- Email: [email protected]
A probabilistic investigation into deterioration of CFRP–concrete interface in aggressive environments
Construction and Building Materials 41 (2013) 49–59
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
A probabilistic investigation into deterioration of CFRP–concrete interface in aggressive environments Yail J. Kim a,⇑, Mozahid Hossain b, Jun Zhang c a
Department of Civil Engineering, University of Colorado Denver, Denver, CO 80217, USA Department of Civil and Environmental Engineering, University of South Carolina, Columbus, SC, USA c Department of Industrial and Manufacturing Engineering, North Dakota State University, Fargo, ND, USA b
h i g h l i g h t s " Performance of CFRP–concrete interface is examined. " Probability-based models predict experimental findings. " Design recommendations are presented.
a r t i c l e
i n f o
Article history: Received 28 April 2012 Received in revised form 17 November 2012 Accepted 22 November 2012 Available online 3 January 2013 Keywords: Bond Durability Fiber reinforced polymer Interface Probability
a b s t r a c t This paper presents a probabilistic investigation into the deterioration of CFRP–concrete interface subjected to aggressive environments. A total of 53 single-lap shear specimens are exposed to freeze– wet–dry, wet–dry, and constant cold temperature conditions, 7 of which are unconditioned control specimens. Test parameters include the number of environmental cycles up to 150 and the degree of temperature as low as 30 °C for 2000 h. Upon completion of the planned environmental cycling, the residual capacity of the CFRP-interface (i.e., local interfacial fracture energy) is evaluated. The effect of freeze– wet–dry and constant cold temperature exposure is noticeable on the deterioration of the interface, whereas that of wet–dry is negligible. Probability distribution of the interfacial capacity is found to be normal and statistical uncertainty increases with the number of environmental cycles. Refined design factors are suggested using a Monte-Carlo simulation to ensure the sustainable performance of CFRP-retrofit systems for climatic regions with which freezing environment is associated. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The performance of constructed reinforced concrete members may be improved by carbon fiber reinforced polymer (CFRP) composites. Structural retrofit is readily implemented on site by bonding CFRP sheets to the tensile soffit of a member, thereby enhancing load-carrying capacity or serviceability [1]. Epoxy adhesives are a commonly used bonding agent for such an application. Despite the promising track-record of CFRP-retrofit, deterioration of CFRP–concrete interface needs further examinations because premature debonding of the CFRP can significantly influence the efficacy of the retrofit. The research community has been struggling with a number of issues with regard to bond of CFRP, including the sources of deterioration and failure mechanisms [2]. Elastic solutions provided an understanding of stress-development and propagation [3], while fracture mechanics approaches were suc⇑ Corresponding author. Tel.: +1 303 352 3653. E-mail address: [email protected] (Y.J. Kim). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.11.101
cessful in determining the capacity of CFRP–concrete interface [4]. One of the major challenges to be addressed is the long-term durability of externally-bonded CFRP [5,6]. A number of experimental programs have been conducted to examine the behavior of CFRP–concrete interface exposed to aggressive conditions such as freeze–thaw or moist environments [7–9]. Most design provisions currently available are based on deterministic investigations and do not explicitly take into account uncertainty that could be associated with long-term effects on site [10]. The emphasis of major design guidelines such as ACI440.2R [11] is primarily on precluding the failure of a CFRP-retrofit system, rather than on providing performance-based refined recommendations (e.g., progressive deterioration of a CFRP system under longterm loads and corresponding in situ performance depending upon the intensity of such loads). Some research has adopted probabilistic approaches to examine the failure of externally bonded CFRP [10,12], whereas limited effort is made on the probability of interface deterioration that requires more attention from a service perspective. This paper presents a probability-based investigation into
50
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
the performance of CFRP–concrete interface subjected to aggressive environments. A single-lap shear test was conducted and experimental results were probabilistically modeled to provide design recommendations, including refined resistance factors. 