Seismic retrofit of infilled RC frames with textile reinforced mortars: State-of-the-art review and analytical modelling

Journal Pre-proof Seismic retrofit of infilled RC frames with textile reinforced mortars: State-of-the-art review and analytical modelling D.A. Pohoryles, D.A. Bournas PII:

S1359-8368(19)33693-5

DOI:

https://doi.org/10.1016/j.compositesb.2019.107702

Reference:

JCOMB 107702

To appear in:

Composites Part B

Received Date: 31 July 2019 Revised Date:

6 November 2019

Accepted Date: 12 December 2019

Please cite this article as: Pohoryles DA, Bournas DA, Seismic retrofit of infilled RC frames with textile reinforced mortars: State-of-the-art review and analytical modelling, Composites Part B (2020), doi: https://doi.org/10.1016/j.compositesb.2019.107702. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

1

Seismic retrofit of infilled RC frames with textile reinforced mortars:

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State-of-the-art review and analytical modelling

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D. A. Pohoryles1 and D. A. Bournas2

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Abstract

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Significant damage to existing reinforced concrete (RC) frame structures during recent earthquakes

6

has highlighted the potential detrimental effect of non-structural masonry infills. Several experimental

7

studies have hence investigated the use of composite materials for in-plane retrofitting to reduce the

8

risk of brittle collapse of the infills. In this review, the state-of-the-art on strengthening infilled RC

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frames with textile-reinforced mortars (TRM), a new class composite material consisting of open-

10

mesh textiles embedded in a cementitious matrix, is presented, highlighting the great potential of this

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retrofit solution for large scale interventions on the existing building stock. A database of

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experimental results is compiled to evaluate the effect of different parameters on the effectiveness of

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the retrofitting applications. The stiffness of the fibre material, as well as the angle of application are

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found to be crucial factors. To ensure adequate analytical modelling for predicting the retrofitted

15

behaviour, a macro-model, using an additional tensile tie to account for the TRM, is first calibrated by

16

means of the experimental data gathered from the literature. Correlation between experimental

17

parameters and the obtained effective strain is then assessed and an empirical formulation of effective

18

strain in terms of fibre stiffness and retrofit amount is finally proposed.

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Keywords: textile reinforced mortar; seismic retrofit; infilled RC frames; masonry infills; macro-

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model

1

European Commission, Joint Research Centre (JRC), Ispra, Italy. Email: [email protected]

2

European Commission, Joint Research Centre (JRC), Ispra, Italy. Email: [email protected]

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1. Introduction

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Empirical evidence of heavy damage observed in recent earthquakes has highlighted the vulnerability

23

of infilled reinforced concrete (RC) structures [e.g.: 1–4]. While the effect of masonry infills is

24

typically ignored in structural design, their presence was found to cause brittle damage and failure

25

mechanisms in existing buildings. Local failure of the infill panels due to in and out-of-plane

26

mechanisms, but also due to their combination, can lead to a sudden drop in capacity and hence cause

27

global brittle failure of the structure. Even at lower intensity earthquakes, damage to infilled frames

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can lead to high economic losses and loss of life [1].

29

These vulnerable masonry infilled structures however constitute one of the most typical building

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typologies constructed between the 1960s and 1990s in Europe [5]. They generally tend to have high

31

occupancy and include schools and hospitals, next to commercial and residential properties. There is

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hence a need for fast, reliable and effective retrofit strategies applicable at scale for the existing

33

European building stock. Typical retrofit strategies aim to strengthen the infills to prevent brittle

34

collapse modes and to provide adequate connection to the frame, thus ensuring a global lateral load

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resistance mechanism. Conventional techniques such as RC jacketing [6] are generally seen to be

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labour intensive, use large quantities of materials and lead to a significant increase in wall thickness.

37

Aiming to reduce the thickness of the jacket, researchers have suggested steel reinforced plasters [7,

38

8], or mortars combined with short composite fibres (ECCs) [9, 10]. The application of thin layers of

39

non-corrosive lightweight epoxy-based materials, such as fibre-reinforced polymers (FRP) have also

40

gained attention [11–15], as they lead to improved durability, reduced mass and quicker application.

41

This study instead focusses on the use of an innovative composite system, the so-called textile

42

reinforced mortars (TRM) and their recent application for the in-plane seismic retrofit of the masonry-

43

infilled RC frames. TRM constitutes a new generation of composite materials [16] in which

44

unidirectional fibre sheets are replaced by textiles (typically bidirectional – see Figure 1a) and the

45

epoxy resin is replaced by a cementitious matrix, shown in Figure 1b. This novel composite, uses

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open-mesh textiles produced typically from knitted or woven fibre rovings of high-strength (e.g.

2

47

carbon, glass or basalt), but can also take advantage of textiles made from natural fibres (e.g. hemp or

48

flax).

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TRM has been proven effective for strengthening both concrete [17–22] and masonry [23, 24]

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structures. Due to the combination with inorganic binders, such as lime or cement based mortars,

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which are granular unlike epoxy resins, a mechanical interlock between the textile layers and binder is

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activated. Moreover, the good mechanical behaviour of inorganic matrices at high temperatures

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renders TRM more fire-resistant than epoxy based composites [21, 22].

