DSpace at VNU: Retrofitting Earthquake-Damaged RC Structural Walls with Openings by Externally Bonded FRP Strips and Sheets

DSpace at VNU: Retrofitting Earthquake-Damaged RC Structural Walls with Openings by Externally Bonded FRP Strips and She...

Retrofitting Earthquake-Damaged RC Structural Walls with Openings by Externally Bonded FRP Strips and Sheets

Bing Li1; Kai Qian, A.M.ASCE2; and Cao Thanh Ngoc Tran3

Abstract: The majority of research studies on the behavior of reinforced concrete members with externally bonded fiber reinforced polymer (FRP) sheets have been focused on beams, columns, and beam-column joints However, limited experimental studies have been conducted to investigate the performance of structural walls retrofitted by wrapping FRP strips or sheets, especially on structural walls with openings The validated retrofitting schemes for strengthening damaged walls without openings may not be suitable for walls with openings Therefore, a series of experimental studies were carried out at Nanyang Technological University, Singapore, to study the effectiveness of the proposed repair and strengthening schemes in recovering the seismic performance of the damaged walls with irregular or regularly distributed openings The strut-and-tie approach was utilized to design the repair schemes The repaired walls managed to recover their strength, dissipated energy, and stiffness reasonably, indicating that the strut-and-tie approach can be a good design tool for FRP-strengthening of structural walls with openings Moreover, the shear and sliding capacities of repaired walls were enhanced by using fiber anchors The repaired walls failed primarily because of debonding of the fiber reinforced polymer at the base of the walls DOI: 10.1061/(ASCE)CC.1943-5614 0000336 © 2013 American Society of Civil Engineers

CE Database subject headings: Earthquakes; Seismic effects; Fiber reinforced polymer; Walls; Openings; Bonding; Rehabilitation Author keywords: Repair; Fiber reinforced polymers; Wall; Opening; Strut-and-tie; Reinforced concrete

Introduction

RC structural walls play a very important role in carrying lateral

loading and resisting drift in tall buildings Piercing a wall with

openings may significantly influence its behaviors, such as

chang-ing its force transfer mechanism, deductchang-ing its strength and

stiffness, and decreasing its ductility level Although walls with

openings have been studied by some researchers (Yanez et al

1992;Ali and Wight 1991;Marti 1985), the effects of the regular

and irregular openings on the seismic performance of RC walls are

still not fully understood Thus, two 3-story reinforced concrete

model walls, scaled to one-third, were tested under reversed cyclic

lateral load Sspecimens W1 and W2 were designed with similar

dimensions and details as Yanez et al (1992) and Marti (1985),

respectively Moreover, for detailed results of these two control

specimens refer to Wu (2005) and Zhao (2004), respectively The

goal of this paper is to investigate whether the damaged walls with

openings could restore their seismic performances after proposed

retrofitting Fiber reinforced polymers (FRP) were utilized in this

study because of their high strength-to-weight ratios, corrosion

resistance, ease of application, and tailorability In addition, the

orientation of the fiber in each ply can be adjusted to meet specific strengthening objectives (Engindeniz et al 2005)

Although numerous research studies had been conducted to strengthen or repair the structural components, such as beams, col-umns, and beam-column joints (Lam and Teng 2001;Teng and Lam 2002;Pampanin et al 2007;Teng et al 2009;Li and Chua

2009;Li and Kai 2011;El-Maaddawy and Chekfeh 2012), there are limited experimental studies that were conducted to investigate the effectiveness of FRP retrofitting the damaged RC structural walls, especially for walls with openings

Neale et al (1997) have tested wall-like columns that were strengthened using FRP, including wall-like columns with different arrangements of externally bonded FRP reinforcements subjected

to uniaxial compression only Lombard et al (2000) performed rehabilitation of structural walls using carbon fiber reinforced polymer (CFRP) externally bonded to the two faces of the wall to increase its flexural strength The use of unidirectional carbon fi-bers with the fifi-bers aligned in the vertical direction increased the flexural capacity and precracked stiffness and the secant stiffness at yield Several nonductile failure modes of the wall were attributed

to the loss of anchorage or tearing of the fibers Antoniades et al (2003) tested squat RC walls up to failure and then repaired them using high-strength mortar and lap-welding of fractured reinforce-ment The walls were subsequently strengthened by externally bonded FRP sheets as well as by adding FRP strips to the wall edges FRP increased the strength of the repaired walls by approx-imately 30% compared with traditionally repaired walls However, the energy dissipation capacity of the control walls could not be restored completely Li and Lim (2010) retested four seismically damaged structural walls (two low-rise walls and two medium-rise walls) after conventionally repaired and strengthened by wrapping with FRP sheets It was reported that the repaired and strengthened walls were able to restore the performance of the damaged RC walls This repair method is relatively easy

1 Associate Professor and Director, Natural Hazards Research Centre at

Nanyang Technological Univ., Singapore 639798 (corresponding author).