2. Research significance Recent research has reported the provisions of ACI440.2R [11] need to be refined [13,14]. The reason is that their applicable ranges are not object-specific when externally bonded CFRP materials are subjected to progressive deterioration, such as fatigue and environmental damage. For example, a single environmental reduction factor of 0.85 is given to CFRP systems exposed to aggressive environments, regardless of the period of exposure and the degree of aggressiveness. Such an approximation may be a convenient means for design and practice, whereas the actual behavior of CFRP systems with time is questionable and cannot be adequately projected. Of interest is the performance of CFRP– concrete interface in service, rather than debonding failure, because deterioration of the interface is dominantly observed on site. Most existing experimental research is concerned with qualitative examinations on the deterioration of CFRP–concrete interface when subjected to environmental load. The applicability of individual research results is, therefore, limited to actual design and practice. The challenge associated with prognosticating the long-term performance of CFRP bonded to a concrete substrate is that interface deterioration is stochastic in nature. Accordingly, refined design factors have not been readily available. To overcome such an impediment, a probabilistic approach was taken in this research program. A combined experimental and modeling study was conducted to generate refined design factors for CFRP-retrofit in aggressive environment (i.e., cold regions). The methodology proposed here has significant potential for developing refined design factors in various long-term loading conditions (e.g., fatigue and creep) that are vulnerable to the in situ performance of CFRP–concrete interface. 3. Experimental program 3.1. Details of materials and test specimens The unidirectional CFRP sheet used here had a tensile modulus of 227 GPa and corresponding strength of 3800 MPa with an equivalent thickness of 0.165 mm [15]. Tested CFRP coupons (15 mm wide 200 mm long) showed an average tensile modulus of 231 GPa with corresponding strength of 3590 MPa. Concrete was manually mixed in the laboratory, including a 5.5% air-entrainer. The water-to-cement ratio was 0.45. The use of air-entrainer is particularly important for concrete exposed to aggressive environment to preclude disintegration of the constituents [16]. The specified compressive strength was 20 MPa, while the average 28-day strength tested was 23 MPa. A two-part epoxy adhesive was used to bond the CFRP to concrete. The epoxy had a strength of 54 MPa and a tensile modulus of 3 GPa [17]. Concrete blocks (100 mm wide 50 mm deep 150 mm long) were cast and cured, and a single layer of precut CFRP sheet (75 mm wide 250 mm long) was bonded to the substrate of the concrete with the bonding agent, as shown in Fig. 1. It is important to note that the bond length of the CFRP (100 mm) exceeded the effective length ranging from 52 mm to 57 mm according to existing expressions [11,18] beyond which no further increase in strength of the CFRP–concrete interface would be achieved. Prior to bonding the sheet, the concrete surface was roughened using 80-grit sand paper and a water-jet. The prepared specimens were cured for a minimum of 1 week at room temperature. Seven specimens were tested to serve as control, whereas 46 specimens were conditioned as described below. 3.2. Test protocol To examine the effect of aggressive environments on the behavior of CFRP–concrete interface, a three-phase test protocol was designed (Fig. 1b). The first phase was freeze–wet–dry: one cycle of freeze–wet–dry included 16 h of freezing at 30 °C, 4 h of submerging in a water bath, and 4 h of drying at room temperature (25 °C). An environmental chamber equipped with a digital temperature adjustment function was used to simulate cold temperature. The fraction of such simulation hours was determined based on literature concerning the durability of CFRP in
cold region environment [7,16,19]. The second phase was wet–dry: one cycle of wet–dry was 16 h of submerging in a water bath and 8 h of drying at room temperature. These two phases were repeated up to 150 cycles, determined from previous research [7,20]. A comparison between the first and second phases would provide the effect of freezing on the behavior of the CFRP–concrete interface. The last phase was constant cold temperature: test specimens were subjected to four different temperatures at 0 °C, 10 °C, 20 °C, and 30 °C for 2000 h (3 months). The purpose of the third phase was to study the effect of a continued cold temperature condition that was frequently observed in cold climate regions. The simulated hours of the constant cold temperature exposure were determined based on the temperature of cold regions in the US typically showing about 3 months of sub-zero temperatures per winter [21]. It is worthwhile to note that refined durability investigations may improve the predictive response of CFRP-strengthened members even though accelerated durability tests are dominantly used to examine the long-term behavior of such members. Table 1 summarizes test specimens and environmental conditions. The identification code of each specimen indicates the type of exposure (R = control; FWD = freeze–wet–dry; WD = wet–dry; and CT = constant temperature), the number of environmental cycles and repetition (e.g., Specimen WD3100 means the specimen was the third repetition for 100 cycles of wet–dry), and temperature (e.g., Specimen CT-30-4 was subjected to 30 °C and was the fourth repetition). 3.3. Test set-up and instrumentation Upon completion of the planned environmental conditioning, all specimens were monotonically loaded until failure occurred at a rate of 2.5 mm/min using an MTS 810 hydraulic testing machine. A custom-made loading frame allowed a stable loading environment for the single-lap shear test (Fig. 1c). The clamping area of the CFRP was 38 mm 50 mm. The displacement and applied load were measured from the stroke of the loading-head and a built-in load cell, respectively. Strain gages were bonded along the CFRP at 20 mm on center to monitor the progression of CFRP-debonding when loaded. All test data were recorded by a data acquisition system.
