Local post-strengthening of masonry structures with fiber-reinforced polymers (FRPs)

Construction and Building Materials 25 (2011) 3393–3403

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Local post-strengthening of masonry structures with fiber-reinforced polymers (FRPs) Werner Seim a,⇑, Uwe Pfeiffer b a b

Department of Structural Engineering, University of Kassel, 34125 Kassel, Germany André Rotzetter + Partner AG, Consulting Engineers, 6341 Baar, Switzerland

a r t i c l e

i n f o

Article history: Received 7 May 2010 Received in revised form 26 January 2011 Accepted 1 March 2011 Available online 12 April 2011 Keywords: Masonry Post-strengthening FRP Debonding Adhesive Anchoring

a b s t r a c t In-plane loaded masonry structures can be post-strengthened effectively with fiber-reinforced polymers (FRP). This applies to shear walls under vertical and horizontal loading, as well as to walls with additional cut-outs or single loads. A mechanical model is required in all cases for the detailing and design of poststrengthening measures and to characterize load transfer within the wall and, from this, to calculate stresses of masonry and FRP materials. To establish a three-step model for local post-strengthened masonry walls, extensive testing on different scales has been carried out at the University of Kassel within the last few years. Firstly, the load transfer between single masonry units and FRP was addressed. Overall, 91 bonding tests were carried out with seven types of bricks and blocks to examine failure modes and the bonding strength for a broad variety of bricks and blocks. Two different types of adhesive were used in combination with four types of glass- and carbon–fibers. Based on the results of the bonding tests, 24 anchoring tests overall on two different types of masonry – clay brick and calcium–silicate – were carried out under different geometrical and loading conditions. The test results of all test series will be explained by a combination of fracture mechanics and strut-and-tie modeling. A mechanical model based on fracture energy provides the background for the theoretical explanation of the debonding phenomena. The model can be used to predict failure of bonding on single bricks as well as bonding geometries with more than one brick where the bonding area is separated by bed or head joints. Comparison of data from calculations and testing exhibited good correlation. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The application of surface-bonded fiber-reinforced polymers (FRPs) for the post-strengthening of concrete structures is common practice in the engineering and building construction sector. Generally accepted design guidelines have been established in different countries (e.g. [1]). Post-strengthening of concrete structures mainly provides additional reinforcement for the bending resistance of beams or slabs, for the confinement of short columns or moment-resisting beam column connections. An overview of the potential of FRPs for the post-strengthening of masonry structures is given by Seim et al. [2]. The load-bearing capacity of masonry columns could be more than doubled by confinement with glass–fiber and carbon–fiber reinforced polymers (GFRP and CFRP), as was shown by Bieker et al. [3] in 2002. An outstanding practical application of FRPs in the field of cultural heritage is documented by Cosenza and Iervolino [4] for a medieval tower and by Croci [5] for the retrofit the

⇑ Corresponding author. Tel.: +49 561 8042625; fax: +49 561 8047647. E-mail address: [email protected] (W. Seim). 0950-0618/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.conbuildmat.2011.03.030

masonry vaults of the St. Francis Basilica of Assisi after an earthquake in 1997. For in-plane loaded masonry walls – which are typically unreinforced in Middle Europe – the lack of tension strength is always a kind of disadvantage which leads to different failure modes and limited deformation capacity. Therefore, it is not astonishing that the application of FRPs for the post-strengthening of masonry walls has been introduced by different authors. Ehsani et al. [6,7] used glass–fiber sheets for the repair of a one-story commercial building, which was damaged during the Northridge earthquake in 1994. Schwegler [8] describes the post-strengthening of an office building in Basel (Switzerland) against earthquake impact. Seim et al. [9] have already demonstrated that FRPs can also be used effectively for local post-strengthening of in-plane loaded masonry walls. This might be of importance if cut-outs are required for additional openings or in areas where additional single loads lead to horizontal tension stresses. The application of FRPs for the post-strengthening of masonry walls is comparatively simple. If it is necessary, the masonry surface has to be smoothed by grinding. Sand blasting, which is indispensable for concrete surfaces, is not necessary for masonry if the surface is clean and if the surface tensile strength was checked by

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pull-off testing. The ‘‘wet lay-up’’ technique will usually be used: In this case, one or more layers of fiber sheets are embedded in the adhesive which was applied to the masonry surface. The adhesive provides both matrix material for the FRP and adhesion. Depending on the type of adhesive used in combination with the masonry surface, it might be necessary to apply a primer first. Most of the research which was carried out over the last few years focused on post-strengthening measures to improve shear strength and ductility, in particular against earthquake impacts. Tumialan et al. [10] and Jai et al. [11] used carbon–fibers, glass–fibers and aramid-fibers in combination with epoxy adhesives, whereas Wallner [12] combined different types of fibers with epoxy adhesives and with polymer cement mortar. In these cases of full-surface or strip-like post-strengthening, debonding between the FRP and masonry surface was not considered or debonding was excluded by the anchoring of the FRPs onto concrete elements such as slabs or foundations. If FRPs are used for local post-strengthening, it is essential to know precisely about bonding and debonding. Fig. 1 depicts a modeling strategy which consists of three steps at three scales: (1) global equilibrium and load transfer considering FRP reinforcement, (2) the anchoring of the FRPs and (3) bonding between FRP and masonry units. For the first step, different modeling tech-