E-mail: cbli@ntu.edu.sg

2 Research Associate, Natural Hazards Research Centre at Nanyang

Technological Univ., Singapore E-mail: qiankai@ntu.edu.sg

3 Lecturer, Dept of Civil Engineering, International Univ., Vietnam

National Univ., Ho Chi Minh City, Vietnam E-mail: tctngoc@hcmiu

.edu.vn

Note This manuscript was submitted on February 24, 2012; approved

on September 25, 2012; published online on September 27, 2012

Discus-sion period open until September 1, 2013; separate discusDiscus-sions must be

submitted for individual papers This paper is part of the Journal of

Com-posites for Construction, Vol 17, No 2, April 1, 2013 © ASCE, ISSN

1090-0268/2013/2-259-270/$25.00.

The available research conducted on the rehabilitation of walls

using FRP was promising; however, the repaired walls were

with-out openings in the previous tests and the effectiveness of repairing

RC walls with openings (irregularly and regularly distributed) by a

similar method needs to be further investigated Understandably,

some of the repair and strengthening schemes for walls without

openings may not be suitable for the repair of damaged walls with

openings For example, wrapping integrated FRP sheets on the face

of the walls cannot be used in retrofitting of walls with openings

Bonding discrete FRP strips or sheets could be a good alternative to

recover the seismic performance of the damaged walls with an

opening However, the direction, width, and the number of layers

of each FRP strip had to be determined properly The strut-and-tie

model was a truss model of a structural member, or of a D-region in

such a member, made up of struts and ties connected at nodes and

capable of transferring the factored loads to the supports or to

adjacent B-regions (ACI 2008) Thus, this study employed the

strut-and tie model to determine the direction, width, and number

of layers of the individual FRP strip

Strut-and-tie models have been used intuitively for many years

in design work, whereby complex stress fields inside a structural

member arising from applied loads are simplified into discrete

com-pressive and tensile force paths With the aid of the strut-and-tie

model, a better visualization and understanding of the distribution

of internal force and the mechanism of force transfer can be

achieved The research program in this study taps this advantage

to propose FRP-strengthening techniques for RC structural walls

with openings

Experimental Program

The first part of the paper briefly presents the seismic behavior

of two one-third scaled RC structural walls as control specimens

that were tested under reversed cyclic load After studying the

fail-ure modes of the control specimens, the damaged RC walls were

repaired by epoxy injection, the loose concrete was replaced by

high strength mortar and subsequently strengthened by externally

bonded FRP strips, which were designed according to the proposed

strut-and-tie models Then these repaired specimens were retested

under similar loading conditions

Description of Control Specimens

Control Specimen W1 had irregularly distributed openings The

dimensions of Specimen W1 are given in Fig 1 and had three

subassemblies as follows: (1) the top beam, (2) the web, and

(3) the foundation beam W1 was 2,000 mm wide, 2,300 mm high,

and 120 mm thick, with an aspect ratio of approximately

hw=lw¼ 1.27, where hw¼ 2; 540 mm was the vertical distance

from the lateral loading point to the wall base (Fig 1), whereas

lw¼ 2; 000 mm was the width of the wall The size of each

irregu-larly distributed opening was 600 mm × 600 mm Two deep

flanges (120 mm × 400 mm) were added to the side edge of the

wall The reinforcement details are also presented in Fig.1 The

reinforcements applied in a certain place are denoted according

to their quantity, steel types, and diameters as illustrated in Fig.1

For example, 6T10 means there are six T-bars whose diameters are

10 mm High yield strength steel deformed bars and the mild steel

plain bars are indicated as T-bars and R-bars, respectively

Control Specimen W2 had regularly distributed openings The

size of each regularly distributed opening was400 mm × 400 mm

Similar to W1, W2 also had three subassemblies: the top beam, the

web, and the foundation beam W2 was 2,600 mm wide, 2,300 mm

high, and 120 mm thick, with an aspect ratio of 1.0 Thus, both W1

Fig 1 Dimensions (mm) and detailing of Specimen W1

Fig 2 Dimensions (mm) and detailing of Specimen W2

and W2 are low-rise or squat walls However, the cross section of

Specimen W2 is rectangular and without flanges The vertical and

horizontal reinforcement details are shown in Fig.2 The web of the

wall was divided into beam, column, nodal, and panel zones based

on the openings, as shown in Figs.1and 2

Material Properties

Ready-mix concrete, which had a characteristic strength of 30 MPa,

13 mm maximum size aggregate, and a slump 100 mm, was used

to cast the specimens The measured compressive strength fc0 of

Specimens W1 and W2 are 36.9 MPa and 39.1 MPa, respectively

A high yield steel bar with nominal yield strength of 460 MPa and a

mild steel bar with nominal yield strength of 250 MPa were used