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Very recently, a new generation of composites, combining TRM with advanced thermal insulation

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materials or systems (see Figure 2), offered new avenues for the concurrent seismic and energy

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retrofitting of existing building envelopes [25–28]. Their novel use for the in-plane [29] and out-of-

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plane strengthening [30, 31] of masonry-infilled RC frames is of particular interest to this study.

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Experimental efforts on TRM strengthened infills are rather limited, but there is still a lack of research

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on their analytical modelling. In particular with the emergence of new fields such as concurrent

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seismic and energy retrofitting using TRM, compiling the available experimental evidence is crucial

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to reveal promising avenues for research and to establish safe design recommendations for such

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composites as retrofit materials.

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In order to gain better understanding of TRM retrofitting for masonry-infilled RC framed structures,

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this study presents an exhaustive review of experimental efforts in the field. A detailed database of

65

experimental parameters and obtained results, including damage mechanisms is developed. Based on

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this newly compiled database of recent research efforts on TRM-strengthened infills, a simplified

67

modelling approach is used to assess the effective strain in the textile reinforcement. The correlation

68

of experimental parameters with the effective strain in the composite material is then evaluated.

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Finally, an empirical equation for effective strain of the textile reinforcement is proposed to be used

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within simplified macro-models of infilled RC frame. This new empirical definition for TRM

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effective strain is based on all available experiments, and hence a step towards the generation of

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design-oriented equations for TRM retrofits of infills.

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2. Background

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Strengthening masonry infilled frames with TRM aims to achieve a reliable building response,

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utilising the strength and stiffness of the infills. As shown in Table 1, TRM forms part of a family of

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composite materials that have been tested in the literature. Composite can be applied as bands or strips

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or over the full surface of the infill. The orientation of the fibres can be orthogonal, with fibres in the

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vertical and horizontal directions, at ±45° or in the diagonal angle of the infill. A variety of composite

79

strengthening materials can be used, ranging from fibre-based textile meshes embedded in mortar

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(TRM), unidirectional fibre-sheets bonded using epoxy raisins (FRP) and short fibres randomly

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orientated and embedded in mortar (ECCs), to steel meshes for reinforcing thin layers of plaster.

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2.1. Retrofitting of infills with composite materials

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Composite retrofits using FRP sheets applied in the diagonal of the infill wall [12] or as a series of

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horizontal strips [11] have been tested. The latter was however found not to increase the lateral

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capacity of the infilled frames. Their small thickness increase, important for architectural reasons, and

86

corrosion resistance make FRP a very popular retrofitting material, their behaviour at high

87

temperature and difficulty of application at low temperatures, as well as on wet surfaces are however

88

practical constraints. Instead of using epoxy-based resin as binder, inorganic matrices, such as

89

cementitious mortars or plasters, are a viable alternative. Their advantages over FRP systems are a

90

better fire resistance and behaviour at high temperatures [21,22], better bond and strain compatibility

91

with masonry [23], as well as their applicability at low temperatures or on wet surfaces and lower

92

costs. Moreover, unidirectional FRP as a retrofit material can rupture in the weaker orthogonal

93

direction, which can be avoided when using randomly arranged fibres or orthogonal meshes [32,33].

94

In terms of retrofits with cement-based composites, using (sprayable) engineered cementitious

95

composites (EEC) for masonry infills is increasingly studied [9,10,34–37]. The disadvantage of ECCs

96

is however the non-directionality and uncertainty of equal distribution of fibres, which make

97

predicting the strength increase more challenging. Reinforced plasters, on the other hand, consist of

98

mesh reinforcement with two orthogonal directions embedded in a thin layer of plaster for

99

strengthening infills [7,8]. This kind of retrofit is analogous to the orthogonal TRM strengthening 4

100

method, but instead of fibres woven into a textile mesh, a steel reinforcement mesh is used, which can

101

be associated to similar durability concerns regarding corrosion as RC jacketing.

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2.2. Retrofitting of infills with TRM

103

Focussing on TRM applications, a summary of retrofitted infilled RC frame specimens tested in the

104

literature can be found in Table 2. It indicates the scale of the tested specimens, the height (H) and

105

width (W) of the frame, the angle of the diagonal (θ), the infill wall thickness (tinf) and its compressive

106

strength (fm,inf), as well as properties of the retrofit, including the TRM fibre type (glass, basalt, carbon

107

or steel), the elastic modulus of the fibres (Ef), mesh size, number of sides retrofitted (ns), number of

108

textile layers per side (nt), the angle of the fibres (αT) and the anchorage used (steel ties or bolts,

109

textile anchors or no anchorage). The main experimental results are also shown, including the shear

110

capacity of the retrofitted specimen (Vexp), the difference in capacity to the control specimen (∆Vexp),

111

the drift at maximum (∆max), as well as the observed damage patterns. The damage patterns of interest

112

include infill-related damage, namely crushing of bricks in the corners (CC), horizontal sliding (HS),

113

infill detachment from the frame (ID), diagonal cracking (DC), but also TRM related damage

114

including partial debonding (PTB) and rupture of fibres (PTR), as well as RC frame damage, such as

115

joint shear failure (JS), column shear failure (CS) and column bar buckling (CB). The main damage

116

observation from the control and respective retrofitted specimens for all studies is summarised

117

schematically in Table 3. It is important to note that the failure of retrofitted frames occurred at much

118

larger values of drift compared to their respective control specimens.