niques from the Finite-Element-Method (FEM) to simplified stress-fields or strut-and-tie models are established for masonry with and without additional reinforcement [13]. For steps (2) and (3) – anchoring and debonding – the knowledge seems to be more fragmentary. Triantafillou already addressed the bending strength and shear strength of post-strengthened masonry in 1998 [14]. Aiello and Sciolti [15] and Wallner [12] tested the bondingstrength of certain brick-FRP respective to stone-FRP combinations. However, a mechanical model which represents the anchoring of FRP on masonry surfaces for a wide variety of material combinations is still lacking. Extensive research was therefore carried out at the University of Kassel during the last five years. The main results of experimental testing of bonding and anchoring are presented and explained in the following. Furthermore, a mechanical model which is able to cover bonding and anchoring based on fracture mechanics will be presented and verified. The research focuses on FRPs glued to the masonry surface. The technology of Near-Surface-Mounted (NSM) FRPs was not considered. 2. Material characteristics Seven types of solid bricks, three types of adhesives and four types of fiber sheets were considered in various combinations for bonding tests to represent the variety of brick materials which are to be found within existing structures. The wall specimens to be used for the anchoring tests were manufactured from two types of bricks (KS20, Mz 20) and a lime-cement mortar. An overview of brick characteristics is given in Table 1 and Table 2. According to definitions which are common practice in Germany, KS and Mz stand for calcium–silicate and clay bricks, respectively. The number 20 represents the minimum of the compression strengthening in N/mm2.The focus on solid bricks seems to be reasonable because this material represents a large fraction of masonry walls in existing buildings and it gives the possibility of excluding the influence of inhomogeneity from cores. From previous research on the debonding of FRPs from concrete surfaces, it is already known that compression strength fst,z and tensile surface strength fst,tz perpendicular to the bonding surfaces are the critical material parameters to characterize bonding strength. For a definition of material axes see Fig. 2. The compression strength perpendicular to the surface was derived from cylindrical cores, each of 50 mm diameter and length, which were drilled from the bricks. Pull-off testing with a steel stamp (diameter of 50 mm) provided data for surface tensile strength fst,tz. In this context, values from standard testing (fst,tz,DIN) with predrilled circular cut are compared to values derived with a newly developed testing device, which does not need predrilling (fst,tz,DP). Both test methods and the results are explained in detail by Seim and Pfeiffer [16]. The two parameters which control the masonry compression strength are the compression strength of the bricks fst,x and the compression strength of the mortar fmo. Compression tests on whole bricks were carried out. The compressive strength of the lime-cement mortar fmo was tested with prisms of a length and width of 160 mm and 40 mm, respectively. Compression strength of the masonry in the xdirection – which is usually the vertical direction – was calculated as b c fx ¼ a  fst;x  fmo

Fig. 1. Post-strengthened masonry walls – three steps of modeling.

ð1Þ

Table 1 Compression strength for different types of bricks. Dimensions bst/lst/hst (mm/mm/mm)

Compression strengtha n (–)

fst,z (N/mm2)

sst,z (N/mm2)

115/240/71 115/240/71 115/240/71 115/240/71 115/240/71 120/250/65 115/240/71

5 5 5 5 5 5 5

26.0 26.2 34.3 31.2 40.2 22.2 86.5

0.85 1.84 2.30 2.35 2.47 3.22 12.0

Brick type

KS 12 KS 20 KS 28 Mz 12 Mz 20 hiMz Sa a

Calcium–silicate Calcium–silicate Calcium–silicate Solid clay bricks Solid clay bricks Solid clay bricks Sandstone

brick brick brick

from an existing building

Tested on cylindrical cores (diameter and length: 50 mm), parallel to bed joints.

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W. Seim, U. Pfeiffer / Construction and Building Materials 25 (2011) 3393–3403 Table 2 Surface tensile strength for different types of bricks. Adhesive

Surface tensile strength DPa

Surface tensile strength DINb

2

n

2

fst,tz,DP (N/mm )

sst,tz,DP (N/mm )

n

fst,tz,DIN (N/mm2)

sst,tz,DIN (N/mm2)

Brick type

a b

KS 12

A B

5 5

2.35 2.75

0.23 0.31

5 5

1.78 1.62

0.50 0.45

KS 20

A B

15 15

2.62 2.64

0.24 0.24

15 15

2.32 2.13

0.41 0.38

KS 28

A B

5 5

2.70 2.84

0.19 0.28

5 5

1.81 1.80

0.27 0.40

Mz 12

A B

15 –

2.07 –

0.26 –

15 15

1.78 1.68

0.24 0.27

Mz 20

A B

15 15

2.35 2.30

0.60 0.34

15 15

2.30 2.03

0.61 0.58

hiMz

A B

5 5

1.67 2.11

0.23 0.20

5 5

0.56 0.97

0.21 0.41

Sa

A B

5 5

3.21 3.69

0.21 0.08

5 5

2.28 2.49

0.73 0.44

Pull-off testing with a stamp (diameter of 50 mm) without circular cut on brick surface (DP). Pull-off testing with a stamp (diameter of 50 mm) with circular cut on brick surface (DIN).