The properties of the steel bars and FRP are shown in Tables 1

and 2, respectively

Test Setup

The testing rig, shown in Fig.3, consisted of two systems: an

in-plane loading system and an in-in-plane base beam reaction system

The in-plane loading system included a double action hydraulic

jack and four steel beams The jack had a capacity of 2,000 kN

in compression and 1,200 kN in tension The stroke of the jack

was 405 mm The steel frame was arranged in a configuration such

that two-direction lateral loadings could be applied to the wall

Four high strength steel rods were preset in the loading beam to

enable lateral loading to be applied on the top loading beam

The base beam reaction system was designed to resist the rotation

and sliding of the wall specimen when the load was applied They

were attached to a strong floor by high strength rods Reaction

foot-ings were provided to balance the lateral loading A prestress

scheme was applied to every steel rod so that the rotation and

slid-ing durslid-ing the test could be restrained efficiently No axial force

was applied in the test because the lateral force transfer

mecha-nisms in the walls were the focus in this study and low axial load

levels are common for low-rise shear walls in practice

Instrumentation and Test Procedure

To record data from the experimental setup, a dynamic actuator, strain gauges, linear variable displacement transducers (LVDTs), and displacement transducers were utilized An LVDT was set up

at the center of the top beam to measure the top drift LVDTs were arranged vertically in the walls to detect the flexural deformation The panel shears deformations measured by the LVDTs distrib-uted along diagonal directions of the panels Local strains in the reinforcement bars were measured by electric resistance wire strain gauges (TML FLA-5-11-5LT), which were installed on the bars before casting of the specimens

The specimens were tested under cyclic lateral loading, which was applied to the top of the wall The loading cycles were dis-placement-controlled in which the top displacement was expressed

as a factor of the vertical height of 2,540 mm from the base of the wall to the point where the load was applied The factors used were 1=2;000, 1=1;000, 1=600, 1=400, 1=300, 1=200, 1=150, 1=100, 1=75, and 1=50 multiplied by the vertical height of 2,540 mm from the wall base to the point where the load is applied The typical loading procedures are illustrated in Fig.4

Seismic Behavior and Failure Modes of the Control Specimens

Control Specimens W1 and W2 had been tested to failure and sus-tained severe damage Specimen W1 developed a sliding failure at the bottom panel, but the sliding face was approximately 200 mm above the base of the wall The damage sustained by Specimen W1 included severe concrete crushing and spalling at the bottom

Table 1 Measured Steel Bar Properties

Types

Yield strength

fy (MPa)

Ultimate strength

fu(MPa)

Table 2 Tyfo Fiberwrap Composite System

Parameter

Properties a GFRP with epoxy, Tyfo

SEH-51A composite

CFRP with epoxy, Tyfo SCH-41 composite

Ultimate tensile strength 90 degrees to the primary fiber direction 25.8 MPa 40.6 MPa

a Property values given are based on test value by supplier (FYFE Asia Pte Ltd in Singapore).

Fig 3 Typical experimental setup

flanges and the right bottom corner of the bottom panel

Further-more, the shear force had to be sustained by the bottom panel

because the bottom right column, where the concrete cracked

severely, could not bear the shear force When the sliding face

was formed, the strength of the wall decreased significantly The

severe sliding shear failure that occurred in W1 could be attributed

to several causes First, low-rise (squat) shear walls had a much

higher propensity for shear failure compared with slender walls

Second, boundary elements (deep flanges) significantly increased

the flexural strength of a wall but simultaneously jeopardized the

shear strength compared with a rectangular wall Third, piercing the

wall with openings further weakens its shear strength Moreover,

most of the steel bars in the flanges buckled, and some steel bars

were fractured The final crack pattern of Specimen W1 is

illus-trated in Fig 5 On the other hand, Specimen W2 had obvious

movement observed along the diagonal cracks that appeared on

every panel The four bottom columns were damaged severely

but no sliding shear failure was observed In particular, extremely

severe concrete crushing was observed at the two columns near to

the bottom edges Significant spalling of the concrete cover and

buckling of the steel bars were also observed The final crack

pattern of Specimen W2 is illustrated in Fig.6

Strut-and-Tie Models

As mentioned previously, strut-and-tie models were utilized to aid

in designing the strengthening schemes of the damaged specimens

because of the openings, which changed the load path and stress distribution significantly In general, a strut-and-tie model would simplify a structural member as a hypothetical truss The compres-sive concrete struts and tensile steel ties joined together at the nodal zones The following assumptions were made in the development