119

Initial work by Koutas et al. [29] consisted of cyclic tests up to failure of a 2/3-scale three-storey fully

120

infilled RC frame retrofitted with TRM. The aim of the retrofit was to achieve a more ductile failure

121

mechanism with a regular displacement demand along the height of the structure. The scheme

122

consisted of applying two layers of glass TRM (G-TRM) in the first storey and one in the second and

123

third storeys, using previously tested textile anchors [43] at the perimeter of the infills. Moreover, the

124

column-ends were wrapped with TRM to prevent shear failure observed in the control specimen.

125

The as-built specimen failed in a brittle single-storey mechanism, with damage concentrated in the

126

ground storey. As shown in Table 3, for the ground storey, diagonal cracking along the infill surface 5

127

was observed, with spalling of the bricks closer to the corners, and finally shearing of the columns at

128

the top corner. The retrofitted structure instead presented a behaviour characterised by a regular

129

distribution of lateral storey displacements along the height of the structure, which led to an enhanced

130

deformation capacity (+52%). Shear damage to the columns was successfully prevented by the local

131

TRM jacketing. The use of anchors at the infill perimeter successfully delayed debonding of TRM

132

and hence ensured an adequate lateral load resisting system with a good infill-frame connection up to

133

localised rupture of the TRM fibres at the interface. Looking at the results in Table 2, an increased

134

lateral strength (+54%) and initial stiffness (twofold) were observed for the retrofitted structure. The

135

cracking pattern on the TRM surface indicated horizontal sliding of the bricks. After removal of the

136

retrofitting material, significant corner crushing was observed in the underlying infill. The observed

137

damage appears to indicate that the TRM retrofit successfully confined the infill wall and allowed it to

138

ultimately reach crushing of the bricks, without losing full integrity of the wall up to large levels of

139

lateral displacement. The test on a three-storey specimen also highlighted that a non-uniform

140

distribution of lateral displacements, leading to soft-storey failure, can be successfully prevented by a

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well-designed TRM retrofit with different numbers of layers along the height of the structure.

142

Selim et al. [41] tested two non-seismically designed 1/3-scale infilled RC frames, of which one was

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retrofitted with G-TRM. The retrofit consisted of two layers of TRM on each face of the infill wall,

144

extended onto the columns and using five fabric anchors applied through the infill. Due to inadequate

145

detailing and high localised forces in the corners of the infilled frame, the control specimen failed by a

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beam-column joint shear failure mechanism, combined with extensive corner crushing observed in the

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infill wall. A brittle failure at 1% drift with 79.2 kN lateral force was observed. The TRM retrofit

148

ensured the corner crushing and joint shear mechanisms were prevented. TRM jacketing of the infill

149

ensured crushing of the bricks was prevented, despite the higher sustained lateral loads of 131.7 kN

150

(+66.3%, Table 2). TRM contribution in tension was demonstrated by increased diagonal cracking

151

(see Table 3) and an improved ductility. While damage to the RC frame was generally reduced by the

152

retrofit, ultimately, failure due to column bar buckling at the foundation was observed.

6

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Da Porto et al. [39] studied the effect of TRM strengthening on eight full-scale RC frames infilled

154

with light clay masonry walls. After in-plane cycling testing up to 1.2% drift, the out-of-plane residual

155

capacity of the specimens was assessed in this study. Two test series were conducted, using stronger

156

masonry mortar for the first four specimens (two control and two retrofitted) and a weaker mortar to

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bind the bricks in the latter four. As shown in Table 2, for the textile, a combined glass and steel fibre

158

mesh was used for one specimen, while a basalt and steel fibre mesh was used for the other three. The

159

influence of the inorganic binder used for the TRM was also investigated with high strength mortar

160

(fm,f = 5.4 MPa) used for two retrofitted specimens (3-GC-NR and 4-GC-FN), while for two other

161

specimens (6-BG-NR and 8-BC-NR), low strength gypsum plaster or natural hydraulic lime plasters,

162

respectively, were used (fm,f = 1.1 MPa). The gypsum plaster has the benefit of being more

163

environmentally friendly and able to capture volatile organic pollutants. Finally, anchorage of the

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mesh to the upper beams using steel-ties was provided for one specimen (4-GC-FN).

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During the in-plane tests, the control specimens experienced heavy damage, including spalling and

166

crushing of masonry units at the corners. This was not observed for any of the retrofitted units, for

167

which damage was delayed significantly, with no cracking up to 0.5% drift. For the specimens

168

retrofitted using low strength mortar, a higher level of damage was observed, with visible cracking

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initiating at 0.5% drift, compared to 1.2% for the higher strength mortar. For the specimen with

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weaker masonry mortar, horizontal sliding was observed for the control and retrofitted specimens. For

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the three unanchored specimens, limited local detachment of the TRM was observed. This ultimately

172

led to localised crushing at the corners of the infills in two specimens, which was prevented in the

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specimen with steel tie anchorage. Despite the reduction in damage, the recorded results in Table 2

174

indicate that in-plane strength and stiffness were not affected by the retrofit. Still, prevention of brittle

175

failure in the retrofitted specimens resulted in considerably improved ductility and reduced post-peak

176

strength degradation. This allowed the retrofitted walls to behave better in the subsequent out-of-plane

177

tests, with higher residual strength recorded compared to the control specimens.