Fig. 2. Definition of material axes: (a) bricks and (b) wall elements.

This empirical formulation is capable of considering a large variety of different brick – mortar combinations and was therefore adopted for international codes such as EC 6 [17]. According to Schubert [18], parameters a, b and c are  a = 0.70, b = 0.74, and c = 0.21 for calcium-silicate bricks KS20 and  a = 0.73, b = 0.73 and c = 0.16 for clay bricks Mz20. For the modeling of the complete load transfer of the anchoring zone, the compression strength of the masonry in the horizontal y-direction has to be introduced. According to Glitza [19], this parameter can be specified as

fy ¼ 0:75  fx

were used for the bonding tests. Furthermore, a high strength concrete mortar, which might be advantageous in terms of fire resistance, was used as the matrix material in combination with glass–fiber sheets. The main characteristics of adhesives are documented in Table 3. Material characteristics of FRPs were tested on strips according to DIN 2747 [21]. The dimensions of the strips were 50 mm wide and 250 mm long. The tension strength values, as documented in Table 4, are mean

Table 3 Characteristics of adhesive materials.

ð2Þ

Three different types of glass–fiber sheet and one type of carbon–fiber sheet were used in combination with two epoxy resins and one high performance cement mortar. Full documentation of all materials and test results is given by Pfeiffer [20]. If the FRP material is applied directly to the surface of the member to be strengthened, then both functions – matrix and adhesion – are assigned to the adhesive. It is obvious that in this case the viscosity of the adhesive has a major influence on the bonding strength. This was already shown by Ehsani et al. [7]. Therefore, two epoxy resin adhesives with a comparatively high and a low viscosity

Adhesive

Type

Strength (N/mm2)

Viscosity

Density (kg/l)

Color

A

Epoxy resin Epoxy resin Cement mortar

30.0 (tensile)a

High

1.31a

Grey

B C a

35.0 (tensile)

a

74.0 (compression)

Data as given from manufacturer.

Low

1.11

High

–

a

Semitransparent Grey

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W. Seim, U. Pfeiffer / Construction and Building Materials 25 (2011) 3393–3403

Table 4 Material characteristics of GFRP.a Adhesive

A B B B B a

Number of layers

1 1 2 3 4

Thickness

Fiber fraction

Young’s modulus 2

Ultimate strain

Tensile strength

(mm)

(%)

(N/mm )

(–)

(N/mm2)

(kN/m)

0.70 0.57 1.14 1.55 2.08

20 24 24 27 27

19.345 20.582 22.548 24.253 25.616

0.0181 0.0153 0.0190 0.0149 0.0136

350 314 428 363 349

245 179 488 562 726

Results are mean values out of three tests for each material.

values. For the anchoring tests, the focus was put on FRPs from glass–fibers which were identified as most adequate not only to increase the load bearing capacity, but also to enhance the deformation capacity of typical masonry structures.

3. Bonding tests Overall, 91 bonding tests were carried out using the test set-up as shown in Fig. 3. The bricks were usually just cleaned with air pressure. Only the historical clay bricks (hiMz) received pretreatment with a steel brush. After that, a first layer of adhesive was applied to the brick surface. For the bonding tests, generally one layer of fiber sheet was placed into the adhesive with a roller. The test set-up consisted of a steel frame to apply the tension– compression loading of the specimens. The bricks were therefore fixed into the frame and the FRP sheet was anchored against a rounded steel block. The width of FRP sheets was 65 mm for the historical clay bricks and 70 mm for all other samples. The bond length of 240 mm was kept constant in the first series A and was varied between 60 mm and 180 mm in the second series B. The tests were carried out under displacement control with a loading rate of 0.35 mm per minute. The test results are documented in Table 5. It should be noted that the ultimate forces Fu are related to two FRP strips respective to two bonding areas, at one brick. The combination of GFRP sheets with a lower viscosity adhesive (adhesive B) leads to increasing failure loads of about 40% compared to the specimens with adhesive A. This phenomenon is independent of the type of bricks, as Fig. 4 depicts. Therefore, epoxy adhesives with lower viscosity are recommended for application.

