW™ software.Fig. 3 shows the test setup configuration with the instrumentation including loadcells, LVDT’s, and strain gauges.

2.4. Results

2.4.1. Discussion of resultsExperimental results in terms of ultimate load capacity, average load for each

set, and failure mode are presented in Columns (1), (2) and (3) of Table 3, respec-tively. The failure load described in this section relates to the maximum applieddiagonal load, Pu, which was measured by the load cells. Since the tested walls weresquare in shape, the horizontal shear component, Vu, was simply obtained bymultiplying the peak load, Pu, by the cosine of 45� (Fig. 4).

on test setup.

Fig. 3. Test setup.

246 S. Babaeidarabad et al. / Construction and Building Materials 65 (2014) 243–253

2.4.1.1. Control walls. As stated in Column (3) of Table 2, failure of three controlspecimens was by diagonal tensile cracking starting at the upper corner of the walland progressing diagonally in the blocks (see Fig. 5a). Diagonal tensile crackingoccurs when the principal tension stress induced by combination of shear and com-pressive forces reaches the tensile strength of the masonry. The average ultimateload at failure, Pu,ave, registered for three control specimens was 109.4 kN(24.6 kips).

2.4.1.2. 1-ply FRCM strengthened walls. The three URM walls strengthened with 1-ply failed by toe crushing (see Fig. 5b). The average ultimate load was 212.9 kN(47.9 kips) which was about two times that of the control walls (Column (2) ofTable 2). FRCM was effective in increasing the shear capacity by constraining diag-onal tensile cracking and transferring tensile stresses across diagonal cracks. Somesplit cracking of the blocks was observed as shown in Fig. 5b.

2.4.1.3. 4-ply FRCM strengthened walls. The three URM walls strengthened with 4-ply FRCM showed toe crushing failure at the loaded corners (Fig. 5c). Toe crushingfailure preceded shear failure similar to the case of 1-ply strengthening. The averageultimate load was 257.6 kN (57.9 kips) only about 17% higher than that of the wallstrengthened with a single ply (Column (2) of Table 2). The relatively small increaseis justified by the fact that the compressive strength of the masonry controls failure.The presence of 4-ply FRCM, because of its thickness, provides more contributionthan the single ply FRCM.

In order to compute effectiveness of FRCM, strength enhancement is defined asthe ratio between the average maximum applied load for each set of walls and thecontrol. It is observed that strength enhancements are 1.95 and 2.36 for 1-ply and4-ply FRCM, respectively.

2.4.2. Shear stress–shear strain diagramsASTM E519/E519M-10 [30] assumes that a uniform shear stress flow, s, takes

place along the loaded diagonal of a square wall when subjected to diagonal com-pression. The Mohr’s circle corresponding to this condition is shown in Fig. 4. Theshear stress is equal to both tensile and compressive principal stresses, representinga pure shear stress state [3]. According to ASTM E519/E519M-10 [30], the shearstress of any value of P is calculated as s = 0.707 P/An, where P and An are the diag-onal applied load and net cross-sectional area of the un-cracked section of the wallpanels (An = 72903 mm2 (113 in2)), respectively. The shear strain, c, was computedas c = ec + et, where the strains, ec and et, are the principal compressive and tensilestrains along the diagonals, respectively [2,9,10,22,30]. During testing of thestrengthened walls, ec and et were measured by strain gauges attached at the centerof the masonry panel on each face. The average strains in the un-strengthened wallswere computed from the displacement measured by the LVDT’s over the compres-sion and tension diagonals of the wall. Based on ASTM E519/E519M-10 [30] andassuming uniform shear strain along the loaded diagonal (pure shear stress state),these two methods are comparable. These measurements were used to plot shearstress versus shear strain diagrams for each specimen as shown in Fig. 6a–c for eachset of walls. Each graph shows three curves, indicating the three repetitions. Thetest outcomes show a clear and consistent pattern.