4. Probability modeling for interface deterioration 4.1. Interfacial fracture energy Extensive effort has been made on examining the interfacial fracture energy of CFRP materials bonded to a concrete substrate (i.e., the energy required to fracture CFRP–concrete interface). Table 2 summarizes selected expressions to predict the fracture capacity of CFRP–concrete interface. Typical parameters considered include the properties of constituents (tensile or compressive strength, tensile modulus, and thickness) and geometric configurations (CFRP-bond width). Given all of these equations have been empirically developed, a comprehensive assessment may be necessary to identify their dissimilarity, if any. The tensile strength of concrete for the expressions shown pffiffiffiffi in Table 2 was consistently assumed here using fr ¼ 0:62 fc0 where fc0 is the compressive strength of concrete in MPa, which is equivalent to the modulus of rupture available in ACI-318 [22]. 4.2. Fundamental properties To predict the performance of CFRP–concrete interface subjected to aggressive environments, a probabilistic approach was employed. Of interest was the probability of interface deterioration. For modeling convenience, interfacial fracture energy was classified into two categories: Gfc and Gfn are the mean capacities of the conditioned and control specimens, respectively. The local interfacial fracture energy can be measured from the area of the shear stress versus CFRP–slip relationship of a single-lap test specimen (Fig. 1). The local shear stress and corresponding slip may be experimentally determined using Eqs. (1) and (2), respectively.
s ¼ Ef t f s¼
Z
x2 x1
e2 e1
x2 x1
eðxÞdx
ð1Þ
ð2Þ
51
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 1. Specimen details and test set-up: (a) schematic of the test and instrumentation; (b) test protocols; (c) single-lap shear test; (d) freezing inside environmental chamber (30 °C); (e) wet; (f) drying at room temperature (25 °C).