178

More recently, Akhoundi et al. [38,44] tested two G-TRM retrofitted frames, using a commercial and

179

a custom-made braided textile, respectively. The braided textile, previously tested on masonry [45], 7

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was specifically designed to maximise the mechanical interlock between textile mesh and mortar. To

181

enhance the effectiveness of the retrofit, twelve glass fibre connectors through the infill and four

182

connectors at the interfaces to each RC member were used for anchorage. As shown in Table 2, next

183

to a significant increase in initial stiffness, strength increases of 25% and 30% were obtained for the

184

commercial and braided TRM. The commercial TRM surface was fully cracked along the diagonal

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after testing, while the braided TRM specimen only presented infill detachment cracks at the

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interfaces. After removal of the jacket post-testing, crushing of the infill corners was observed for

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both specimens, but more extensively for the specimen using a commercial TRM. No diagonal cracks

188

in the brick infill were observed. Overall, the use of the braided textile achieved the same global

189

behaviour as the commercial material, while reducing the amount of visible damage significantly.

190

Ismail et al. [42] performed cyclic tests on infilled 2/3-scaled frames with three different TRM

191

layouts, including an orthogonal full-surface application and two diagonal band configurations with

192

varying width (one-sixth and one-third of the diagonal length of the infill). The latter diagonal band

193

application is similar to the application of FRP strips for infill strengthening (see Table 1). For the

194

diagonal application, the effect of three different fibre materials was evaluated (carbon, basalt and

195

glass), while the orthogonal application employed B-TRM only. Low extend of damage was observed

196

for all retrofitted specimens. Some infill-frame separation was observed in all cases and for the

197

diagonal application of TRM, cracks perpendicular to the strips were observed to form at drift levels

198

above 0.3%. For the full-face TRM retrofit, only minor cracks appeared in the bottom interface and a

199

small extend of diagonal cracks was observed on the TRM surface, with limited debonding. The

200

initial stiffness of the specimens was not found to be affected the retrofit, with differences between

201

5% up to 24% observed. Interestingly, the stiffness was found to be higher for the specimens with the

202

thinner TRM strips. In terms of lateral load capacity, large increases in capacity were observed for all

203

specimens. The increase in width of the diagonal TRM layers was not found to significantly affect this

204

strength increase and the behaviour of the full-surface retrofit was similar to the diagonal

205

strengthening layout. Interestingly, despite the carbon textile had the highest strength of the three fibre

206

materials, the highest strength increase was obtained with the basalt TRM (+ 99%). For the carbon

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TRM the peak was reached at a load 40% higher than the control specimen, while the glass TRM

208

retrofit achieved a slightly lower increase of up to 32%.

209

Finally, Sagar et al. [40] looked at the interaction of in- and out-of-plane damage in masonry infilled

210

RC frames with TRM retrofitting. Six single-storey half-scale frames were tested under cyclic in-

211

plane loading, with out-of-plane testing on a shake table carried out at different levels of in-plane

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drift. The TRM was applied in a single layer to the outer face of the infills only. The investigated

213

parameters were the angle of the fabric mesh (orthogonal vs ±45° in Table 1), the contribution of

214

mechanical anchors, as well as the sequence of fabric placement. In direct bond tests, the latter was

215

found to affect bond strength, with a direct application of the textile on the wall having a higher bond

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strength (0.83 MPa) compared to 0.63 MPa obtained for the conventional “sandwich application”,

217

with a base layer of mortar applied on the infill. In three specimens, mechanical anchors (steel bolts),

218

were installed and a tighter mesh size of the fabric (8 mm instead of 25 mm) was used at the frame-

219

infill interface, to improve transfer of forces to the anchors, but also to strengthen the interface. The

220

experimental results focused on the interaction of in-plane damage and out-of-plane behaviour, with a

221

reduction in connection between frame and infill observed due to out-of-plane plane damage. For the

222

anchored specimens, a better out-of-plane behaviour was observed, however without anchorage, the

223

connection between frame and infill was significantly reduced. This also meant that the in-plane

224

behaviour displayed a more gradual strength degradation for the specimens with anchorage. The

225

specimens with orthogonal TRM application presented a more ductile and dissipative behaviour. In

226

general, strength increase was very similar for all retrofitted specimens, with values close to +30%.

227

2.3. Main observations

228

Based on the reviewed experimental campaigns a number of interesting observations can be made.

229

Firstly, in terms of retrofit application, TRM was generally applied with one or two layers on both

230

sides of the wall, with the exception of Sagar et al. [40] who tested a one-sided intervention. It is note-

231

worthy that even in the one-sided configuration, a significant strength increase was obtained despite

232

additional out-of-plane damage. Applying the fibres at an angle achieved higher strength increase then

233

equivalent orthogonal applications [40,42], as it also controls the shear sliding of the infill and is 9

234

applied in the direction of largest tensile strain. In terms of anchorage, steel ties and bolts, as well as

235

fibre anchors have been used. Compared to non-anchored specimens, anchorage was found to prevent

236

or delay TRM debonding [e.g.: 39], retrofits with anchorage were hence found to give the highest

237

strength increase. Still, significant increase was also observed without any anchorage [e.g.: 42].