According to ASTM E519/E519M-10 [30], the shear modulus of rigidity, G, is theslope of the elastic portion of the s–c diagram. G is computed here as the ratio scr/ccr, where ccr is defined as the shear strain corresponding to the shear stress at thecracking point. scr is assumed as 70% of the maximum shear stress [3,31,32]. Thestiffness of the retrofitted walls increases with the amount of FRCM (see Columns(5) in Table 3 and Fig. 6).

2.4.3. Pseudo-ductilityThe wall pseudo-ductility, l, (see Column (6) in Table 4) is defined as the ratio

cu/ccr where cu is the shear strain at ultimate corresponding to the maximumstrain in the shear stress–strain curve [1,2,4,9,33,34]. There is no agreement inestablishing the value of shear strain at cracking, ccr, for strengthened walls: someauthors [1,2,4,9] define ccr as the bend-over point where the in-plane shearstress–strain curve tends to become flat. Other authors [33,34] define ccr as theshear strain corresponding to the shear stress taken as 75% of the shear strength,and others use 70% of this value [3,31,32]. In this paper, ccr is based on the shearstress at cracking, scr, assumed as 70% of the shear strength. Columns (1), (2), (3),and (4), in Table 4 illustrate the shear stress and shear strain at the ultimate andcracking points, respectively. Columns (5) and (6) present shear modulus andpseudo-ductility, respectively. In general, the higher the pseudo-ductility ratio,the higher the ability of strengthened masonry walls to redistribute stresses aswell as to increase global deformation capacity and energy dissipation. FRCMmakes the strengthened wall achieve higher shear stress and pseudo-ductility.However, pseudo-ductility increments are not proportional to the amount of rein-forcement. Referring to Table 3 and Fig. 6, results demonstrate that 4-ply FRCMattained lower pseudo-ductility than 1-ply FRCM, because of its stiffness andinduced brittle failure. Pseudo-ductility ratios are low compared to other dataavailable in literature for clay masonry because failure was due to toe crushing[22].

2.4.3.1. Comparison of test results with FRP. Table 4 presents specimens tested underdiagonal compression taken from other research programs. Columns (1) and (2)list the first author’s last name with the date of publication and the original spec-imen codes. Columns (3) present the strengthening schemes which include NSMGFRP bars, externally-bonded GFRP laminates, and GFRP grid reinforced polyureastrips [1,2,10,11]. Experimental results derived from this research program arecompared to those reported from the other programs after normalizing the data.The shear capacity of each wall is normalized as shear strength by dividing theshear force by the cross-sectional area of un-cracked masonry wall. Furthermore,the wall calibrated reinforcement ratio, xf, is defined as qEf/Em (see Column (5) ofTable 5); where q is the ratio between the FRCM or FRP reinforcement area(Column (1)) and the net masonry area (Column (2)). Ef and Em are the moduliof elasticity of FRCM or FRP (Column (3)) and masonry (Column (4)), respectively.The calibrated reinforcement ratio is shown to affect the shear capacity andfailure mode. Table 5 and Fig. 7 illustrate the shear strength (Column (7)) as afunction of the calibrated reinforcement ratio. The graph shows that the shearstrength increases proportionally to the calibrated reinforcement ratio and theresults achieved for FRCM match well those obtained with FRP. When the rein-forcement ratio index exceeds 1.5%, substrate toe compression controls thefailure mode; therefore, adding more reinforcement is ineffective (either FRCMor FRP).

3. Analytical approach

In-plane shear capacity of retrofitted walls consists of themasonry and FRCM contributions according to ACI 549-13 [25].FRCM contribution is considered only after masonry cracking[2,8,10,12,22,25,34]. The nominal shear capacity, Vn, is computedin accordance with Eq. (1):

Vn ¼ Vm þ Vf ð1Þ

Fig. 4. (a) Schematic of in-plane load test of wall. (b) Mohr–Coulomb circle. (c) Detail of steel shoe.

S. Babaeidarabad et al. / Construction and Building Materials 65 (2014) 243–253 247

where Vm and Vf are the masonry and FRCM contributions,respectively.