Maximum forces of about 27.8 kN could be reached for a bond length of 240 mm for the CFRP material. Generally, the failure for all brick materials occurred in a typically brittle manner within the bricks in an area close to the surface (Fig. 3). Three phases of debonding could be identified during the tests. At the beginning, the bond between the brick and FRP was intact and no cracks were visible until the second phase. In this second phase, wedge-shaped cracking developed. The third phase was a complete bonding failure within the brick material. Fig. 5 depicts two typical load–displacement curves. Both graphs exhibit two nearly linear parts (pre- and post-failure) connected by a non-linear section. The transition from the linear to the non-linear section occurred when the first cracks formed. This point was defined as F 0u;exp . Subsequent increase of bond forces can be assigned to friction effects. This phenomenon of friction contribution was already documented by Aiello and Scolti [15]. Obviously, the contribution of friction depends on the bonding length and on the roughness of the area after debonding. This roughness is considerably higher for clay bricks compared to calcium–silicate bricks. By the interpretation of load–deformation curves, friction action could be conservatively evaluated to 5% for calcium–silicate bricks and to 20% for clay bricks for a bond length of 240 mm. This leads to the following formulation:

F 0u;exp ¼ f  F u;exp

ð3Þ

with f = 0.95 for calcium–slicate bricks and sandstone, f = 0.80 for clay bricks.

Fig. 3. Bonding test A50 (Mz20-B-Sa397G): (a) test device, (b) and (c) failure mode with formation of ‘‘teeth’’.

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W. Seim, U. Pfeiffer / Construction and Building Materials 25 (2011) 3393–3403 Table 5 Bonding tests – material combinations, validation of test results. Test

Brick

Adhesive

Sheet

fst,z (N/mm2)

fst,tz,DP (N/mm2)

lv (mm)

F 0u;exp (kN)

F cal: (kN)

F 0u;exp =F cal:

A1-A4 A5-A8

KS20 KS20

A B

SW430G

26.16 26.16

2.62 2.64

240 240

10.25 16.82

13.10 16.66

0.78 1.01

A9-A12 A13-A16

KS20 KS20

A B

SP90/10G

26.16 26.16

2.62 2.64

240 240

9.39 15.37

12.42 15.48

0.76 0.99

A17-A19 A20-A22 A23-A25 A26-A28 A29-A31 A32-A34 A35-A37 A38-A40 A41-A43 A44-A46 A47-A49 A50-A52 A53-A55 A56-A58 A59-A61 A62-A64 A65-A67 B1-B3 B4-B6 B7-B9 B10-B12 B13-B15 B16-B18

KS12 KS20 KS28 Mz12 Mz20 Sa hiMz KS12 KS20 KS28 Mz12 Mz20 Sa hiMz Hlz KS20 Mz20 KS20 KS20 KS20 Mz20 Mz20 Mz20

A

Sa397G

25.98 26.16 34.27 31.22 40.43 86.47 22.19 25.98 26.16 34.27 31.22 40.43 86.47 22.19 – 29.11 40.43 26.16 26.16 26.16 40.43 40.43 40.43

2.35 2.62 2.70 2.07 2.35 3.21 1.67 2.75 2.64 2.84 – 2.30 3.69 2.11 – 2.96 2.30 2.64 2.64 2.64 2.30 2.30 2.30

240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 240 180 120 60 180 120 60

9.10 9.46 13.40 12.71 12.24 16.79 12.42 13.00 14.94 17.07 17.70 14.14 22.58 15.93 11.44 23.98 22.25 14.63 15.18 13.96 14.96 14.74 14.39

11.15 11.48 12.38 11.31 12.46 16.29 9.14 15.02 14.89 16.22 – 16.04 21.83 12.54 – 28.54 29.08 14.76 14.76 14.50 16.04 16.04 15.83

0.82 0.82 1.08 1.12 0.98 1.03 1.36 0.87 1.00 1.05 – 0.88 1.03 1.27 – 0.84 0.76 0.99 1.03 0.96 0.93 0.92 0.91

B

SP240C Sa397G

bv = 65 mm for hiMZ, bv = 70 mm for all other tests.

16

brick 14 adhesive B - low viscosity

12

FRP Fu

Ff [kN]

10

Ff

8

Ff

A1-A4

6

A5-A8 A9-A12

4

A13-A16

adhesive A - high viscosity

A20-A22

2

A41-A43 A62-A64

0 0

500

1000

1500

2000

2500

3000

3500

Ef · A f [kN] Fig. 4. Comparison between the FRP tension stiffness and ultimate bond forces.

Overall, seven different FRPs were manufactured by combining four types of fibers with two types of resins to study the influence of FRP stiffness on bonding strength (Table 5). Here, a nearly linear relation was detected with higher FRP stiffness leading to higher ultimate bond forces. The explanation of this phenomenon will be given in Section 5.1. The increase of FRP tension stiffness can be realized with different materials (e.g. glass–fiber versus carbon–fiber) or by the number of FRP layers. The bonding test on solid bricks and blocks allowed the presumption that the compressive strength and tensile strength of the bricks are the critical parameters for debonding. This presumption will be reassured in Section 5. Again, it should be stated that, in this case, tensile strength should always be equalized with sur-

face tensile strength; and surface tensile strength has always to be determined for the specific adhesive material. Additionally, the bond characteristic between vertical coring bricks and GFRP was studied with three bonding tests (Hlz). The failure occurred not in debonding, but through a crushing of the bricks’ internal structure. Moreover, the bond characteristics of GFRP sheets applied with high performance cement mortar were tested with two test series. The use of a cement mortar might be advantageous if a comparatively low bonding strength is sufficient, such as for full-surface applications on masonry walls. It could be shown that in the case of cement mortars, the failure occurred interlaminar between the glass–fibers and the mortar with ultimate bond forces of about 5 kN independent of the type of brick.