of the strut-and-tie models of Specimen W1: (1) the beam and column zones (as shown in Figs.1and2) were subjected to axial tensions when the entire zones were under tension in the load paths; (2) all reinforcements in the beam or column zones were lumped into one tie, and its position was located in the centriodal axis of the reinforcement lumped into it; and (3) the strut position was deter-mined by keeping the concrete compressive stress in it lower than the strength limitations suggested by Schlaich et al (1987), which

is0.68 f0

cfor a concrete strut with cracks parallel to it or0.51 f0

cfor

a concrete strut with skew cracks According to these assumptions, the tie area and its influence region can be easily determined However, the real geometry of a strut may sometimes be difficult

to illustrate because the strut may represent a bottle-shaped stress field In normal practice, the strut can be idealized into a prismatic

or uniformly tapered shape according to the geometry of the nodal zone For a concentrated node, its geometry can be clearly defined

by the boundary of the bearing plate or tie In the case of walls with an irregular opening where generally no bearing plate presents, the geometries of the nodes and struts are determined based on the divisions of the beam and column zones and the posi-tion of the openings For example, the details of the strut, nodes, and compressive stress of each strut of Specimen W1 are presented

in the Appendix The greater details of the experimental results of the strut-and-tie models are described in Wu (2005) and Zhao (2004) for Specimens W1 and W2, respectively As the load path and force magnitude of the struts and ties are the most important factor considered in the FRP retrofitting design, the load path and force magnitude of Specimens W1 and W2 are illustrated in Figs.7 and 8, respectively In the models, the compression struts were shown as dotted lines, whereas the tensile steel ties were shown

as solid lines The load path of the strut-and-tie model of each specimen was determined based on the crack pattern observed from the tests and the principal stress flows obtained from the numerical analysis As shown in Fig.7, the strut-and-tie models of Specimen W1 in positive and negative loads were different owing to the exist-ence of an irregular opening However, the strut-and-tie models of Specimen W2 were symmetrical in these two load directions as shown in Fig 8 The widths of the FRP strips were calculated according to the load magnitude and were placed in the direction and location of the load paths in the strut-and-tie models

-60

-40

-20

0 20

40

Cycle number

1/2000 1/1000 1/600 1/400 1/300

1/200 1/150

1/100 1/75 1/50

Fig 4 Typical loading procedures

P(+)

Fig 5 Typical cracking patterns of Specimen W1 after test

P (+)

Fig 6 Typical cracking patterns of Specimen W2 after test

Repair and Strengthening Schemes

The walls were first visually inspected for cracks and loose

concrete Then, the loose/spalled concrete was removed using

hammers and chisels before repairing the cracks For cracks of

width larger than 0.3 mm but less than 20 mm, epoxy resin was

injected to seal them For cracks with crack width larger than

20 mm but less than 50 mm, patch repair using a bonding agent

and polymer modified cementitious mortar was adopted The depth

of each layer of the patch repair could not exceed 20 mm For

regions where the depth of the concrete removed exceeded 50 mm,

it was repaired by pumping grout into the damaged region using a

pressurized grouting method The grout consisted of prepacked

20-mm-diameter aggregates mixed with cement treated with super

plasticizer, and grout fluidifier was used to achieve high strength

and workability

The specimens were then left to cure for 1 day because the ep-oxy resin required a minimum of 24 h for curing Subsequently,

as mentioned previously, the damaged control specimens were strengthened by externally bonded FRP strips aligned along the load path of the strut-and-tie models The repaired and strengthened wall specimens were denoted RW1 and RW2, respectively Figs.9 and 10show the proposed FRP-strengthening schemes of Speci-mens RW1 and RW2, respectively

As shown in Fig.9(a), the tie-strengthening scheme of Speci-men RW1 is described as follows: The width and number of layers

of the FRP sheets were determined based on the tensile force of the tie determined by the strut-and-tie models (refer to Fig.7) The tensile force of the tie was assumed provided by the externally bonded FRP strips only Thus, for example, the design width of the glass fiber reinforced polymer (GFRP) strip #1 was determined

as follows:

Ws¼ Ts=2

fFRP× dFRP

¼2 × ð575 × 1.3Þ248.8 × 103 ¼ 166 mm ð1Þ

where Ws = design width of the FRP sheet; Ts= tensile force of the tie along the FRP sheet (the tie force of strip #1 is 248.8 kN);

fFRP= tensile strength of the FRP sheet; and dFRP= thickness of the FRP sheet (One layer of FRP was assumed in the preceding calculation If the spacing was restrained, more layers of FRP could be designed.)