Table 1 Test specimens. ID
R1 R2 R3 R4 R5 R6 R7 FWD1-25 FWD2-25 FWD3-25 FWD4-25 FWD1-50 FWD2-50 FWD3-50 FWD4-50 FWD1-100 FWD2-100 FWD3-100 FWD4-100 FWD1-150 FWD2-150 FWD3-150 FWD4-150 WD1-25 WD2-25 WD3-25 WD4-25
Env. effect
None None None None None None None 25 cycles 25 cycles 25 cycles 25 cycles 50 cycles 50 cycles 50 cycles 50 cycles 100 cycles 100 cycles 100 cycles 100 cycles 150 cycles 150 cycles 150 cycles 150 cycles 25 cycles 25 cycles 25 cycles 25 cycles
Pu (kN)
17.3 15.2 17.6 13.5 20.0 18.0 17.3 19.2 17.2 17.4 12.5 13.5 17.0 16.2 15.1 16.7 7.0 18.9 15.2 10.7 16.4 15.7 13.5 15.9 14.7 19.2 14.5
Local interfacial fracture energy (N/mm) Gfc
Ave
S
0.26 0.20 0.27 0.23 0.26 0.30 0.24 0.29 0.30 0.23 0.18 0.16 0.32 0.22 0.20 0.20 0.09 0.27 0.23 0.14 0.21 0.27 0.18 0.23 0.18 0.29 0.25
0.25
0.03
0.25
0.06
0.23
0.07
0.20
0.08
0.20
0.05
0.24
0.05
ID
Env. effect
WD1-50 WD2-50 WD3-50 WD4-50 WD1-100 WD2-100 WD3-100 WD1-150 WD2-150 WD3-150 CT0-1 CT0-2 CT0-3 CT0-4 CT-10-1 CT-10-2 CT-10-3 CT-10-4 CT-20-1 CT-20-2 CT-20-3 CT-20-4 CT-30-1 CT-30-2 CT-30-3 CT-30-4
50 cycles 50 cycles 50 cycles 50 cycles 100 cycles 100 cycles 100 cycles 150 cycles 150 cycles 150 cycles 0 °C 0 °C 0 °C 0 °C 10 °C 10 °C 10 °C 10 °C 20 °C 20 °C 20 °C 20 °C 30 °C 30 °C 30 °C 30 °C
Pu (kN)
6.3 13.9 14.1 16.1 13.0 17.3 20.0 17.2 15.6 17.6 16.2 17.1 18.1 10.5 14.1 15.5 13.0 16.4 18.0 19.1 18.2 17.0 13.6 12.3 15.0 15.8
Local interfacial fracture energy (N/mm) Gfc
Ave
S
0.09 0.20 0.16 0.23 0.13 0.34 0.29 0.20 0.19 0.27 0.34 0.25 0.29 0.20 0.21 0.32 0.23 0.31 0.22 0.25 0.27 0.21 0.14 0.18 0.21 0.23
0.17
0.06
0.25
0.11
0.22
0.04
0.27
0.06
0.27
0.06
0.24
0.03
0.19
0.04
Env. effect = environmental effect; Ave = average; S = standard deviation; Pu = ultimate load; su = maximum average shear stress; Gfc = interfacial fracture energy.
where s is the local shear stress; Ef and tf are the tensile modulus and thickness of the CFRP, respectively; s is the local slip of the CFRP; and e(x) is the strain increment at arbitrary locations based on e1 and e2 at the locations of x1 and x2. For this research, the post-peak energy of test specimens was ignored because interfacial
failure was brittle. The design margin index (g) is a convenient tool to assess the existing design expressions (Table 2):
g¼
ðGfci Gfd Þ Gfci
ð3Þ
52
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
be required to determine the cycle-dependent interfacial fracture energy, Gfc(N). For the convenience of probabilistic investigations, the probability distribution of Gfc(N) and Gfn(N) is transformed to standard normal so that g(Gfc, Gfn) becomes g(U, N) where U is the standard normal random variables, as shown in
Table 2 Existing interfacial fracture energy for design (Gfd in N/mm). Reference
Model
Neubauer and Rostasy [37] JSCE [38] Ueda et al. [39]
Gfd ¼ 0:204f r Gfd ¼ 0:5 N=mm 0:352 fc0:236 ðEp tp Þ0:023 Gfd ¼ 0:446 Gtaa
Ulaga et al. [40]
Gfd ¼ 0:045fc rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2b =bc pffiffiffiffiffiffiffi Gfd ¼ 0:03 1þb f=400 fc fr
CNR [41]
gðU; NÞ ¼ ½Gfc ðNÞ þ rfc ðNÞU fc ðNÞ ½Gfn ðNÞ þ rfn ðNÞU fn ðNÞ
2=3
The gradient of the initial random variable U0 is defined as
f
Dai et al. [42] Lu et al. [27]
ð10Þ
Gfd ¼ 0:514fc0:236 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi 2:25b =b Gfd ¼ 0:308b2w fr in which bw ¼ 1:25þbf =bcc f
fr = Compressive strength of concrete; fr = tensile strength of concrete; bf = width of bonded FRP; fc = width of concrete substrate.