3.1. Masonry contribution (Vm)

Depending on physical and mechanical properties of a wall, fourpossible failure modes have been identified [2,3,8,22]. A wall failswhen the value of the applied shear force reaches the minimumshear capacity, Vm, [2,8,12,22] computed in accordance with Eq. (2):

Vm ¼ MinðVss; Vsf ; Vdt ; VcÞ ð2Þ

(a) Shear sliding (Vss): failure takes place along a single bed jointcaused by bond failure between concrete block and mortar[2,8,22,34]. Shear sliding capacity is calculated in accordancewith Eq. (3):

Vss ¼s0

1� l0 tan hAn ð3Þ

where s0 is the shear bond strength between mortar and

block estimated to be 3% of the masonry compressivestrength [2,8,22,34]. The coefficient of shear friction, l0, isassumed to be equal to 0.3 [2,8,22]; h is the inclined angle

Table 2Experimental, analytical, and design results.

Specimen ID Experimental results Analytical results Exp./An. ratio Designresults*

Exp./Des. Ratio

Max. appliedload

Ave. maximumload

Failure mode Max. load Failure mode

Pu kN (1) Pu,avg kN (2) (3) Pn,An. kN (4) (5) Pu,avg/Pn,An – (6) /v Pn,Des kN (7) Pu,avg//v Pn,Des – (8)

Control-1 116.7 Diagonal tensilecracking

Joint sliding

Control-2 115.6 109.4 65.5 1.7 49.1 2.2Control-3 95.8

1 ply-1 237.5 Toe crushing Toe crushing1 ply-2 197.6 212.9 161.5 1.3 73.7 2.91 ply-3 203.7

4 ply-1 261.6 Toe crushing Toe crushing4 ply-2 255.1 257.6 161.5 1.6 73.7 3.54 ply-3 256.2

Note: 1.0 kN = 0.23 kips.* / factor and maximum 50% increase limits apply.

248 S. Babaeidarabad et al. / Construction and Building Materials 65 (2014) 243–253

between horizontal and main diagonal of the wall; and An isthe net cross-sectional area according to ASTM E519/E519M-10 [30].

(b) Shear friction (Vsf): failure is controlled by the loss of bondbetween the mortar and concrete blocks in the stepped-stairformat [2,8,22,34,35]. Shear friction capacity is calculated inaccordance with Eq. (4):

Vsf ¼s0;m

1� lm tan hAn ð4Þ

where

s0;m ¼s0

1þ 1:5l0h

W

ð4-aÞ

and

lm ¼l

1þ 1:5l0h

W

ð4-bÞ

where h and w are the height and length of the block,

respectively.

(c) Diagonal tension (Vdt): failure occurs when the principaltension stress produced by the combination of shear andcompressive forces reaches the tensile strength of the wall[2,8,22,34]. Diagonal tension shear capacity is calculated inaccordance with Eq. (5):

Vdt ¼tan hþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi21:16þ tan2 h

p10:58

f 0t AnLH

� �ð5Þ

where f 0t is the tensile strength assumed 0:5ffiffiffiffiffif 0m

p(MPa) for the

concrete block wall [8]. L is the wall length in the direction ofthe shear force, and H is the un-reinforced concrete masonrywall height.

(d) A wall fails by toe crushing when the stress generated at acorner reaches the masonry compressive strength[2,8,22,34]. Shear capacity controlled by compression iscalculated in accordance with Eq. (6):

Vc ¼2Wf 0m

3hþ 2W tan hAm ð6Þ

where h, and w are the height and length of the concrete

block, and Am is defined as the interface loading area betweensteel shoe and wall along the horizontal direction.

A numerical example on how to calculate Vm is given inAppendix A for the case of the wall tested in this research program.