Thus, a one-layer GFRP sheet with 150 mm width was applied

on both faces of the wall (#1 strip) For tie strengthening, the designed FRP strips were applied on the wall in sequence as shown

in Fig.9(a) For strut strengthening (see the Appendix), the strut stresses are normally less than the limitation (0.68f0

c) suggested by Schlaich

et al (1987), except for strut QW However, the influence of the flanges has not been considered in the strut width of the strut QW Thus, no crushing of the struts was observed in the failure mode of Specimen W1 Similar behavior was observed in Specimen W2 Thus, the strut strengthening primarily relied on the epoxy injection

to fill the cracks and external bonded the FRP sheets [as shown in Fig.9(b)] These FRP sheets along the cracks not only improved the effectiveness of the epoxy repairing but also delayed the crack development during the test because the fibers perpendicular to the primary fibers could provide a slight tensile strength (as given in

600 X 600 Opening

534 kN

329.2 kN

846.

4kN

114.4 kN 248.8 kN 379.2 kN

70.8 kN

O A

4.4 kN

Y

600 X 600 Opening

600 X 600 Opening

509.0 kN

N 66 6.4 kN

K

L

U 282.8 kN

P (+)

34 3.2 kN

34 8.0kN

600 X 600 Opening

600 X 600 Opening

600 X 600 Opening

Fig 7 Strut-and-tie models for Specimens W1

400 X 400 Opening

P (+)

163.7

22 4.5

160.5 11 4.3

20 3.0

160.

7

146.6

17 5.8

168.9

78 0 98.1 13 5.3

180.5

22

37 8

55.8

94 3

305.0

Fig 8 Strut-and-tie models for Specimens W2

Table2) In the future, to further restore the seismic performance

of damaged walls with openings, tie strengthening in conjunction

with concrete tensile strength strengthening [bond FRP strips along

the direction of principal tensile strength, as shown in Fig.9(c)] was

recommended

For Specimen RW2, similar to Specimen RW1, tie-strengthening

strips were first applied on the surface of the wall The tensile strips

were designed based on the magnitude of the tie force as determined

by the strut-and-tie models (refer to Fig.8) Fig.10(a)illustrates

the final tie-strengthening scheme of Specimen RW2

However, for strut strengthening, RW2 was slightly different from that of Specimen RW1 For RW1, diagonal FRP sheets were applied along the direction of the diagonal struts For RW2, to evaluate whether resolving the diagonal compressive force of the strut into horizontal and vertical components and applying the FRP strips according to the magnitudes of these components could be

an effective alternative method, part of the diagonal struts were strengthened through a pair of vertical and horizontal FRP strips Fig.10(b)shows the final strut-strengthening scheme on both faces

of the wall

Fig.5shows the failure mode of Specimen W1, indicating that sliding failure was observed at the bottom panel, which was ap-proximately 200 mm above the base of the wall Thus, a one-layer L-shaped GFRP sheet was applied on both faces of the base of Specimen W1 (as shown in Fig 11) Similarly, L-shaped GFRP sheets were applied on both faces of the base columns of Specimen RW2 Moreover, for Specimen RW2, GFRP sheets with 400 mm width were utilized to wrap each of the bottom columns because severe damage and concrete crushing was observed in these columns (as shown in Fig 6) Moreover, to prevent premature delamination of the L-shaped GFRP sheets, a series of fiber anchors were mounted (the locations of the fiber anchors of RW1 and RW2 are shown in Figs.11and12, respectively) The fiber anchor con-sisted of two parts: the anchor bolt and the protruding fibers The total length of the fiber anchors used was approximately 110 mm The length and diameter of the anchor bolt were approximately 50 and 7 mm, respectively First, holes (10 mm in diameter) were drilled at a depth of 50 mm on the wall faces before the application

of the FRP sheets After the application of the FRP sheets, the anchor bolts were inserted through the epoxy resin into the holes The protruding fibers were bent and spread out in circles with a radius of approximately 60 mm to act as the base of anchorage

To ensure good adherence between the FRP sheets and concrete, the surface was first cleared of dust and any deleterious substances that might act as bond barriers Sharp edges and protrusions were also removed by mechanical grinding