rgðU 0 ðNÞÞ ¼
@gðU; NÞ @gðU; NÞ ¼ ðrfc ðNÞ; rfn ðNÞÞ ; @U fc @U fn
ð11Þ
Assuming the initial random variable U0(N) = (0, 0) for Ufc(N) and Ufn(N)
gðU 0 ðNÞÞ ¼ Gfc ðNÞ Gfn ðNÞ
ð12Þ
The norm of vector rg(U0(N)) is calculated by where Gfci is the interfacial fracture energy of the ith test specimen and Gfd is the design fracture energy. The bias factor (k) can provide the degree of conservatism of the design interfacial fracture energy:
Gfci k¼ Gfd
ð4Þ
The probability distribution of test specimens may be assumed to be normal if the median positioning associated with a leastsquare fit (Eq. (5)) tends to be linear with respect to corresponding z scores (Eq. (6)) [23].
FðGfc Þ ¼
i 0:3 n þ 0:4
ð5Þ
krgðU 0 ðNÞÞk ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2fc ðNÞ þ r2fn ðNÞ
ð13Þ
The ratio of the gradient of the performance function to corresponding norm, a0, is shown in
a0 ¼
rgðU 0 ðNÞÞ krgðU 0 ðNÞÞk 0
1
rfc ðNÞ rfn ðNÞ B C ¼ @qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA 2 2 2 2 rfc ðNÞ þ rfn ðNÞ rfc ðNÞ þ rfn ðNÞ
ð14Þ
The norm of the initial random variable, b0, is then:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U 2fc0 þ U 2fn0
where i is the ith test specimen of n ordered residual interfacial fracture energy (Gfc).
b0 ¼ kU 0 ðNÞk ¼
zi ¼ U1 ½FðGfc Þ
The most probable point within the probabilistic domain, U, may be found using
ð6Þ
where U is the standard normal distribution. Once the distribution of the test specimens is found to be normal, the probability distribution of the interfacial fracture energy can be expressed as
1 1 Gfc Gfci f ðGfc Þ ¼ pffiffiffiffiffiffiffi exp 2 rfc r 2p
b ¼ kU k
ð17Þ
The probability of interface deterioration is calculated using
Pr ¼ UðbÞ or UðbÞ
4.3. Formulation of first-order reliability method The first-order reliability method (FORM) may be used to prognosticate the progressive deterioration of CFRP–concrete interface with environmental cycles, given that interface deterioration is fundamentally stochastic. The benefit of using such a method includes that a probability formulation can be done with only the mean and corresponding standard deviation of a random variable [24]. The following briefly describes the FORM method, while further details and theoretical background may be available in any reliability textbook or papers [25,26]. A linear performance function of CFRP–concrete interface is expressed as
ð8Þ
where Gfc(N) and Gfn(N) are the interfacial fracture energy and corresponding control capacity at an environmental cycle N, respectively. Taking into account practical significance in design, Gfn(N) may be assumed to be constant irrespective of the number of environmental cycles. Based on Eq. (8), the probability of interface deterioration is defined as
PrðNÞ ¼ PrðgðGfc ; Gfn Þ 6 0Þ ¼ PrðGfc ðNÞ 6 Gfn ðNÞÞ
ð16Þ
The norm of the U will be the reliability index, b, as shown in
ð7Þ
where rfc is the standard deviation of the Gfc.