238

In terms of materials, as shown in Table 2, a variety of fibre materials have been used in the

239

experimental campaigns, including Carbon (C), Basalt (B), Glass (G) and Steel (S) fibres. The retrofit

240

applications were made with a range of orthogonal mesh sizes between 8 and 25 mm, the thickness

241

per layer of TRM (textile + mortar) is between 4 and 20 mm and the elastic moduli range from 13.8

242

GPa for softer glass textiles to 252 GPa for stiffer Carbon textiles. The effectiveness of the retrofit

243

was found to be affected more by the stiffness of the fibres than the amount of material applied [42].

244

Moreover, the stiffest textiles were found not to provide the highest strength increase and therefore

245

glass or basalt textiles would appear to be more cost effective than carbon. The textile mesh was

246

found to have an effect on visible damage and strength increase, with an increased mechanical

247

interlock with the mortar for braided textiles.

248

Finally, in terms of observed damage mechanisms, generally cracking was delayed for larger levels of

249

drifts for all retrofitted specimens. This reduction in in-plane damage was generally found to improve

250

the out-of-plane residual capacity significantly [39,40]. Cracking at the interface to the frame was

251

observed for all retrofitted specimens, indicating that separation of the infill from the frame cannot be

252

prevented, albeit it was significantly delayed in most cases. It is worth noting that strengthening with

253

orthogonal fibre orientation is effective in preventing diagonal shear cracks, but cannot prevent

254

sliding shear as observed in specimens with relatively low strength masonry mortar [29,39].

255

3. Analytical modelling

256

The effectiveness of TRM retrofitting was highlighted by various experimental campaigns in the

257

literature. Albeit limited, the experimental data gathered on TRM strengthened frames is used here to

258

develop an empirical equation for effective strain for simplified macro-modelling applications.

259

Macro-modelling of infilled frames is a well-studied topic in the scientific literature, with multiple

10

260

approaches leading to an appropriate representation of their response [e.g.: 46–50]. For TRM-

261

strengthened infills, finite-element modelling approaches have been investigated [51,52]. Reliable

262

simplified models are however important to facilitate the use of TRM for the existing building stock.

263

However, only one macro-model developed by Koutas et al. [53] can be found in the literature. This

264

model was calibrated for effective strain in the textile using the first available experiments [29]. With

265

the range of new experimental results, a modification of the model parameters is hence proposed. The

266

analytical model used consists of a one-strut model in compression with an additional tensile tie,

267

accounting for the added strength from the retrofit in tension described in 3.1 and 3.2.

268

3.1. Infill strut model

269

Here the empirical equation for the calculation of the equivalent strut width ( w) by Mainstone [48,54]

270

is taken, as it is not only widely used in the literature [e.g.: 55–57], but also suggested in the FEMA

271

306 [58] guidelines. For the maximum strength of the infill w can be expressed by equation (1): = 0.56

∙

.

∙

[m]

(1)

272

In which H is the height of the frame, dm the diagonal length, and λ represents the relative panel-to-

273

frame stiffness, defined based on the elastic moduli of the infill and the concrete framing member0,s

274

Em and Ec, respectively, in equation (2) by Stafford Smith and Carter [59]: =

$

∙ ∙ sin 2 [m % ] 4 ∙ ∙ ! ∙ ℎ#

(2)

275

Where t is the wall thickness, hw is the wall height, I the second moment of area of the column. To

276

obtain the maximum sustained shear force, the maximum compressive stress carried by an area of

277

infill defined from the equivalent strut width, w, and the actual infill thickness, t, is calculated. The

278

maximum compressive stress can be defined according to multiple failure mechanisms, however,

279

corner crushing is generally seen to be the most crucial to define the maximum force developed in the

280

infill, while other mechanisms like sliding shear usually precede this state [58]. A commonly adopted

281

empirical equation formulated by Decanini et al. [60] is chosen here. Such an approach is compatible

11

282

with the chosen strut width definition and is based on the vertical infill compressive strength fm,inf, the

283

strut angle θ and the relative panel-to-frame stiffness λ, as given by equation (3): &

284 285

'

=

1.12 ∙ & /1 ∙ ∙

,*+, ∙ sin ∙ cos .%0 + /2 ∙ ∙

.

(3)

Where K1 and K2 are empirical parameters defined based on the values of λ [60].

3.2. TRM tie model

286

Following the approach by Koutas et al. [53], the tensile force in the retrofit material is evaluated in

287

the diagonal of the infill, assuming a multilinear stepped-crack pattern. The force developed in the tie

288

depends on the relative orientation of the tie angle θ, angle of the fibres, α, and the angles θcr,j of the

289

assumed cracks. These consist of an inclined crack (j=1), defined as the linear approximation of a

290

stepped crack, and a horizontal crack (j=2). The total force mobilised in the two axes i of the TRM

291

fibres is then transformed geometrically into the direction of the diagonal tie as in equation (4): 0

0

23*4 = 5 5 *9% 89%

63,* : ∙ 7* 34,*

3,*

∙

8

∙ ;cot

=,8

+ 2> − 3 ∙ cot A* B ∙ sin A*

(4)

292

Where, At is the area of TRM and Et the elastic modulus from a TRM coupon test, βi the angle of the

293

fibres to the level normal to the tie-axis, si is the textile mesh spacing and dj the crack lengths, both

294

projected to the normal to the tie-axis [53]. To predict the shear force of the strengthened specimen,

295

Koutas suggested that the effective strain developed in the textile at maximum load, εte, is the main

296

parameter. The same assumption is generally made for FRP strengthened members [32,61]. In this

297

model, TRM effective strain can be considered as a smeared average strain along the length of the tie.