Results and Discussion Failure Modes and Response under Cyclic Loading After repairing and strengthening of the damaged control speci-mens, the repaired Specimens RW1 and RW2 were retested under

a similar reversed cyclic lateral load, and the test results were illus-trated For repaired specimens, the lateral displacement was re-peated for two cycles before the drift ratio reached 1.0% After that, only one cycle of the lateral displacement was applied However, for the control specimens, the lateral displacement was repeated for two cycles until the failure of the specimens For Specimen RW1,

no visible cracks or debonding were observed during the initial cycles of the test At the drift ratio of 0.25%, hairline cracking was distributed along the height of the wall Because the RC walls

at this point were wrapped by FRP sheets, the presence of the cracks was inferred from the thin marks in the epoxy resin at the exterior surface of the FRP sheets At the drift ratio of 0.33%, the breaking of epoxy resin was heard and a horizontal flexural crack formed at the interface of the repair mortar and the anchor block at the right base of the wall Subsequently, the crack opened substantially During the first cycle at the drift ratio of 0.67%, the GFRP sheet at the right base of the wall delaminated at the edges, exposing the concrete underneath Horizontal flexure cracks also started to form at the center of the wall base near the opening

In the second cycle, the GFRP sheet at the left base of the wall

(Width x layers) Unit (mm)

C-shape Wrap (1 Layer)

1

6 5

2 4 3

Front Face of Tie Strengthening

200 x 1 (G)

200 x 1 (G)

C-Shape (1 Layer) (C)

150 x 1 (G)

250 x 1 (G)

S3 S1

S2

S4 S6 S5

G=Glass fiber

C=Carbon fiber

Note:

=Strain gauge

(a)

Front Face of Strut Strengthening

280 x 1 (C)

290 x 1 (C)

150 x 1 (C)

240 x 1 (C)

360 x 1 (C)

C-Shape (1 Layer) (G)

C-Shape

(1 Layer)

(G)

(Width x layers) Unit (mm)

G=Glass fiber C=Carbon fiber Note:

=Strain gauge

7 8 9

10

190 x 1 (C)

190 x 1 (C)

11 12

15

(b)

7 8 9

10 11 12

15

(c)

Fig 9 Proposed FRP strengthening schemes for Specimen RW1:

(a) tie-strengthening scheme; (b) currently used strut-strengthening

scheme; (c) refined strut-strengthening scheme

debonded As the drift ratio increased, loud cracking resulting from

the debonding of the FRP sheets was heard At the drift ratio of

1.00%, the GFRP sheet delaminated completely from the base

The FRP sheet at the right base of the wall was then completely

delaminated It was obvious that Specimen RW1 had a flexural

fail-ure, which was concentrated between the base and the foundation

For Specimen RW2, the breaking of epoxy resin was heard at

the drift ratio of 0.25% At the first cycle of the drift ratio of 0.50%,

visible epoxy resin cracks were observed at the base of the wall

Cracks started to appear at the wall base at the drift ratio of

0.67% At the drift ratio of 1.00%, diagonal cracks on the wall

were observed, and the cracks were primarily at the lower part

of the wall As the drift ratio increased, the FRP strips debonded from the wall to the base A vertical crack was formed, propagating from the base edge upwards, with a crack length of 150 mm When the maximum strength was reached, the whole wall tilted forward

in the out-of-place direction

Load-Displacement Hysteresis Responses Fig.13shows the load-displacement hysteresis loops of the control and repaired specimens The hysteretic behavior was evaluated in

(Width x layers) Unit (mm)

=Strain gauge

30x1

40x1 20x1

50x1 20x1

C-shape Wrap

C-shape Wrap

Front Face of Tie Strengthening

C-shape Wrap (1 Layer)

S6

20x1 40x1 60x1 40x1 20x1

(a)

60x3 70x3

25x1 25x1 45x1 35x1 35x1 50x1 45x1 45x1

70x1

50x1

70x1

Note: (Width x layers); Unit (mm)

70x2 70x2 50x4 70x2 40x1 50x3 50x1 50x3 70x2

70x3 60x3 25x1 45x1 35x1 35x1 50x1 45x1 45x1

60x3 70x1 90x1 70x2 50x2 60x2 80x2 50x4 80x1

60x3 70x1 90x1 70x2 50x2 60x2 80x2 50x4 80x1

70x1

50x1

70x1

(b) Fig 10 Proposed FRP strengthening schemes for Specimen RW2: (a) tie-strengthening scheme; (b) currently used strut-strengthening scheme