3.2. FRCM contribution (Vf)

The contribution of FRCM reinforcement is calculated per ACI549-13 [25]. The ultimate FRCM tensile strain, efu, is the averageminus one standard deviation obtained from tensile test per-formed according to AC434-13 [26]. The tensile strain in theFRCM shear reinforcement, efv, is calculated in accordance withEq. (7):

efv ¼ efu 6 0:004 ð7ÞThe tensile strength in the FRCM shear reinforcement, ffv, is

calculated in accordance with Eq. (8):

ff v ¼ Ef ef v ð8Þ

where Ef is the tensile modulus of elasticity of the cracked FRCM.FRCM contribution, Vf, is calculated according to Eq. (9):

Vf ¼ 2nAf Lff v ð9Þ

where Af, n, L are the area of the fabric reinforcement by unit widthin both directions (horizontal and vertical), the number of layers offabric, and the length of the masonry, respectively. Appendix Ashows how to compute Vf for the case of the 1-ply FRCM wall testedin this research program.

The nominal shear capacity, Vn, is computed as the sum ofmasonry and FRCM contributions. Analytical results in terms ofmaximum load, Pn,An., and failure modes in each set of walls arepresented in Table 3 Columns (4) and (5). Column (6) presentsthe ratio of experimental to analytical capacity. Results show thatthe analytical model conservatively predicts the shear capacity andfailure modes of strengthened walls. In both analysis and experi-ments, substrate toe crushing controls the failure mode ofstrengthened walls. The same analytical procedure to compute Vn

is applicable to clay brick masonry walls strengthened with FRCMunder diagonal compression [22].

4. Design provisions

Following ACI 549-13 [25] design provisions, the increase inshear capacity of the strengthened walls is limited to 50% of theun-strengthened wall shear capacity to limit the total forcetransferred to the substrate of the masonry per unit width.Additionally, the strength reduction factor for shear, Uv, is equal to0.75. It can be observed that these design provisions are conserva-tive (see Columns (7) and (8) in Table 3 and Fig. 6 (horizontal solidlines)).

Fig. 5. Failure mode of wall specimens: control (a); 1-ply (b); and 4-ply (c).

(a)

(b)

(c)

0

0.5

1

1.5

2

2.5

3

3.5

τ τ [M

Pa]

0

0.5

1

1.5

2

2.5

3

3.5

τ τ [M

Pa]

0

0.5

1

1.5

2

2.5

3

3.5

τ τ [M

Pa]

Control-1Control-2Control-3Control-AnalysisControl-Design

γ γ [mm/mm]

1ply-11ply-21ply-31ply-Analysis1ply-Design

0 0.0004 0.0008 0.0012 0.0016

γ γ [mm/mm]

0 0.0004 0.0008 0.0012 0.0016

γ γ [mm/mm]

0 0.0004 0.0008 0.0012 0.0016

4ply-14ply-24ply-34ply-Analysis4ply-Design

Fig. 6. Shear stress–shear strain diagrams of wall specimens: control (a); 1-ply (b);and 4-ply (c) (Note: 1.0 MPa = 145 psi; 1 mm = 0.039 in).

S. Babaeidarabad et al. / Construction and Building Materials 65 (2014) 243–253 249

Table 5Comparison of experimental results with FRP.

Specimen ID Area of FRCMor FRP

Net area ofURM wall

Elastic modulusof strengthenedmaterial

Elastic modulusof URM wall

Calibratedreinf. ratio

Exp. shear force Exp. Shearstrength

Af mm2 (1) An mm2 (2) Ef MPa (3) Em MPa (4) q Ef/Em % (5) Vu,exp kN (6) su,exp MPa (7)

1 ply-1 FRCM 168.0 2.31 ply-2 248 1.55 139.7 1.91 ply-3 72,903 79,726 17,513 144.1 2.04 ply-1 6.19 185.0 2.54 ply-2 991 180.4 2.54 ply-3 181.2 2.5

WC1 Yu 2007 [11] FRP 154 0.29 135.2 1.0WC2 307 36,584 13,590 0.58 168.1 1.2WC3 154 0.29 109.4 0.8WC4 307 0.58 159.2 1.1

COW 2 Li 2005 [2] 230 50,166 0.54 141.5 1.0COW 3 137.9 1.0COW 8 130.3 0.9COW 9 266 54,636 0.68 134.8 0.9COW 10 230 141,935 50,166 15,079 0.54 170.4 1.2COW 11 132 0.31 98.3 0.7COW 12 99 50,166 0.23 134.8 0.9