298

3.3. Model calibration

299

The main difficulty in defining the effective strain is the lack of experimental measures. Based on a

300

single experiment, Koutas calculated an effective strain of 0.8% for one layer of TRM for matching

301

their experimental results. For multi-layered TRM, the effective strain was reduced using a hypothesis

302

formulated for FRP [62], rendering a value of 0.57 % strain for double-layer TRM. Here, to determine

303

a new expression for effective strain, the tie- model is calibrated to match experimental strengths for

304

the specimens found in the literature. This approach assumes the capacity of the infilled frames to be 12

305

dominated by the infills and not by the frame (Vframe) and that the TRM retrofit does not significantly

306

influence the secant stiffness, a behaviour which is in line with experimental observations.

307

As the macro-modelling of retrofitted frames is the main objective, it is important not to accumulate

308

the error from modelling the control specimens. To avoid this effect, the assessment of the retrofit

309

model is done based on the increase in strength due to retrofitting. As shown in equations (5) to (7),

310

the difference in capacity between retrofitted and control specimens, ∆V = VR – Vcon, can be defined

311

based on the additional force generated by the TRM tie, Vtie, and any difference in compressive strut

312

force, ∆Vstrut. The latter corresponds to the difference of the retrofitted specimen (Vstrut,R) and the strut

313

force in the control specimen (Vstrut,C) due to potential differences in fm,inf related to: 1) differences in

314

material properties of bricks and mortar; 2) small increase in compressive strength due to the retrofit.

CI = C,=E

315

4

C D+ = C,=E

4

+ CF3=G3,I + C3*4 = C,=E

+ CF3=G3,H 4

+ CF3=G3,H + ∆CF3=G3 + C3*4

∆C = C3*4 + ∆CF3=G3

(5) (6) (7)

3.4. Material properties

316

To model the specimens tested in the literature, some mechanical properties of materials may be

317

unavailable. Table 4 summarises the empirical equations (9) to (11) used to quantify the missing

318

mechanical properties of the infills based on well-accepted equations from design guidelines and

319

standards. It is not an aim of this study to evaluate the effect of the material parameters of the control

320

specimens, which have been studied extensively in the literature [e.g.: 57]. For the mechanical

321

properties of TRM, most researchers only provided manufacturer data for the textile and did not

322

perform coupon tests. The equation provided by Bilotta et al. [63] is used to convert the elastic

323

modulus of the fibre, Ef, to the value Et of the TRM coupon needed for the tensile tie equation (4).

324

4. Results and discussion

325

Calibration of the macro-model using the experimental data in the literature was used to obtain the

326

required effective strain, εeff, for the tie-model. The effective strain required to achieve the

327

experimentally obtained strength increase for all experimental specimens retrofitted with TRM is 13

328

shown in Figure 3. Note that while 20 TRM-retrofitted specimens are found in Table 2, only 16 of

329

these are used for the evaluation, as specific material data was lacking and no strength increase was

330

observed by da Porto et al. [39]. The average effective strain was found to be equal to 0.24%, whereas

331

its maximum and minimum values were equal to 0.66% (with G-TRM) and 0.03% (with C-TRM),

332

respectively. A very low effective strain value for the two specimens retrofitted with C-TRM by

333

Ismail et al. [42] can be related to the high stiffness of the textiles used. Note that a value of 0.4%,

334

corresponds to the design limit for masonry walls in ACI 549.4R [66].

335

4.1. Correlation between experimental and modelling parameters

336

To adequately assess the effect of geometric and material properties on the effective strain, their

337

correlation coefficient r is evaluated. The r-values and hence correlation between the factors is

338

summarised in Table 5. An r-value of 0.37 between the angle of the tie θ and the effective strain is

339

obtained, indicating a low to moderate positive correlation. This is reasonable, as a lower aspect ratio

340

will lead to higher forces developed in the diagonal and hence also increase the effective strain in the

341

TRM. This effect is however not very pronounced due to the combination of a diagonal and horizontal

342

crack considered in the definition of the tie. In turn a strong positive correlation (r = 0.83) between the

343

area ratio of textile, given as a fraction of the infill wall surface (ρt), and the effective strain is

344

obtained. This effect is differing from observations for strengthened RC members with FRP [62].