gðGfc ; Gfn Þ ¼ Gfc ðNÞ Gfn ðNÞ
rgðU 0 Þ U ¼ a0 b0 þ krgðU 0 Þk
ð15Þ
ð9Þ
where Pr(N) is the probability of interface deterioration at an arbitrary environmental cycle N. A regression analysis of test data may
ð18Þ
where U(b or b) is the cumulative density function of the standard normal distribution. It is worthwhile to note that U(b) is used when Gfc(N) is greater than Gfn(N), which could happen in experimental investigations, and U(b) is used for an opposite case. 5. Test results 5.1. Residual capacity of CFRP–concrete interface Table 1 provides the single-lap shear test results with and without environmental conditioning. The average shear stress versus displacement behavior of selected specimens is given in Fig. 2. The mean failure load of the control specimens was 17.0 kN with a standard deviation of 2.1 kN. The measured interfacial fracture energy (i.e., area under average shear stress versus CFRP–slip curve) was 0.25 N/mm, on average, and corresponding coefficient of variation was 0.12. It should be noted that the experimental local shear stress versus slip (Fig. 3) was typically bilinear as is for the case of other test programs [27]. The failure load and interfacial fracture energy of the specimens subjected to freeze–wet–dry decreased with cycles, as shown in Table 1; for example, an average decrease of 20.0% in the facture energy was measured for the specimens exposed to 150 cycles of freeze–wet–dry when compared
53
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
others because of an outlier specimen (the CFRP was wet-lay-up and thus bond between the CFRP and concrete substrate was not ideal). The degree of constant cold temperature affected interfacial strength. The specimens exposed to 30 °C for 2000 h exhibited a decrease of 29.6% in the average interfacial fracture energy when compared with those subjected to 0 °C. The increased brittleness of the interface with lowering temperature is believed to accelerate the dislocation of the interface constituents. All test specimens showed typical interfacial shear failure, as shown in Fig. 1c. 5.2. Variation of interfacial fracture energy
Fig. 2. Average shear stress versus displacement response.
A regression analysis was conducted to provide empirical equations forming the base of the probabilistic investigation. All measured interfacial fracture energies with environmental effects shown in Table 1 were fitted using a logarithmic term (i.e., the average coefficient of determination of the interfacial fracture energy was 0.48). The predictive equations for the interfacial capacity of the specimens subjected to freeze–wet–dry and wet–dry cycles (Gfc(N)) are shown in Eqs. (19) and (20), respectively.
Gfc ðNÞ ¼ 0:0302 ln ðNÞ þ 0:3444 6 Gfn
for FWD
ð19Þ
Gfc ðNÞ ¼ 0:0058 ln ðNÞ þ 0:1961 6 Gfn
for WD
ð20Þ
where N is the number of environmental cycle (N > 0). Average differences between the tested interfacial capacities and the predicted values using Eqs. (19) and (20) were 2.3% and 13.2%, respectively. The coefficient of variation of these two test categories was fitted as well:
GfcCOV ðNÞ ¼ 0:0479 ln ðNÞ þ 0:0971 for FWD
ð21Þ
GfcCOV ðNÞ ¼ 0:0323 ln ðNÞ þ 0:1598 for WD
ð22Þ
Fig. 3. Local shear stress versus slip of control (Specimen R4).
with that of the control. The average coefficient of variation in the interfacial fracture energy of the freeze–wet–dry specimens was 248.8% greater than that of the control specimen. This increase illustrates that experimental uncertainty (i.e., dispersion of test data) has increased due to the environmental conditioning: bond between the CFRP and concrete deteriorated in a non-uniform manner. Contrary to the freeze–wet–dry test, there was no obvious trend in decreasing the interfacial capacity of the wet–dry test specimens. The coefficient of variation was, however, influenced by the wet–dry environment: an average increase of 246.5% was noticed when compared to the coefficient of variation of the control specimens. This observation implies that the wet–dry effect might not be sufficient to influence the capacity of the CFRP–concrete interface; however, such an effect can increase experimental uncertainty from a statistical point of view. It should be noted that the average capacity of the WD-50 category was lower than that of
The margin of error in the predicted coefficient of variation was 15.0% and 36.9% for Eqs. (21) and (22), respectively, on average. Such relatively large differences in comparison to the case of the interfacial fracture energy (Eqs. (19) and (20)) are attributed to the limited number of the test specimens; however, these fitted coefficients of variation were acceptable (to be discussed in Section 6.1). 5.3. Strain development Fig. 4 shows the development of strains along the bonded CFRP sheet (only selected specimens are given here since other specimens demonstrated similar behavior). As checked in Section 3, the bonded length was sufficient to transfer the applied load from the CFRP to concrete substrate without premature peeling failure. Due to stress concentrations, higher strains near the loaded-end
Fig. 4. Strain development: (a) control (Specimen R4); (b) freeze–wet–dry at 150 cycles (Specimen FWD4-150).