WL 2 Grando 2003 [1] 126 0.50 111.2 0.8WL 3 108 83,123 14,893 0.65 208.2 1.5

Wall IL2 Tumialan 2001 [9] 230 0.51 161.6 1.1Wall IL3 329 40,679 12,969 0.73 178.9 1.3Wall IL4 168.2 1.2

Note: 1.0 mm2 = 0.0016 in2; 1.0 MPa = 145 psi; 1.0 kN = 0.23 kips.

Table 4Strengthening schemes of URM walls from other research program with FRP.

Resources (1) Specimen ID (2) Strengthening schemes (3)

Yu 2007 [11] WC1 Four 114 mm wide horizontal GFRP grid -polyurea strip at 305 mm on centersWC2WC3 Four 114 mm wide vertical GFRP grid -polyurea strip at 305 mm on centersWC4

Li 2005 [2] COW 2 Seven 6.4 mm diameter GFRP bars at every bed jointCOW 3 Four 6.4 mm diameter GFRP bars at every other bed joint (front) and three 6.4 mm

diameter GFRP bars at every other bed joint (back)COW 8 Seven 6.4 mm diameter GFRP bars at every bed jointCOW 9 Seven 6.4 mm diameter GFRP bars every bed joint and four vertical GFRP stripsCOW 10 Seven 6.4 mm diameter GFRP bars at every bed jointCOW 11 Four 6.4 mm diameter GFRP bars at every second bed jointCOW 12 Three 6.4 mm diameter GFRP bars at every second bed joint

Grando 2003 [1] WL 2 GFRP laminates with the thickness of 51 mm at every jointWL 3 GFRP laminates with the thickness of 76 mm at every two joints

Tumialan 2001 [9] Wall IL2 Seven 6.4 mm GFRP bars at every horizontal jointWall IL3 Seven 6.4 mm GFRP bars at every horizontal and three 6.4 mm GFRP bars at every vertical jointsWall IL4 Seven 6.4 mm GFRP bars at every horizontal joints (front) and three 6.4 mm GFRP bars at vertical joints (back)

Note: 1 mm = 0.039 in.

Table 3Test results.

Specimen ID su MPa (1) cu mm/mm (2) scr MPa (3) ccr mm/mm (4) G GPa (5) l – (6)

Control-1 1.13 0.0004 1.13 0.0004 3.14 1.0Control-2 1.12 0.0003 1.12 0.0003 3.22 1.0Control-3 0.93 0.0003 0.93 0.0003 2.83 1.0

1 ply-1 2.30 0.0013 1.61 0.0004 3.82 3.21 ply-2 1.91 0.0011 1.34 0.0003 3.88 3.31 ply-3 1.97 0.0012 1.38 0.0004 3.54 3.1

4 ply-1 2.53 0.0004 1.77 0.0004 4.81 1.34 ply-2 2.47 0.0005 1.73 0.0004 4.74 1.44 ply-3 2.48 0.0004 1.74 0.0003 5.27 1.2

Note: 1.0 GPa = 145.03 ksi; 1.0 MPa = 0.145 ksi; 1.0 mm/mm = 1.0 in/in).

250 S. Babaeidarabad et al. / Construction and Building Materials 65 (2014) 243–253

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0

1 ply-1

1 ply-2

1 ply-3

4 ply-1

4 ply-2

4 ply-3

WC1 (Yu)

WC2 (Yu)

WC3 (Yu)

WC4 (Yu)

COW 2 (Li)

COW 3 (Li)

COW 8 (Li)

COW 9 (Li)

COW 10 (Li)

COW 11 (Li)

COW 12 (Li)

WL 2 (Grando)

WL 3 (Grando)

Wall IL2 (Tumialan)

Wall IL3 (Tumialan)

Wall IL4 (Tumialan)

Calibrated Reinforcement Ratio [%]

Nor

mal

ized

She

ar C

apac

ity

[MP

a]

Fig. 7. Comparison of the shear stress of strengthened concrete URM walls againstcalibrated reinforcement ratio (Note: 1.0 MPa = 145 psi).