345

An important material parameter is the elastic modulus of the fibres. In the database a variety of

346

different fibre types with different values of Ef are found. It appears that the effective strain is anti-

347

proportional to the elastic modulus of the material, with a correlation coefficient of -0.5. This is an

348

interesting observation with respect to the experimental observations by Ismail et al. [42] in which

349

stiffer fibres led to a lower strength increase. It would hence appear that using high strength C-TRM

350

does not provide any benefit over lower-cost glass or basalt based textiles. Finally, another important

351

aspect to investigate is the effect of the unretrofitted infill wall strength, fm,inf, on the retrofit

352

effectiveness. No correlation with the effective strain in the TRM was however found (r = -0.01). This

353

can be explained by the effective strain not only being governed by the diagonal deformation, but also

354

by horizontal deformation (sliding shear), which is not affected by infill strength. 14

355

4.2. Empirical equation for effective strain

356

In order to facilitate implementation of the TRM macro-models, an empirical equation for εeff is

357

proposed. Using the results from the correlation study between the assessed parameters, it can be

358

deduced that the model needs an empirical formula related to the TRM area ratio (ρt), similar to

359

equations proposed by Breveglieri et al. [32] for FRP. The negative correlation with the elastic

360

modulus of the textiles (Ef), in turn, will lead to an inverse relationship to effective strain.

361

Figure 4 displays the obtained effective strain (in %) against the ratio ρt/√Ef for the experimental data

362

in the literature. It is important to note that the tie force equation (4) used here was developed for fully

363

wrapped infills. To separate the results for specimens tested with diagonal bands of TRM [42] are

364

plotted separately (blue crosses) in Figure 4. By means of multi-variate non-linear regression, two

365

empirical equations for effective strain (in mm/mm) against a ratio of TRM area (ρt in %) and the

366

square root of textile elastic modulus (Ef in MPa) are formulated using the full data set, as well as the

367

data set excluding the specimens retrofitted with diagonal TRM bands. As shown in Figure 4, the

368

factors in the two equations are very similar, however, a higher goodness of fit (R2) is obtained when

369

looking at the fully wrapped specimens only, for which equation (8) is obtained: :4,, =

1.40 ∙ K3 L

,

M 0 = 0.86

(8)

370

The goodness of fit for this equation is acceptable, considering that very low R² values are often

371

observed for effective strain models calculated from empirical data [e.g.: 67]. Still, the concentration

372

of data on the lower end of the x-axis indicates that further experiments are required in order to

373

achieve more reliable empirical equations for design purposes. The empirical equation (8) formulated

374

based on the experimental evidence at-hand is a first step towards creating reliable simplified models

375

of TRM retrofitted infills. The observation of reduced effectiveness for increased stiffness may be an

376

important observation, suggesting the use of less stiff fibre materials for strengthening masonry infills.

15

377

5. Conclusions

378

A state-of-the-art review of infilled frames retrofitted with textile reinforced mortars was presented.

379

The use of this new class of composite that can be made from a range high strength open-mesh

380

textiles in combination with a cementitious matrix was shown to yield satisfactory strengthening

381

results for the variety of materials and layouts tested thus far. Damage to the infills can be reduced

382

significantly and larger lateral forces can be sustained, as well as providing larger out-of-plane

383

residual capacity. The use of anchorage was found to be beneficial, but not necessarily critical to

384

achieve strength increase. It was observed that very stiff retrofitting textiles may not achieve the

385

highest strength increase and that the fibre orientation is an important factor in retrofit effectiveness.

386

The compiled database of experimental results was used to calibrate a simplified analytical model,

387

using a macro-model based on a pair of compressive strut and tensile tie. The definition of effective

388

strain was found to be crucial in the development of the tensile tie model and factors affecting the

389

effective strain were determined. Based on a correlation study on experimental parameters to the

390

calibrated effective strain, an empirical equation for effective strain based on the TRM area ratio and

391

elastic modulus was proposed.

392

The empirical equation provided a relatively good fit, however it highlighted that currently only

393

limited experimental data is available. Moreover, a majority of the experimental data comes from

394

scaled specimens, and it was shown in previous research that scaling has a non-proportional effect to

395

retrofit effectiveness for composite materials [68,69]. There is also a lack of data for a wider range of

396

TRM area ratios and frame aspect ratios. To develop more precise and reliable macro-models, a

397

systematic testing campaign and detailed finite-element modelling are hence required. Future work

398

will further look at considering the increase of compressive strut force as a result of TRM jacketing,

399

which may constitute a strengthening mechanism of importance.

400

6. Acknowledgements

401

The work of this study was carried out under the European Commission, Joint Research Centre (JRC)

402

Exploratory Research project iRESIST+. 16

403

References

404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453

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594

Figure captions

595

Figure 1. (a) Carbon based textile (b) Application of textile with inorganic matrix on masonry infill walls.

596

Figure 2. Concept for concurrent seismic and energy retrofitting with TRM [28].

597

Figure 3. Calibrated effective strain and experimental increase in lateral capacity for each retrofitted specimen.

598

Figure 4. Empirical fit equation for effective strain for the analytical model.

599

20

600

Figures

601 602

Figure 1. (a) Carbon based textile (b) Application of textile with inorganic matrix on masonry infill walls.

603

604 605

Figure 2. Concept for concurrent seismic and energy retrofitting with TRM [28].

606 607

21

608 609

Figure 3. Calibrated effective strain and experimental increase in lateral capacity for each retrofitted specimen.

610

611 612

Figure 4. Empirical fit equation for effective strain for the analytical model.

613

22

614

Tables

615

Table 1. Summary of composite retrofit applications in the literature.