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10 ultimate bond-force Ff

9 8 7

Ff [kN]

6

part of friction for test A41

part of friction for test A52

part of bond-force for test A41

part of bond-force for test A52

region where the first crack occurred Ff'

5

brick

4 3

FRP relative displacement δv

2 test A52: Mz20-B-Sa397G

1

Fu Ff

Ff

test A41: KS20-B-Sa397G

0 0.0

0.5

1.0

δv

1.5

2.0

2.5

[mm]

Fig. 5. Comparison of typical load–displacement curves for solid calcium–silicate bricks KS20 and clay bricks Mz20.

4. Anchoring tests For the modeling of post-strengthened masonry walls, it is important to understand the load transfer between the FRP material and the masonry surface at the anchoring regions. Therefore, a test set-up (Fig. 6) was developed which is able to represent this situation. The geometrical parameters for masonry specimens and FRP material are documented in Table 6. The thickness of the masonry was 115 mm for all specimens. Two different directions of the fibers parallel and perpendicular to the bed joints are considered (|| and \). The location of hydraulic jacks and abutments lead to an inclination of the compression forces as illustrated in Fig. 12. To consider the typical loading conditions within in-plane loaded masonry walls, the test specimens were prestressed with 50 kN for FRP fibers parallel and with 12.5 kN for FRP fibers perpendicular to the bed joints. The tests were carried out with two types of bricks, a solid calcium–silicate brick (KS20) and a solid clay brick (Mz20). As the bricks came from a new delivery of the manufacturer, both compression strength and tensile surface strength were tested – again on five samples each. The mean values from material testing are documented in Table 6. COV (standard derivation) was similar to the tests as documented in Table 1. Again the FRP was manufactured and applied by wet lay-up technique. The results from bonding tests suggested the use of

glass–fiber sheets in combination with a low viscosity epoxy resin adhesive (type B). Stiffness of the FRP was varied by the number – one to four – of the layers. See Table 4 for the material characteristics of the FRP material. The specimens were loaded under displacement control with a loading rate of 2 mm per minute. The failure was typically introduced by first cracks between FRP and masonry at the beginning of the bonding area (Fig. 7). After the onset of debonding, no more load increase was possible (Fig. 8). The failure occurred by the pulling off of a layer of brick material approximately 5 mm to 30 mm deep. The orientation of FRPs perpendicular to the bed joints leads to an increase of maximum bond forces up to 35% compared to orientation parallel to the bed joints. This is easy to understand because there are considerably more brick elements which are activated for bonding. A theoretical explanation of this phenomenon will be given in the following section. Increasing bonding strength goes along with the increasing tension strains of the FRPs. It could be observed that the formation of cracks declined for the higher tension stiffness of the FRP which is equal to more layers of FRP, and a nearly linear connection could be found between the FRP width and the ultimate bond forces achieved. Additional information of the test results is given by Pfeiffer [20].

Fig. 6. Geometry of wall elements.

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W. Seim, U. Pfeiffer / Construction and Building Materials 25 (2011) 3393–3403 Table 6 Anchoring tests – material combinations, geometry of wall specimens and test results. Test

Brick

fst,z (N/mm2)

fst,tz,DP ([N/mm2)

Number of layers and direction to bed joints

bf (mm)

la (mm)

lx/ly (mm)

Fu,exp. (kN)

C1-C3 C4-C6 C7-C9 C10-C12 C13-C15 C16-C18 C19-C21 C22-C24

KS20

37.8

2.98

2

100

490

Mz20

26.6

2.66

25.4

2.60

820/740 750/740 820/740 750/740 820/740 750/740 820/740 910/740

75.9/66.7/66.3 73.8/76.0/75.2 59.9/56.9/52.2 72.7/82.8/76.2 97.1/89.5/88.3 106.7/103.9/120.6 140.4/106.8/140.3 138.8/157.9/144.7

3 4 3

|| \ || \ || \ || ||

150 200

615 570 740

Fig. 7. Typical failure modes for FRPs parallel (test C8) and perpendicular (test C6) to the bed joints.

Fig. 8. Typical load displacement-curves for anchoring tests.

5. Modeling of bond and anchoring

5.1. Modeling of bond

An efficient strengthening of the masonry with FRPs requires full knowledge of the load transfer within the building structure, as well as of the load transfer between the FRP and the masonry surface. For the building structure, FE modeling or simplified strut-and-tie models might be adequate. Both modeling techniques are based on structural mechanics. For the description of the load transfer between the FRP and the masonry surface, fracture mechanics can be used to explain the bonding and anchoring phenomena.