54
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
were recorded prior to the initiation of CFRP-debonding (i.e., a sudden increase in strain reading). When the applied load increased, the debonded region shifted towards the free-end of the specimens and the CFRP–concrete interface eventually failed. Conspicuous debonding of the CFRP was not observed within service load levels irrespective of the environmental effects (up to 150 cycles of freeze–wet–dry and wet–dry, and 2000 h of continued cold temperature exposure). Once CFRP-debonding was noticed, its development was rapid. The measured strains at the tip of the CFRP were slightly lower than those of other locations because of stress re-distribution associated with experimental uncertainty such as non-uniform debonding of the CFRP and the presence of aggregates on the concrete surface. Other experimental programs reported a similar trend [28,29]. Although the environmental conditioning did not significantly influence the debonding strain of CFRP (all test data are not shown here for brevity), it was obvious that such conditioning altered debonding characteristics of the CFRP (Fig. 4). The empirical predictors shown in Eqs. (19) and (20) confirm these qualitative observations. 6. Predicted probability 6.1. Probabilistic response To implement the probability modeling described previously, the control interfacial fracture energy (Gfn) serving as a limit for interface deterioration was first evaluated. Fig. 5a compares the existing design models (Table 2) with the control specimens tested in this research program. The design margin index (Eq. (3)) is presented in Fig. 5b, based on the average Gfn value of 0.25 N/mm.
Most of the models were conservative, while the degree of conservatism varied from 0.28 to 4.38 as per the design margin index. Fig. 6 shows the effect of the environmental exposure on the bias factors of the test specimens (Eq. (4)). The bias factors were positioned between 0.28 and 0.44. This observation indicates that the experimental capacity of the CFRP–concrete interface exceeded the design capacity even though a trend of deterioration was noticed, in particular when associated with cold temperature exposure. The design interfacial capacity was estimated using the average Gfd value of the design equations available in Table 2 (Gfd = 0.61 N/mm). The probability distribution of the test specimens was determined based on the normality test (Fig. 7a). Significant linearity was observed in all cases with an average coefficient of determination (R2) of 0.976. It was, therefore, reasonable to conclude that the test data were normally distributed from a probability perspective. Such an observation supports the adequacy of the probability study presented here even though the number of the test specimens was limited; in other words, the normal probability distribution function will virtually cover all possible test results within the investigation range given in this research program (regardless of the number of test specimens). After generating probability distribution functions using Eq. (7), corresponding cumulative distributions were obtained (Fig. 7b). Fig. 8 compares the fitted coefficient of variation (Eqs. (21) and (22)). This comparison confirms the adequacy of the current probabilistic study. Although the present research accepted a variable coefficient of variation with environmental cycles (Eqs. (21) and (22)), such a statistical parameter is frequently assumed to be constant for simplicity [30].
Fig. 5. Evaluation of proposed design equations for local interfacial fracture energy, Gfd (Dai = Dai et al. [42]; Ueda = Ueda et al. [39]; JSCE = JSCE [38]; CNR = CNR [41]; Exp = present experimental data of control specimens): (a) parametric comparison between experiment and models; (b) design margin index with averaged experimental capacity.
Fig. 6. Bias factor for interfacial fracture energy with averaged experimental capacity per test category: (a) freeze–wet–dry and wet–dry; (b) constant temperature for 2000 h.
55
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
(a)
(b)
Fig. 7. Validation of probability distribution: (a) normality test; (b) cumulative distribution of selected cycles in freeze–wet–dry.
Fig. 8. Evaluation of coefficient of variation for probability modeling.