S. Babaeidarabad et al. / Construction and Building Materials 65 (2014) 243–253 251

5. Conclusions

This experimental investigation aimed to assess the effective-ness of a carbon FRCM strengthening system to improve in-planebehavior of URM concrete walls. The following conclusions canbe drawn:

(1) The test results prove the technical viability of FRCMstrengthening of un-reinforced concrete masonry wallswhen subjected to diagonal compression. Depending onthe amount of FRCM, retrofitted concrete masonry wallshear capacity increased between 1.95 and 2.36 times thatof the control specimen.

(2) Experimental evidence and analysis show that the keyparameter in the shear capacity and failure modes of FRCMstrengthened walls is the calibrated reinforcement ratio.This implies that FRCM and FRP strengthening methods pro-vide similar increments in shear capacity, if normalizedaccording to the calibrated reinforcement ratio.

(3) The substrate toe crushing controlled failure in the strength-ened walls with the calibrated reinforcement ratio morethan 1.5% (e.g., 1-ply FRCM). Consequently, adding moreFRCM layers beyond this threshold is not productive.

(4) FRCM strengthening is effective in increasing the stiffness ofURM walls. Pseudo-ductility gain is limited due to toe crush-ing failure in both cases of 1-ply and 4-ply strengthenedwalls, with the former showing higher values.

(5) Analysis as per ACI 549-13 [25] showed reasonable agree-ment with the experimental results. Similarly, design valuesare conservative when applying the limits of 50% maximumincrease and the strength reduction factor, Uv of 0.75.

Acknowledgements

The authors acknowledge the National Science Foundation(NSF) for the support provided to the Industry/University Centerfor Integration of Composites into Infrastructure (CICI) at the Uni-versity of Miami and its industrial member Ruredil S.P.A., SanDonato Milanese, Italy for the financial support under Grant No.IIP-0933537. The authors also thank Titan America Inc., Medley,FL for their support to this research. Any opinions, findings, andconclusions or recommendations expressed in this material are

those of the authors and do not necessarily reflect the views ofthe NSF.

Appendix A

A.1. Design of concrete masonry wall strengthened with 1-Ply FRCM

Calculate the analytical and design shear capacity of a concretemasonry wall strengthened with 1-ply FRCM according to ACI 549-13 [25], using actual geometry and material properties obtainedfrom coupon and prism tests. The shear capacity of a strengthenedwall is computed in three steps: (1) calculate the shear capacity ofthe URM wall; (2) calculate the contribution of FRCM reinforce-ment; (3) calculate the sum in accordance with Eq. (1). Summa-rized in the following is the wall information:

A.2. Masonry properties

Height of the wall

H = 1220 mm (48 in) Thickness of the wall tm = 92 mm (3.63 in) Length of the wall L = 1220 mm (48 in) Height of the block h = 194 mm (7.63 in) Length of the block w = 397 mm (15.63 in) Net cross-sectional area An = 72903 mm2 (113 in2) Compressive strength of masonry f0m = 19.46 MPa (2823 psi) Compressive strength of mortar fc = 22.01 MPa (3193 psi) Tensile strength of masonry f0t = 2.21 Mpa (320 psi) Masonry elastic modulus Em = 900 f 0m = 17513 MPa

(2540 ksi)

Shear bond strength in mortar

joint

s0 = 0.58 MPa (84.7 psi)

Coefficient of internal shearfriction in mortar joint

l0 = 0.3

A.3. FRCM properties

Area of fabric per unit width (bothdirections)

Af = 0.10 mm2/mm(0.004 in2/in)

Ult. tensile strain (mean minus onestandard deviation)

efu = 0.0086 mm/mm(in/in)

Tensile modulus of elasticity

Ef = 80 GPa(11563 ksi)

A.4. Masonry contribution (Vm)