In the following, the modeling of debonding is based on fracture mechanics. The ultimate bond force Ff can be generally found with the formulation of Eq. (4), in dependence of the bond width bv, the bond length lv and the shear function sv (x):

F f ðlv Þ ¼ bv 

Z

x¼lv

x¼0

sv ðxÞdx

ð4Þ

Eq. (4) can be derived from the solution of the differential equation of the elastic bond (Fig. 9),

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d00v  sv ðdv Þ 



1 1 þ Ef  t f Est  t st



¼0

ð5Þ

with dv and sv as shear strains and shear stresses over bonding length. Ef and Est represent Young’s Moduli and tf and tst the thickness of the bonded materials. This formulation – sometimes called Volkersen’s theory – was first published in 1953 [22]. If the relation of shear stresses over strains is assumed to be linear (Fig. 9c), then the solution of the differential equation is given by Eq. (6) with x as an auxiliary value. The ultimate bond force depends on the width of FRP bv, the fracture energy Gv, the Young’s Modulus of the FRP Ef, the thickness of FRP tf, and the bond length lv. The ultimate shear stress sv1 can be derived based on the Mohr– Coulomb failure criteria from Eq. (7).

F f ðlv Þ ¼ bv  1 2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  Gv  Ef  t f  tanhðx  lv Þ

ð6Þ

qffiffiffiffiffiffiffiffiffiffiffiffiffiffi

sv 1 ¼  fst  fst;t

ð7Þ

A comparison of the ultimate bond forces from testing and from calculation is given in Fig. 10, with F 0u;exp according to Eq. (1) and Fu,cal. = 2Ff according to Eq. (6). The comparison of the bond forces demonstrates a good correlation between the results from testing and from calculation. The maximum difference is less than 25% if the historical bricks are not considered. These bricks showed higher bond forces compared to the ultimate forces from calculation. This can be explained by the porous structure of these bricks, which allows comparable deep infiltration of adhesive into the brick surface. However, it must be stated that the coefficient cv is only valid for the FRP-adhesive combination for which it was derived. Therefore, any calibration must be carried out with specific adhesives and sheet types on various types of brick surfaces. Then the calibration is obviously able to cover different brick materials. The maximum bond-force Fu,cal. will be achieved with the critical bond-length lv,max.

lv ;max ¼ 4 

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2  Gv  Ef  t f

x¼

s2v 1

ð8Þ

2  Gv  Ef  tf

The fracture energy Gv is equivalent to the dissipated energy and can be interpreted as the area under the stress–strain relation for shear (Fig. 9c). For linear stress–strain relations, Gv is given with

Gv ¼

1 1  dv 1  sv 1 ¼  dv 1  2 4

qffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffi fst  fst;t ¼ cv  fst  fst;t

ð9Þ

When sv1 is predefined as a material value according to Eq. (7), the maximum relative displacement dv1 is unknown. This value can neither be calculated theoretically nor measured experimentally. Therefore, the introduction of a coefficient cv for calibration is common practice. The coefficient cv could be derived from bonding tests A17 to A58 considering individual strength parameters of the brick surface:

adhesive A ðhigher viscosityÞ : cv ¼ 0:030 for f st;t;DP ; cv ¼ 0:034 for f st;t;DIN

A bond-length less than lv,max leads to a nonlinear reduction of ultimate bond-forces. On the other hand, the maximum bond forces reach a plateau if the bonding length exceeds the critical bondlength. This behavior is well known from research on the poststrengthening of concrete beams [23]. As it was already stated in Section 3, there is a considerable influence of friction on debonding. For bonding lengths of lv,max and less, it can be assumed that the influence of friction is comparatively low and that it is justified to neglect friction contribution in these cases. If the bonding length is more than lv,max, then the friction contribution is assumed to increase linear over bondinglength as is documented in Fig. 10a and c. The comparison of theoretical and experimental results which are calculated on this basis show good accordance as Fig. 10b and d depict. This applies to bonding lengths between 60 mm and 240 mm, which are representative for typical brick geometries. 5.2. Modeling of anchoring

adhesive B ðlower viscosityÞ : cv ¼ 0:058 for f st;t;DP ;

Within the three scales of modeling of post-strengthened masonry walls, the mechanical model of the anchoring region is an

cv ¼ 0:075 for f st;t;DIN

(a)

ð10Þ

s2v 1

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

(b)

bst

dNst Nst

bv Detail

x

Nf ust u δv f

x

lst dx

lv

τv(δ v)

ττv(x)

Nst

Nf dNf

Ff

brick adhesive FRP

Ff

(c)

τv τ v1

δv τ v (δ v) = τv1 δ v1

δ v1

δv

Fig. 9. (a) Bonding area, (b) detail of the bonding area with forces and stresses and (c) linear stress–strain relations for shear.