Front Face

Locations of Fiber Anchorage in the Bottom

Back Face

Locations of Fiber Anchorage in the Bottom

Fig 11 Proposed fiber anchorage schemes in the base of the wall of Specimen RW1

terms of lateral resisting capacity and maximum displacement The

lateral resisting capacity of Specimen RW2 was significantly higher

than the corresponding control Specimen W2 in the positive and

negative loading cycles, respectively The maximum peak strengths

in each positive and negative cycle of control Specimen W2 were

334 and 348 kN, respectively, and were reached at the drift ratio of

0.50% For repaired Specimen RW2, the maximum peak strengths

in each positive and negative cycle were 456 and 411 kN, respec-tively This indicated that the proposed repair and strengthening schemes were effective for repairing the damaged walls with regu-larly distributed openings However, for repaired Specimen RW1, the maximum strength was reached at the drift ratio of 0.50% for both the control and repaired specimens At this drift ratio, the maximum strengths in the positive and negative direction of control Specimen W1 were 385 and 394 kN, respectively, whereas those

of repaired Specimen RW1 were 411 and 308 kN, respectively Thus, the lateral resisting capacity of the repaired specimens was only slightly higher than that of their corresponding control spec-imens in the positive loading cycles, and repaired Specimen RW1 did not reasonably recover the strength of Specimen W1 in the neg-ative loading cycles The strengthening schemes of Specimen W1 were asymmetrical owing to the irregularly distributed openings

In addition, as shown in Fig 9(b), the FRP sheets were applied

on the face of the wall according to the strengthening scheme of the positive load cycle first Thus, the FRP sheets that were sub-sequently applied for strengthening the wall in the negative loading cycle helped to anchor the previously applied ones and indirectly improved the effectiveness of the strengthening sheets for the pos-itive loading cycle

Load-Displacement Envelopes

To study the lateral resisting capacity and ultimate displacement capacity of the specimens, a comparison between the envelopes

of hysteretic loops of the tested specimens is shown in Fig 14

Locations of Fiber Anchorage in the Bottom

Front Face

Fig 12 Proposed fiber anchorage schemes in the base of the wall of

Specimen RW2

-600

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

Horizontal Displacement (mm)

W1 RW1

0.5 %

-1.0 % -0.5 %

2.0 % 1.5 % 1.0 %

-1.5 % -2.0 %

Drift ratio

Drift ratio

-600

-500

-400

-300

-200

-100

0

100

200

300

400

500

600

Horizontal Displacement (mm)

W2 RW2 l

0.5 %

-1.0 % -0.5 %

2.0 % 1.5 % 1.0 %

-1.5 % -2.0 %

Drift ratio

Drift ratio

Fig 13 Load-displacement hysteretic loops for control and repaired

specimens

-600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600

Horizontal Displacement (mm)

0.5 %

-1.0 % -0.5 %

2.0 % 1.5 % 1.0 %

-1.5 % -2.0 %

Drift ratio

Drift ratio

RW1

W1

-600 -500 -400 -300 -200 -100 0 100 200 300 400 500 600

Horizontal Displacement (mm)

0.5 %

-1.0 % -0.5 %

2.0 % 1.5 % 1.0 %

-1.5 % -2.0 %

Drift ratio

Drift ratio

RW2

W2

Fig 14 Comparison of load-displacement envelope of control and repaired specimens

The lateral resisting capacity of Specimen RW2 was larger than its

corresponding control Specimen W2 in both the positive and

neg-ative loading cycles by 36.5 and 18.1%, respectively However, its

strength at the drift ratio of 1.33% decreased by 52.0 and 25.4%

in the positive and negative loading cycles, respectively This

faster strength degradation was not favorable for a rehabilitation

objective

In the positive loading cycles, repaired Specimen RW1 only

en-hanced the strength of Specimen W1 by 6.8% Specimen RW1 also

only recovered the strength of Specimen W1 by approximately

78.2% in the negative loading cycles Similar to Specimen RW2,

it was not reasonable for Specimen RW1 to recover the ductility of

Control Specimen W1

Energy Dissipation Capacity

The energy dissipated was based on the cumulative energy

dissi-pated calculated by summing up the energy dissidissi-pated in

consecu-tive loops throughout the test Fig.15shows the comparison of the

cumulated energy dissipated for the control and repaired

speci-mens The repaired specimens not only restored the energy

dissi-pation capacity of the control specimens, its energy dissidissi-pation

capacity also increased by more than twofold For Specimen RW1,

after the drift ratio of 0.4%, the energy dissipated was more than

double that of the control specimens At every drift ratio for

Speci-men RW2, it had very significant improveSpeci-ment in the energy

dis-sipated compared with Specimen W2 At the final stage, Specimen

RW2 reached the maximum dissipated energy of about 280 kNm, whereas that for Specimen W2 only reached 60 kNm

Stiffness Degradation The stiffness of both the control and repaired walls was estimated based on the secant stiffness of the plots of force against displace-ment Fig.16shows the comparisons of stiffness degradation for each tested specimen The comparison of the repaired Specimen RW1 curve with the corresponding curve for control Specimen W1 shows that the initial stiffness of Specimen RW1 was signifi-cantly higher than that of Specimen W1 The repaired Specimen RW1 was not as stiff as the original wall in considering the negative loading cycles; whereas, generally speaking, the repaired Specimen RW1 had recovered the stiffness reasonably On the other hand, the repaired Specimen RW2 not only had much higher initial stiffness but also had delayed stiffness degradation compared with the cor-responding control Specimen W2 This is a desirable property in an earthquake-like situation It was observed in the past earthquake that most of the RC structures failed owing to the sudden loss of stiffness of structural joints with increasing lateral movement of the structure

FRP Strains The readings in the strain gauges attached to the FRP strips are shown in Figs 17 and 18 for Specimens RW1 and RW2,

0 20 40 60 80 100 120

Drift Ratio (%)

RW1

0 20 40 60 80 100 120

Drift Ratio (%)

W2 RW2

Fig 16 Comparison of secant stiffness between control and repaired specimens

0

50

100

150

200

250

Drift Ratio (%)

W1 RW1

0

50

100

150

200

250

300

Drift Ratio (%)

W2 RW2

Fig 15 Comparison of energy dissipation capacity of control and

repaired specimens

respectively As shown in the figures, the recorded strain in the fiber

was relatively low compared with their fracture strain of 1.0%

(10; 000 με), although the strain gauge reading along the

tie-strengthening fibers displayed tensile reading This was possibly

because debonding of the FRP at the wall base prevented the full

development of the strength of the fiber in tie strengthening

More-over, because no special anchorage was designed for these FRPs

in the wall body, it was predictable that the strength of the FRP

strips could not be fully developed For Specimen RW2, similar

to Specimen RW1, all strain readings fell below 350 με, which

was much lower than the allowable value of 1.0% Although some

of the fiber readings were initially compressive, the majority of the

fibers obtained tensile value As the tie force of each tie only had

two sources (steel reinforcement or FRP for tie strengthening),

according to Eqs (2and3), it was understandable that the majority

of the tensile force of the ties was still provided from the steel reinforcement

Fcontribution frp ¼ εmeasured

Fcontribution steel ¼ Ftie− Fcontribution

where Fcontribution frp = FRP’s contribution; Fcontribution

steel = steel rebar’s contribution;εmeasured

frp = measured strain of the FRP strip; Gfrp = tensile modulus of the FRP; Afrp = cross-sectional area of each FRP; and Ftie = tie force obtained from strut-and-tie models Conclusions

In the present paper, the strut-and-tie models were utilized to help

in designing the strengthening schemes for repairing damaged structural wall with openings Based on the observations and the experimental results of this study, the following conclusions can

be made:

• The proposed strengthening schemes designed by the strut-and-tie models can effectively recover the overall behavior (strength, stiffness, and energy dissipation capacity) of damaged speci-mens with irregularly or regularly distributed openings It indi-cates that the strut-and-tie models are effective to help design the strengthening schemes for walls with openings

• Most of the FRP-strain readings indicated that the FRP strips were not fully utilized because the tensile strain was relatively low compared with the fracture strain of the FRP strips This indicated that the majority of the tie force was still provided

by the steel bars This was primarily because the tests were stopped as a result of debonding of the FRP sheets in the con-nection in between the base wall and the foundation Moreover,

no special anchorage was provided in the FRP strips for tie and strut strengthening

• In future practice, replacing the integral FRP sheets along the diagonal cracks with several short FRP strips bonded perpendi-cular with the diagonal cracks will strengthen the strut and in-crease the effectiveness of the FRP strips to delay the reopening

of the diagonal cracks

• Fiber anchors were generally effective in improving the sliding capacity of the walls because few areas on the wall base showed failure in anchorage However, the performance of the repaired specimens could be further improved if the delamination of the FRP sheets could be delayed or prevented, such as by using a steel plate anchorage to replace the fiber anchor in the base of the wall Moreover, special anchorage provided in the FRP strips for tie strengthening could improve the strengthening effectiveness

Appendix Details of the Strut-and-Tie Model of Specimen W1

Fig.19presents the details of the strut and nodes of Specimen W1 The regions of extended nodal zones are also depicted Tables3 and4list the primary properties of the ties and struts, respectively Moreover, Table 5 gives the strut width of Specimen W1 The strut width is measured at the narrowest segment of the strut as shown in Fig.19and is the smallest length of a line from a point

at the strut boundary extending perpendicular to the axis of the strut

0

50

100

150

200

250

300

Drift Ratio (%)

-6 )

S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11

-50

0

50

100

150

200

250

300

350

Drift Ratio (%)

-6 )

S12 S13 S14 S15 S18 S19 S20 S21

Fig 18 FRP strains on Specimen RW2

0

200

400

600

800

1000

1200

Drift Ratio (%)

-6 )

S1 S2 S3 S4 S5 S6

Fig 17 FRP strains on Specimen RW1