� Shear capacity due to shear sliding failure is calculated accord-ing to Eq. (3):

Vss ¼s0

1� l0 tan hAn

¼ 0:58� 10001� 0:3� tan 45�

� 0:0729 ¼ 60:8 kNð13:7 kipsÞ

� Shear capacity due to shear friction failure is calculated accord-ing to Eq. (4):

Vsf ¼s0;m

1� lm tan hAn ¼

s0

1þ 1:5l0h

W � l0 tan hAn

¼ 0:58� 10001þ 1:5� 0:3� 0:194

0:397� tan 45� � 0:3� tan 45�� 0:0729

¼ 46:3 kNð10:4 kipsÞ

252 S. Babaeidarabad et al. / Construction and Building Materials 65 (2014) 243–253

� Shear capacity due to diagonal tension failure is calculatedaccording to Eq. (5):

Vdt ¼tan hþ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi21:16þ tan2 h

p10:58

f 0t AnLH

� �

¼ tan 45� þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi21:16þ tan2 45�

p10:58

� 2:206� 1000� 0:0729

� 12201220

� �¼ 86:7 kNð19:5 kipsÞ

� Shear capacity due to toe crushing failure at the loading end iscalculated according to Eq. (6):

Vc ¼2Wf 0m

3hþ 2W tan hAm

¼ 2� 0:397� 19:46� 10003� 0:194þ 2� 0:397

� ð0:17� 0:092� 0:65Þ

¼ 114:2 kNð25:7 kipsÞ

� URM shear capacity is calculated according to Eq. (2):Vm ¼ MinðVss; Vsf ; Vdt; VcÞ ¼ 46:3 kNð10:4 kipsÞ

A.5. FRCM Contribution (Vf)

� Effective tensile strain of FRCM is calculated according to Eq.(7):

ef v ¼ 0:004 mm=mmð0:004 in=inÞ

� Effective stress level in the FRCM at failure is calculated accord-ing to Eq. (8):

ff v ¼ Ef ef v ¼ 79726� 0:004 ¼ 318:9 MPað46:25 ksiÞ

� FRCM contribution, Vf, is calculated according to Eq. (9):Vf ¼ 2nAf Lff v

¼ 2� 1� 0:1� 1220� 318:9� 10001000� 1000

¼ 79:1 kNð17:8 kipsÞ

A.6. Shear capacity of 1-ply strengthened wall (Vn)

1-ply FRCM wall shear capacity is calculated according to Eq. (1)considering /v is equal to 1.0:

Vn ¼ Vm þ Vf ¼ 46:3þ 79:1 ¼ 125:4 kNð28:2 kipsÞ

Limitation:As per ACI 549-13 [25], the summation of the masonry and

FRCM shear contributions according to Eq. (1) should be checkedagainst the substrate toe crushing capacity computed accordingto Eq. (6):

Vn ¼ MinðVm þ Vf ; VcÞ ¼ 114:2 kNð25:7 kipsÞ

A.7. Design provisions

According to ACI 549-13 [25] design provisions, maximum forcetransferred to substrate should not exceed 50% of un-strengthenedwall capacity.

Vf ¼ Minð2nAf Lff v ; 50%VmÞ ¼ 23:2 kNð5:2 kipsÞ

Vn ¼ Vm þ Vf ¼ 46:3þ 23:2 ¼ 69:5 kNð15:6 kipsÞ

Limitation:Following ACI 549-13 [25] design provisions, the summation of

the masonry and FRCM shear contributions before strengthreduction factors are applied (Eq. (1)) should be checked against

the substrate toe crushing capacity computed according to (Eq.(6)).

Vn ¼ MinðVm þ Vf ; VcÞ ¼ 69:5 kNð15:6 kipsÞ

Shear strength reduction factor /v = 0.75

/vVn ¼ 0:75� 69:5 ¼ 52:1 kNð11:7 kipsÞ

The experimental shear for this wall was:

Vu ¼ 150:5 kNð33:8 kipsÞ

The failure mode for this wall was toe crushing.

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