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22

22

20

20

18

18

16

16

14

14

F [kN]

4

ςv = 0,80

6

ςv = 0,88

6

10 8

ςv = 0,95

ςv = 1,0

8

ςv = 0,97

10

lv,max. = 95 mm

12

180 B10-B12

240 A50-A52

ςv = 0,97

lv,max. = 102 mm

ςv = 1,0

12

ςv = 0,99

F [kN]

W. Seim, U. Pfeiffer / Construction and Building Materials 25 (2011) 3393–3403

4

ζv (raised)

2

ζv (raised)

2 0

0 lv [mm] tests

60 B7-B9

120 B4-B6

180 B1-B3

lv [mm] 60 tests B16-B18

240 A41-A43

(a)

120 B13-B15

(c)

22

22

20

20 lv,max. = 95 mm

lv,max. = 102 mm

18

16

16

14

14

12

parameters for calculation:

10

Gv,DP = 0.482 N/mm = 4.16 N/mm2 Ef = 20582 N/mm2 bv = 2x 70 mm t f = 0.57 mm

8 6

F [kN]

F [kN]

18

12

prameters for calculation:

10

Gv,DP = 0.559 N/mm = 4.82 N/mm2 Ef = 20582 N/mm2 bv = 2x 70 mm t f = 0.57 mm

8 6

4

4

2

2

0

0

lv [mm] tests

60 B7-B9

120 B4-B6

180 B1-B3

240 A41-A43

(b)

60 lv [mm] tests B16-B18

120 B13-B15

180 B10-B12

240 A50-A52

(d)

Fig. 10. Influence of friction on bonding strength and comparison of experimental and theoretical results – (a) and (b) calcium–silicate bricks. (c) and (d) Clay bricks.

important module. If the FRP is stressed, single bricks between the joints become separated. This behavior can be compared to the cracking of concrete beams due to bending. Therefore, a bond model for the anchoring was adopted from Schilde and Seim [23]. The anchoring on multiple bricks is illustrated in Fig. 11 and can – based on the solution for bonding on single bricks (see Eqs. (6)–(9)) – be covered with Eq. (11).

 2  x  Gv  Ef  tf  bv DF f ;i ¼ F f ;i þ F f ;i  coshðx  lv Þ þ sv 1  F f ;i  sinhðx  lv Þ  tanhðx  lv Þ

ð11Þ Fig. 11. (a) Bonding on multiple bricks (b) partial bonding.

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W. Seim, U. Pfeiffer / Construction and Building Materials 25 (2011) 3393–3403

Fig. 12. Test C16–C18: modeling of anchoring.

175 experimental result

150

without friction and without kv without friction and with kv

Fu [kN]

125

with friction and kv

100 75 50 25 0 C1 - C3

C4 - C6

C7 - C9

C10 - C12 C13 - C15 C16 - C18 C19 - C21 C22 - C24

Fig. 13. Anchoring tests C1–C24: comparison of experimental and theoretical results.

The coefficient kv (Eq. (11)) from Holzenkämpfer [24] was adopted to consider the 3-D effects of debonding for the anchoring region.

The ultimate bonding force Fu,cal. will be given by summation of difference forces DFf,i from Eq. (11):

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 kv ¼ 1 þ ðbv =bv ;sup: Þ

F u;cal: ¼ kv 

For the definition of bv and bv,sup. see Fig. 11 (b).

ð12Þ

n X

DF f ;i

ð13Þ

i¼1

The calculation of bond forces at the anchoring region should be carried out step-by-step starting at the end bond element with Ff,i = 0. Then the bond forces at the second element can be calcu-

W. Seim, U. Pfeiffer / Construction and Building Materials 25 (2011) 3393–3403

lated and so on. A simplified algorithm capable of practical application is proposed by Pfeiffer [20]. Full calculation of the anchoring forces cannot be separated from the modeling of the load transfer of the anchoring region. The theory of stress fields was therefore used (see Zimmerli et al. [13]). For the masonry material, the failure criteria of Ganz [25] was adopted. Modeling of the anchoring region was carried out according to the following steps: 1. Step-by-step respectively stone-by-stone calculation of maximum bonding forces. 2. Design of stress fields (inclination, width and depth) considering the failure criteria for masonry. 3. If necessary, reduction of bonding forces which can be activated due to maximum capacity of single stress fields. 4. Verification of masonry stresses ry for reduced strength due to tension stresses perpendicular to the surface. Fig. 12 depicts the modeling of load transfer for specimens C16– C18. Fig. 13 gives an overview of theoretical versus experimental results. It becomes obvious that friction contribution must be considered as it was already detected for single bond units in Section 5.1. Overall, the comparison between experimental results and test results shows good correlation. 6. Summary and conclusions Overall, 91 bonding tests with FRPs and various brick materials were carried out to establish a theoretical model which is able to predict the bonding strength. The influence of bonding length, stiffness of the FRP and of the viscosity of the adhesive could be specified. It could be proved that a linear stress–strain relation for shear can be used to solve the differential equation of elastic bond. The solution of this equation gives reliable values for the bonding strength for various types of brick materials. To establish a three-step modeling for local post-strengthened masonry walls, 24 anchoring tests were carried out. Various bond surface area geometries (490–1480 cm2) in combination with different FRP thicknesses (2–4 layers) were considered for two types of bricks and two different directions (0° und 90°) between FRPs and the horizontal bed joints. Anchoring forces up to 158 kN could be reached. Failure usually occurred by debonding within the masonry material close to the surface. Wall elements with FRPs perpendicular to the horizontal bed joints tended to reach higher anchoring forces compared to FRPs parallel to the bed joints. Stress fields were used to model load transfer between loading, masonry, FRP and abutments. The calculation of the anchoring forces was carried out based on fracture mechanics. The comparison of the results from calculations with the test results show good accordance. Nevertheless, further research is needed to clarify the bond strength reduction within the bricks due to transverse tension stress. Further adjustment of the structure model is necessary for the application of FRPs oriented somehow between parallel and perpendicular to the bed joints. This will include diagonal tension and shear tests. For post-strengthening against earthquake impact, further research will focus on the increase of deformation capacity. In this context, the influence also of the load history – post-

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strengthening of vertical loaded masonry walls – should be addressed. Moreover, the issues of fire resistance and long-term characteristics of adhesive bonding need further consideration. Acknowledgments The research was part of a project which was funded by the German Research Foundation (DFG). Sika Deutschland GmbH, S&P Clever Reinforcement GmbH and SAERTEX GmbH & Co. KG provided fiber materials and adhesives. References [1] FIB Bulletin 14. Design and use of externally bonded fibre reinforced polymer reinforcement (FRP EBR) for reinforced concrete structures. Technical Report by EBR; July 2001. [2] Seim W, Pfeiffer U, Vogt T. Nachträgliche Verstärkung gemauerter Tragwerke mit Faserverbundwerkstoffen. Bautechnik, Heft 2010;2:51–60. [3] Bieker C, Seim W, Stürz J. Post-strengthening of masonry columns by use of fiber-reinforced polymers. In: Third international conference on composites in infrastructure, San Francisco; 2002. [4] Cosenza E, Iervolino I. Case study: seismic retrofitting of a medieval bell tower with FRP. J Compos Constr 2007:319–27. [5] Croci G. Restoring the Basilica of St. Francis of Assisi. CRM J 2001;26–9. [6] Ehsani MR, Saadatmanesh H. Seismic retrofit of URM walls with fiber composites. The Masonry Soc 1996:63–72. [7] Ehsani MR. Strengthening of earthquake-damaged masonry structures with composite materials. Non-metal (FRP) Reinforcement Concr Struct 1995:680–7. [8] Schwegler G. Verstärkung von Mauerwerkbauten mit CFK-Lamellen. Schweizer Ingenieur Architekt 1996;14–6. [9] Seim W, Humburg E, Stürz J. Local post-strengthening of masonry walls by use of fiber-reinforced polymers (FRP). Composites in Construction. University of Calabria; 2003. [10] Tumialan JG, Myers JJ, Nanni A. Field evaluation of masonry walls strengthened with FRP composites at the Malcolm Bliss Hospital. Scientific Report. Department of Civil Engineering, University of Missouri-Rolla; 1999. [11] Jai J, Springer GS, Kollar LP, Krawinkler H. Reinforcing masonry walls with composite materials – model. J Compos Mater 2000:1548–80. [12] Wallner C. Erdbebengerechtes verstärken von mauerwerk durch Faserverbundwerkstoffe – experimentelle und numerische untersuchungen. PhD thesis, University of Karlsruhe; 2008. [13] Zimmerli B, Schwartz J, Schwegler G. Mauerwerk – Bemessung und Konstruktion. Basel: Birkhäuser-Verlag; 1999. [14] Triantafillou TC. Composites: a new possibility for the shear strengthening of concrete, masonry and wood. Compos Sci Technol 1998:1285–95. [15] Aiello MA, Scolti MS. Bond analysis of masonry structures strengthened with CFRP sheets. Constr Build Mater. 2006:90–100. [16] Seim W, Pfeiffer U. A new way to investigate the surface tensile strength of concrete and masonry structures. In: 14th brick and block masonry conference. Sydney; 2008. [17] EN 1996 – Design of masonry structures – part 1–1: general rules for reinforced and unreinforced masonry structures; 2005. [18] Schubert P. Eigenschaften von Mauerwerk, Mauersteinen und Mauermörtel. Mauerwerk-Kalender; 2001. p. 5–22 [19] Glitza H. Druckbeanspruchung parallel zur lagerfuge. Mauerwerk-Kalender; 1988. p. 489–96. [20] Pfeiffer U. Experimentelle und theoretische Untersuchungen zum Klebeverbund zwischen Mauerwerk und Faserverbundwerkstoffen. PhD thesis, University of Kassel, 2009 (free download: ). [21] DIN 2747: Glasfaserverstärkte Kunststoffe: Zugversuch. Berlin: Beuth Verlag; 1998. [22] Volkersen O. Die Schubkraftverteilung in Leim-, Nietund Bolzenverbindungen. Energie und Technik, Hefte 3, 5 und 7; 1953. [23] Schilde K, Seim W. Experimental and numerical investigations of bond between CFRP and concrete. Constr Build Mater 2007:709–26. [24] Holzenkämpfer P. Ingenieurmodell des Verbundes geklebter Bewehrung für Betonbauteile. PhD thesis, University of Braunschweig; 1994. [25] Ganz HR. Mauerwerksscheiben unter Normalkraft und Schub. PhD thesis, ETH Zurich; 1985.