Type

Layout

Strengthening material

Fibre direction

Examples

Orthogonal TRM

Fibre-textile

2

[29,38–41]

TRM at 45°

Fibre-textile

2

[40]

Diagonal TRM bands

Fibre-textile

2

[42]

Diagonal FRP strips

Fibre-sheet

1

Horizontal FRP strips

Fibre-sheet

1

[11]

ECCs

Lose fibres

∞

[9,34–37]

Reinforced Plasters

Steel bars

2

[7,8]

[12]

23

Table 2. TRM strengthened infilled RC frame specimens tested in the literature

Scale H W θ tinf fm,inf Fibre Ef Mesh ns nt αT Anchor Vexp ∆Vexp ∆max Observed m m ° mm MPa GPa mm # # ° kN % % damage Koutas TRM 2/3 2.0 2.5 36.3 110 5.7 G 73 25 2 2 0 fibre 407.0 54.2% 1.00% CC;HS;PTR Selim SRG-2-2-A 1/3 1.0 1.1 40.6 75 2.5 G 72 25 2 2 0 fibre 131.7 66.3% 1.50% DC;CB Da Porto 3-GC-NR 1 2.9 4.2 34.5 120 2.7 G+S 13.8 10 2 1 0 no 422.8 -2.0% 0.29% ID 4-GC-FN 1 2.9 4.2 34.5 120 2.7 B+S 90 10 2 1 0 steel 432.0 0.1% 0.18% ID 6-BG-NR 1 2.9 4.2 34.5 120 2.4 B+S 90 10 2 1 0 no 285.5 -10.7% 0.29% DC;CC;HS 8-BC-NR 1 2.9 4.2 34.5 120 2.4 B+S 90 10 2 1 0 no 283.8 -9.2% 0.19% ID Akhoundi CTRM 1/2 2.2 2.7 36.5 140 1.4 G 72 25 2 1 0 fibre 118.4 25.1% 0.26% CC;DC;ID BTRM 1/2 2.2 2.7 36.5 140 1.4 G 72 25 2 1 0 fibre 122.6 29.6% 0.18% CC;ID Ismail RFG-D3-3 2/3 2.0 2.5 36.3 150 2.1 G 32 20 2 2 36.3 no 206.0 22.6% 0.90% ID RFG-D6-4 2/3 2.0 2.5 36.3 150 2.1 G 32 20 2 2 36.3 no 221.0 31.6% 0.75% ID;DC RFC-D3-5 2/3 2.0 2.5 36.3 150 2.1 C 252 20 2 2 36.3 no 236.0 40.5% 0.75% ID RFC-D6-6 2/3 2.0 2.5 36.3 150 2.1 C 252 20 2 2 36.3 no 231.0 37.5% / ID;DC 2.1 B 89 8 2 2 36.3 no 290.0 72.6% / ID RFB-D3-7 2/3 2.0 2.5 36.3 150 RFB-D6-8 2/3 2.0 2.5 36.3 150 2.1 B 89 8 2 2 36.3 no 335.0 99.4% 1.00% ID;DC 2.1 B 89 8 2 1 0 no 258.0 53.6% / ID RFB-Fu-9 2/3 2.0 2.5 36.3 150 Sagar DU0–90 1/2 1.5 2.5 29.5 76 7.8 G 114 25 1 1 0 no 285.0 25.0% 0.84% DC;CS* DA0–90 1/2 1.5 2.5 29.5 76 8.0 G 114 25 1 1 0 steel 263.0 15.4% 0.78% DC;HS* SU0–90 1/2 1.5 2.5 29.5 76 7.5 G 114 25 1 1 0 no 253.0 11.0% 0.69% ID* 76 9.6 G 114 25 1 1 0 steel 296.0 29.8% 0.98% DC;CS;ID* SA0–90 1/2 1.5 2.5 29.5 DA45 1/2 1.5 2.5 29.5 76 10.4 G 114 25 1 1 45 steel 293.0 28.5% 0.82% DC;HS;ID* Note: fibres: G: glass; C: carbon; B: basalt; S: steel; damage: CC: corner crushing; HS: horizontal sliding; ID: infill detachment; DC: diagonal cracking; CS: column shear; CB: column bar buckling; PTR: partial TRM rupture; PTD: partial TRM debonding; * includes out-of-plane damage Author

Specimen

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Table 3. Observed final damage in control and retrofit frames in the literature.

Study

Control

TRM-retrofitted

Koutas [29]

Selim [41]

Da Porto [39] (strong mortar)

Da Porto [39] (weak mortar)

Akhoundi [44] (Commercial TRM)

(Braided TRM)

Ismail [42]

Sagar [40]

Note:

cracks buckling

crushed or spalled bricks (observed under TRM)

(partial) TRM debonding (partial) TRM rupture

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Table 4. Equations for estimated mechanical properties

Infill Property Compressive strength 1 Elastic modulus Shear modulus 1

Equation &

,*+, =

0.4 ∙ &O

*+, =

.P

∙&

.0

700 ∙ & ,*+, R = 0.4 ∙ *+,

Source (9) EC 6 [64] – eq. 3.1; for Group 3 masonry units (10) ACI 530-11 [65] - 1.8.2.2.1 (11) ACI 530-11 - 1.8.2.2.2

Where fb represents the brick compressive strength and fm the compressive strength of the mortar.

Table 5. Correlation between experimental parameters and the effective strain (r-value).

θ r-value 0.37 Correlation Low

ρt 0.83 High

Ef fm,inf -0.50 -0.01 Moderate None

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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: