Chapter 4. Experimental Results & Analytical Modelling: Large-Scale Slab Specimens
5.2 N ear Surface M ounted FRP B ars
5.2.2.3 Proposed Approach for NSM FRP bars
The transfer o f stresses from a deformed near surface mounted FRP rod to the concrete is assumed to be mainly through the mechanical interlocking o f the lugs to the surrounding adhesive. Due to the shape o f the lugs, the resultant force exerted by the lug to the epoxy is inclined with an angle /? with respect to the axis o f the bar as shown in Fig. 5.8, where l/(tan P) is the coefficient o f friction between the bar and the adhesive, (/u).
Internal cracks Adhesive
NSM bar Adhesive
\ \ \ \ \ \ \ \ \ /3 \+ -
t/ /u
r J
Forces applied to the adhesive
t//u
Major
crack Force components on bar
Fig. 5.8 Forces between near surface mounted FRP bar and epoxy
The radial component o f the resultant force creates zones o f high tensile stresses at the FRP-adhesive interface as well as at the concrete-adhesive interface. Lack o f confinement, uneven distribution o f bond stresses, edge effects and composite interaction between concrete, adhesive and FRP materials complicate the analysis o f near surface mounted FRP bars. Consequently, thick-walled cylinder theory is no longer valid.
In this section finite element analysis is employed to provide in-depth understanding o f the bond characteristics and load transfer mechanism between near surface mounted FRP bars and concrete. The finite element modelling described in this section was conducted
5 .Experimental Results & Analytical Modelling: Bond Specim ens
using ADINA program (Version 7.4). Fig. 5.9 shows the mesh dimensions used in modelling a portion o f a concrete beam strengthened with a near surface mounted FRP bar using epoxy as an adhesive.
ADINA* AU1 v e r s o n M .0 ằ 2 1 N o v e m b e r 2 0 0 1 * L i c e n s e d Tram ADINA R& Dr Ir ConcrdcrEpOKy Interface
A D I N A
Steel bar
oncrete
oxy:in
Radial pressure
All dimensions are in mm
10 r* Plane of symmetry Fig. 5.9 M esh dimensions for a portion o f a concrete beam strengthened with
a near surface mounted FRP bar
The concrete and the epoxy were modelled using eight-node plain strain elements with a 3x3 Gauss integration scheme. Groove dimensions, bar location and properties o f concrete and epoxy were set identical to those used in the bond specimens. Radial pressure was applied at the bar location to simulate the bond stresses transferred from the bar to the surrounding epoxy. Typical principal tensile stress distribution around the FRP bar is shown in Fig. 5.10.
5 .Experimental Results & Analytical Modelling: Bond Specim ens
Concrete
G2d f F R P 4 /'/•</
'ô
G d [frp_ Fpjoxy
Q t d_ j 1 1 \ 1
4 MLd
r , d fFRP
Near surface
q mounted bar i
■*-i w
Fig. 5.10 Typical stress distribution around near surface mounted bar
It should be noted that the elastic modulus o f the adhesive is generally less than that o f the concrete. Such a phenomenon results in a stress discontinuity at the concrete-epoxy interface as shown in Fig. 5.10. High tensile stresses are observed at the concrete-epoxy interface as well as at the FRP-epoxy interface. Two different types o f debonding failures can occur for near surface mounted FRP bars. The first mode o f failure is due to splitting o f the epoxy cover as a result o f high tensile stresses at the FRP-epoxy interface, and is termed “epoxy split failure”. Increasing the thickness o f the epoxy cover reduces the induced tensile stresses significantly. Furthermore, using adhesives o f high tensile strength delays epoxy split failure. This type o f debonding failure forms with longitudinal cracking through the epoxy cover. The second mode o f failure is due to cracking o f the concrete surrounding the epoxy adhesive and is termed “concrete split failure”. This mode o f failure takes place when the tensile stresses at the concrete-epoxy interface reach the tensile strength o f the concrete. Widening the groove minimizes the induced tensile stresses at the concrete-epoxy interface and increases the debonding loads o f near surface mounted bars. Concrete split failure was the governing mode o f failure for the bond
5 .Experimental Results & Analytical Modelling: Bond Specim ens
specimens reported in this investigation. Large epoxy cover and high tensile strength o f the epoxy adhesive provided high resistance to epoxy split failure and shifted the failure to occur at the concrete-epoxy interface [Rizkalla and Hassan, 2002].
Measurements o f bar strains along the embedment length o f near surface mounted FRP bars shows linear strain distribution at high load levels. Therefore, the tangential bond stress, r, can be estimated with an average value of:
r = ± f F R P . (5.3)
4 L d
where d is the diameter o f the bar, and Ld is the embedment length needed to develop a stress o f/frp in the near surface mounted bar. The maximum tensile stress in near surface mounted FRP bars,/ra/>, will be discussed in detail in section 5.2.2.8. I f the coefficient o f friction between the bar and the epoxy is //, the radial stresses, crradiai, can be expressed as:
" ra o o r'-tr® * - w
V 4 v L d
The tensile stresses at the concrete-epoxy interface, a COn-epoxy, and at the FRP-epoxy interface, a'FRP-epoxy, shown in Fig. 5.10 can be expressed in terms o f the radial stress as follows:
^ c o n - e p o x y (5.5)
a FRP - epoxy ~ ° 2 or G '’
4 V L d
d fF R P 4 V L d
(5.6)
5 .Experimental Results & Analytical Modelling: Bond Specim ens
where Gj, G2 and G '2are coefficients determined from the finite element analysis based on a unit radial pressure applied at the bar location and using specified groove dimensions, concrete and adhesive properties. The maximum tensile stress at the FRP- epoxy interface, OFRp-ep0xy, depends on the coefficients G2 and G ; , whichever is greater as shown in Fig. 5.10. Equating the tensile strength o f concrete to Equation 5.5, the minimum embedment length needed for near surface mounted FRP bars to prevent concrete split failure can be expressed as:
( 5 7 )
Equating the tensile strength o f the adhesive to Equation 5.6, the minimum embedment length needed for near surface mounted FRP bars to avoid epoxy split failure shall not be less than:
Ld = ° 2 or G'2 d fFRP
^ epoxy
(5.8)
where f ct and f ep0Xy are the tensile strength o f concrete and epoxy, respectively. Increasing the stiffness o f concrete by using high strength concrete increases the tensile stresses at the concrete-epoxy interface. This is evident by the considerable increase in the value o f G1 by increasing the modular ratio, n as shown in Fig. 5.11. Furthermore, increasing the stiffness o f the adhesive increases the tensile stresses at the FRP-epoxy interface. This is evident by the increase in the values o f G2 and G 2 by decreasing the modular ratio as shown in Fig. 5.12.
n = - E (5.9)
F
5 .Experimental Results & Analytical Modelling: Bond Specim ens where Ec and Ea are the modulus o f elasticity o f concrete and adhesive, respectively.
Groove w idth=2d
0.6 - ■
n=5 0.2 -
1.5 2 2.5 3 3.5 4 0.5 1
C/d
Fig. 5.11 Influence o f concrete and adhesive properties on tensile stresses at concrete-epoxy interface
Groove w idth= 2d
n=20 n7 10
<N
^ 0 .8 - •
Jk
5 0 . 6 - 6 0.4 --
ô=30
0.2 - ■
0.5 1 1.5 2 2.5 3 3.5 4 C/d
Fig. 5.12 Influence o f concrete and adhesive properties on tensile stresses at FRP-epoxy interface
It should be noted that neighbouring steel bars have no adverse effect on the induced tensile stresses in concrete and adhesive. Practical values o f the modular ratio, n, can vary between 5 and 40. This range covers various types o f concrete and adhesives that are commonly used in concrete structures. Fig. 5.13 shows a proposed design chart for the development length o f near surface mounted FRP bars. To simulate the most critical conditions for design purposes, the coefficient G/ was evaluated for a modular ratio o f 40, which represents the case o f high strength concrete and low stiffness adhesive. The coefficients, G2 and G 2 were evaluated for a modular ratio o f 5 to simulate the case o f low strength concrete and high stiffness adhesive. The curves represent the greater o f the two coefficients G2 and G 2. The chart covers a wide range o f possible epoxy covers, C/d, and accounts for three different groove sizes, w.
5 .Experimental Results & Analytical Modelling: Bond Specim ens
b
C/d for G2 and/or G '2 curves
3.5 3 2.5 2 1.5 0.5
1.4
[Concrete 1
| I :p o \\ ^
K — L“ ,_J • . ! ' w=\.5d
— G,
1.2 G2 and/or G '2
1
0.8
0.6 0.8
0.4
,w=2.5d.
0.2
2.5 3 3.5 4
0.5 1 1.5 2
<N bs-
I
<N
b
C/d for Gi curves
Fig. 5.13 Design chart for the development length o f near surface mounted FRP bars
The chart clearly indicates that increasing the thickness o f the epoxy cover, C/d, reduces the tensile stresses in both concrete and adhesive as is evident by the reduction o f G;, G2
and G'2 with the increase o f C/d. Furthermore, using wider grooves, w, increases the tensile stresses at the FRP-epoxy interface (G2 and/or G '2) due to the substantial increase in the area o f adhesive and consequently in its stiffness. Therefore, the tensile stresses at the concrete-epoxy interface (G y ) decrease by increasing the groove width. Using the proposed design chart, the coefficients Gy and the greater value o f either G2 or G 2 could be evaluated for a given groove width, w, and using a specified clear cover to the bar diameter ratio (C/d). The governing development length for near surface mounted FRP bars could be predicted using the greater o f Equations 5.7 and 5.8.
______________ 5. Experimental Results & Analytical Modelling: Bond Specimens 5 . 2 . 2 A Coefficient of Friction (/1)
The coefficient o f friction between the FRP reinforcement and adhesive is a critical parameter in the theoretical analysis. Fig. 5.14 shows the test setup used to determine the coefficient o f friction between C-Bars and different adhesives used in this investigation.
14"
Steel wire
T Dial gauge
WCI Two C-Bars
I poxy
M oving direction Movable base
10 7/8"
Fig. 5.14 Schematic o f friction test setup W eight
The coefficient o f friction was determined according to the ASTM, G 115-98. Both smooth- and rough-surface adhesives were examined as shown in Fig. 5.15. The rough- surface topography was accomplished by printing the lugs’ pattern o f the C-Bar in the adhesive prior to hardening.
Smooth-surface epoxy
______________ 5. Experimental Results & Analytical Modelling: Bond Specimens
The bottom surface o f the adhesive was placed to bear on two pieces o f C-Bars. Force was applied through a horizontal steel wire attached to the adhesive block at the level o f the FRP-epoxy interface. The relative movement between the reinforcement and the adhesive was monitored using a mechanical dial gauge. Force was applied to the steel wire by gradual movement o f the steel base in the direction shown in Fig. 5.15. The maximum load was measured by an electronic scale at impending motion and was equal to the friction force. The test was repeated twelve times. The static coefficient o f friction was calculated by dividing the friction force by the known weight, placed on the top o f the adhesive. Test results showed that the coefficient o f friction between C-bars and different epoxy adhesives used in this investigation has lower and upper bound values o f 0.33 and 0.66, respectively with an average value o f 0.5.
5.2.2.5 Comparison with Experimental Results
Using a groove width equal to twice the diameter o f the bar (w=2d), a coefficient o f friction o f 0.33 and a clear cover to bar diameter ratio o f one (C/d= 1.0), the coefficients Gi and the greater o f G2 and G'2 for the bond specimens reported in this investigation are 0.65 and 1.1, respectively. The diameter o f the bar is 9.525 mm. The average tensile strength o f the concrete and epoxy used in the bond specimens are 4.3 M Pa and 48 MPa, respectively. Using Equations 5.7 and 5.8, the minimum embedment length needed to develop 40 percent o f the ultimate strength o f the bars shall not be less than 834 mm, which coincides with the measured value o f 800 m m [Rizkalla and Hassan, 2002],
■ E xperim ental R esu lts & Analytical M odelling: B ond S p e c im e n s
5.2.2.6 Comparison with ACI— 440
The draft report o f the ACI-440 (2002) suggests the following expression for the development length, Ld, o f FRP reinforcing bars:
where, d is the diameter o f the bar; f u is the tensile strength o f the bar and f ' c is the concrete compressive strength after 28 days. Using the stress limit o f 40 percent o f the tensile strength o f the C-Bars as observed in the experimental program, d=9.525 m m, f ' c
=48 MPa, the development length according to the ACI-440, Equation 5.10, is equal to 221 mm. This value is equivalent to 28 percent o f the value measured when the same bars were used for strengthening the beam in near surface mounted configuration. The results suggest that the ACI expression is not adequate for near surface mounted FRP bars. The significant discrepancy could be attributed to the following reasons:
a) The ACI expression is developed to characterize the bond o f FRP bars to concrete. In near surface mounted FRP bars, the bond is primarily governed by the surface characteristics o f the adhesive, which is considerably smoother than concrete and requires longer development length to achieve the same bond stress compared to concrete.
b) The ACI expression assumes a coefficient o f friction between FRP bars and concrete equal to 1.0. This value is typically used for steel bars bonded to concrete and has been confirmed by many researchers [Goto 1971]. The coefficient o f friction between FRP bars and epoxy is lower and ranges between
Ld = 0 07R n d 2f u (5.10)
c
____________ 5. Experimental Results & Analytical Modelling: Bond Specimens
30 to 60 percent o f the value used by the ACI. Consequently, a longer development length is needed for near surface mounted FRP bars.
c) The ACI-expression is designed for concrete structures reinforced with FRP bars where large concrete covers are' typically used. For near surface mounted FRP bars, the thickness o f the clear epoxy cover is greatly influenced by the location o f the internal steel reinforcement. Therefore, the thickness o f the epoxy cover is always limited. This type o f configuration induces high tensile stresses at both the concrete-epoxy and the FRP-epoxy interface and consequently requires a longer development length.
d) The ACI expression assumes full confinement o f the FRP bars by steel and/or FRP stirrups. Lack o f such confinement in near surface mounted FRP bars results in higher bond stresses and consequently, a longer development length is needed.
Replacing f u with the limited stress level observed in the experimental results, / f r p, in Equation 5.10 and using/.* =0.6 ^ / ' c , d =9.525 mm, Equation 5.10 can be rewritten as:
L d = 0.5027 (5.11)
4 fc t
Using a typical coefficient o f friction between FRP bars and adhesives o f 0.5, Equation 5.11 can be expressed by:
L d = 0 . 2 5 (5.12)
4 /u fct
Equation 5.12 modifies the ACI expression to account for the distinct material characteristics o f adhesives compared to concrete. Comparing Equations 5.7 and 5.12, it
______________ 5. Experimental Results & Analytical Modelling: Bond Specimens
can be concluded that the coefficient Gj is constant and equal to 0.25 regardless o f the clear cover to bar diameter ratio, C/d as shown in Fig. 5.16.
Groove w idth=2d
n= 10 0.6 - ■
n=5 0.4 --
Equation 5.12 0.2 - •
1.5 2 2.5 3 3.5 4
0.5 1
C/d
Fig. 5.16 Comparison o f proposed approach with Equation 5.12
The constant value o f Gj compares well only for the case o f relatively large clear cover to bar diameter ratios (C /d > 4.0). From the above discussion, it is obvious that the influence o f the C/d ratio affects the development length for near surface mounted FRP bars and should be considered in future design guidelines.
5 . 2 . 2 J Detailing Guidelines
The previous sections have demonstrated the applicability o f the proposed approach to evaluate the development length o f near surface mounted FRP bars. Detailing provisions are urgently needed to ensure uniform distribution o f stresses among the bars. Closely spaced arrangement o f near surface mounted bars could magnify the tensile stresses at the concrete-epoxy interface and expedite concrete split failure. In this section, the finite element model was used to investigate the influence o f the clear groove spacing, s, as
■ E xperim ental R esu lts & Analytical M odelling: B ond S p e c im e n s
well as the edge distance, e, on interfacial stresses as shown in Fig. 5.17. The clear spacing between the grooves o f near surface mounted bars was varied from 0.25d to 2.0<i,
The maximum tensile stress at the concrete-epoxy interface due to a unit radial pressure applied at the location o f FRP bars (coefficient Gj) is shown in Fig. 5.18 for various clear groove spacing to bar diameter ratios (s/d). The modular ratio, n, was set to 40 to simulate the most critical conditions for the tensile stresses at the concrete-epoxy interface. 0 _________ ___ _____ ____ _______________
where d is the diameter o f the bar. The groove width was also varied from 1.5d to 2.5d to examine its effect on the induced stresses.
1*1 lôl)[ằll S tr e n g th e n e d co n c re te b ea m
: Concrete
edgei < • • I
F ree! 'p .m y Kpoxy
e |. w I s I w
Fig. 5.17 Detailing parameters
<3
Concrete
w = 2 .5 d 0.25 --
0
0.5 0.75 1.25 1.5 1.75 2
■ E xperim ental R esu lts & Analytical M odelling: B ond S p e c im e n s
The analysis indicates that the tensile stress at the concrete-epoxy interface is greatly influenced by the clear spacing between the grooves o f near surface mounted FRP bars.
Increasing the clear groove spacing to bar diameter ratio reduces the tensile stress considerably up to a clear groove spacing o f 2.0d, where d is the diameter o f the bars.
Increasing the clear groove spacing beyond this limit has a negligible effect on the induced tensile stresses. The limiting value o f the clear spacing o f 2d is independent o f the groove width.
Fig. 5.19 shows the tensile stress at the FRP-epoxy interface, (coefficient G2 and/or G'2) due to a unit radial pressure applied at the locations o f FRP bars. The modular ratio, n, was set to 5 to simulate the most critical conditions for the tensile stresses at the FRP- epoxy interface. The figure clearly indicates that the clear spacing between the grooves o f near surface mounted bars has a negligible effect on the induced tensile stresses at the FRP-epoxy interface. These stresses are influenced by the groove width rather than the clear spacing between the grooves as shown in Fig. 5.19.
Concrete
0.5 -- 0.25 --
0 -I 1---1--- 1---1--- 1---1---1--- 1--- 1---1--- 1---
0.5 0.75 1 1.25 1.5 1.75 2
5 .Experimental Results & Analytical Modelling: Bond Specim ens
Fig. 5.20 depicts contours o f principal tensile stresses for various groove spacing to bar diameter ratios. It should be noted that the proposed design chart, shown in Fig. 5.13 is applicable for s/d > 2.0.
ADINA5 AU1 version 7-5.2. 16 J a n u a ry 2002* L icen sed from ADINA R&Q. Inc.
INFLUENCE o f BAR SPA CIN G ADINA5 AU1 v e rs io n 7.5.2* 16 J a n u a r y 2002* L ic e n s e d fro m ADINA R A D . inc.
IN F L U E N C E O F B A R S P A C IN G
A D I N A
S M 0 O T H E 0 ST R E S S -Z Z
R ST CALC
TIME IjOOO
m a x im u m
* 2*927 MINIMUM
* -1-961
A D I N A
S M O O T r-C D
R S T CALC TIM E 1-GCO
^ 0 .5 0 0
0.000
-0 .5 0 0 - .000
MAXIMUM A 1 .326 MINIMUM
* -2 .1 4 2
a) s/d~0.25 b) s/d^l.O
ADINA8 AUI v e rs io n 7.5*2* 16 J a n u a r y 20CQ* L ic e n s e d ir o m ADINA RAD* inc.
IN FLU EN C E O F B A R S P A C IN G
ADINA* AUI v ersion 7 .5.2. 16 J an u a ry 2 0 0 2 s L icensed h e m ADINA RAD. Inc.
i n f l u e n c eo fb a rs p a c i n g
A D I N A A D I N A
S M O O T H E D
R S T CALC T M E 1-000
1.000 0 .5 0 0
0.000
0 .5 0 0
1.000
5 0 0
2-000
MAXIMUM
* -2 .2 3 2
c) s/d= 1.50
SM OOTHED
ST R ESS-ZZ RST CALC TIME IjOOO
d) s/d=2.0 Fig. 5.20 Tensile stress distribution surrounding near surface mounted bars
due to unit radial pressure
1.000 0-500
0-000
•0 .5 0 0 -1.000 -1*500 -2.000
■ Experimental Results & Analytical Modelling: Bond Specim ens
From the above discussion, it is concluded that the minimum clear spacing between the grooves o f near surface mounted FRP bars should not be less that two times the diameter o f the bars regardless o f the groove width. Using a clear groove spacing to bar diameter ratio less than the proposed value results in overlapping o f the tensile stresses at the concrete-epoxy interface and should be accounted for in design.
Placing a near surface mounted FRP bar close to the edge o f a concrete beam introduces additional tensile stresses at the concrete-epoxy interface. Such a phenomenon is termed
“edge effect”. To determine the minimum edge distance required for near surface mounted FRP bars, the edge distance, e, was varied from 2d to 6d, where d is the diameter o f the bar as shown in Fig. 5.21.
ADINA' AUI version 7.5.2, 2 2 Jan u ary 2 0 0 2 ' L icensed from ADINA RAL ADINA' AUI version 7.5.2, 2 2 Jan u ary 2002= Licensed (torn ADLNA RAD, Inc.
EDGE E FF E C T S ON NSM BARS INFLUENCE OF BAR SPACING
A D I N A A D I N A
e=2d e=6d
Plane o f symmetry Plane o f symmetry
______________ 5. Experimental Results & Analytical Modelling: Bond Specim ens The maximum tensile stress at the concrete-epoxy interface due to a unit radial pressure applied at the location o f FRP bars (coefficient G/) is shown in Fig. 5.22 for various edge distances. In general, increasing the edge distance reduces the induced tensile stresses considerably regardless o f the groove width. The analysis suggests a minimum edge distance o f four times the diameter o f the bars to minimize the edge effect and permit using the proposed design chart, shown in Fig. 5.13.
C /d =1.0
Concrete 1.75 -
1.25 -
0.75 -
w=2.5d
> G i is almost constant 0.25 -
4.5 5 5.5 6
2 2.5 3 3.5 4
e /d
Fig. 5.22 Influence o f edge distance on tensile stresses at the concrete-epoxy interface
5.2.2.8 Maximum Stresses in NSM Bars (fFRp)
Test results showed that the maximum tensile stress in near surface mounted CFRP bars at the onset o f debonding did not exceed 43 percent o f the tensile strength o f the bars regardless o f the embedment length used. Initiation o f the debonding failure was observed at the concrete section where the secondary bottom steel reinforcement was terminated as shown in Fig. 5.3.
5 .Experimental Results & Analytical Modelling: Bond Specim ens
This section investigates the influence o f various configurations o f the bottom steel reinforcement on the behaviour based on a non-linear finite element modelling.
Termination o f the bottom steel reinforcement in the maximum moment region simulates cases where the bottom steel reinforcement is corroded or damaged. Consequently, evaluation o f the existing concrete structure and identifying the conditions as well as the configuration o f the internal steel reinforcement is essential prior to strengthening using near surface mounted FRP bars. Taking advantage o f the symmetry o f the bond specimens, only one quarter o f the beams was modelled by ANACAP using 20-node brick element. Full description o f the finite element model as well as the analysis procedures using ANACAP were reported in Chapter 4, section 4.3.3.2. In the analysis, the embedment length o f near surface mounted C-Bars was set to 550 mm to develop the maximum bond stresses as observed in the experimental program for beams A2 and A5.
Four different configurations for the bottom steel reinforcement were examined as shown
in Fig. 5.23a. t o.i a. o.i a.
550 mm 550 mm
Fig. 5.23a Various configurations for the bottom steel reinforcement
Using Equations 5.3 and 5.7 and rearranging, the bond strength o f near surface mounted FRP bars, rmax, can be expressed as:
ằ f c t
max (5.13)