Prior to conducting an extensive probability simulation, a sensitivity analysis was carried out to examine how sensitive the
(a)
(c)
fracture energy and the coefficient of variation would be when the number of environmental cycles increased. Fig. 9a and b shows the experimental variation of the averaged interfacial fracture energy and coefficient of variation, respectively, for each environmental condition. The interfacial fracture energy and the coefficient of variation varied within a range of less than 0.3 N/mm (Fig. 9a) and 0.3 (Fig. 9b), respectively. The probability of deterioration of the CFRP–concrete interface subjected to freeze– wet–dry (more critical than wet–dry) was prognosticated (Eq. (18)) with possible variation ranges of the control fracture energy (Fig. 9c) and the coefficient of variation (Fig. 9d). The Gfn value was a significant factor influencing the probability of interface deterioration within the investigation range studied here, as shown in Fig. 9c. Such an observation, however, was not a critical concern because the variation of Gfn might not be significant in practice. Table 1 supports the consistency of the measured control fracture energy (Gfn). An increase in the coefficient of variation increased the uncertainty of interface deterioration, including the change of the predicted probability curve (Fig. 9d). This observation indicates
(b)
(d)
Fig. 9. Sensitivity analysis of interfacial fracture energy: (a) averaged experimental interfacial fracture energy (Gfc); (b) averaged experimental coefficient of variation (COV); (c) effect of control fracture energy (Gfn) based on freeze–wet–dry with standard deviation of 0.03 N/mm; (d) effect of COV with Gfn = 0.25 N/mm based on freeze–wet–dry.
56
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
(a)
(b)
(c)
(d)
Fig. 10. Probable frequency of occurrence: (a) freeze–wet–dry; (b) wet–dry; (c) cumulative distribution of freeze–wet–dry; (d) cumulative distribution of wet–dry.
that the coefficient of variation is related to the uncertainty of interface deterioration; however, existing approaches usually assumes a constant coefficient of variation for simplicity [30]. 6.2. Effect of environments Fig. 10 exhibits the effect of environmental cycles on the probability distribution of the interfacial capacity (Gfc). The predicted probability distribution of the freeze–wet–dry shifted to the left with an increasing cycle, indicating that the interfacial fracture energy decreased due to the deterioration of the CFRP–concrete interface (Fig. 10a). The contribution of freeze–wet–dry was significantly greater than that of wet–dry, as shown in Fig. 9a and b. The capacity in wet–dry, however, did not show such a trend until 150 cycles were reached (Fig. 10b). The variation range in the cumulative distribution of freeze–wet–dry was also noticeable in comparison to that of wet–dry, as shown in Fig. 10c and d, respectively.
Fig. 11. Comparison between freeze–wet–dry and wet–dry effects for probability of interface deterioration.
The probability of deterioration of the CFRP–concrete interface subjected to these two environmental conditions is shown in Fig. 11. For the interface exposed to freeze–wet–dry, a gradual increase in the probability of deterioration was noticed after 15 cycles and approached unity when 60 cycles were exceeded. It should be noted that the horizontal line in the freeze–wet–dry at a probability of deterioration of 0.5 was generated due to the boundary condition shown in Eq. (19). This observation implies that CFRP–concrete interface will surely deteriorate in a freeze– wet–dry environment. Noticeable evidence of interface deterioration, however, was not observed up to 150 cycles in the case of wet–dry (Fig. 10).
7. Design recommendation 7.1. Monte Carlo simulation A Monte Carlo simulation was conducted to help develop design recommendations for the deterioration of CFRP–concrete interface subjected to freezing weather. The simulation complemented the limited experimental data through usage of a prescribed set of interfacial fracture energy within a possible probability domain. Random values were generated for the conditioned (Gfc) and control (Gfn) capacities, based on the inverse transformation method [31]. It is worthwhile to note that the random sampling with variable Gfn can broaden the applicable range of the design factors even though Gfn may not significantly vary in practice. The ranges of data sampling for trial-simulations were l ± 3r for Gfc and Gfn, where l and r are the mean and standard deviation, respectively. The sampling range of l ± 3r can cover 99.73% of all possible values in a normally distributed parameter [32]. A typical sampling region is shown in Fig. 12a, including the experimentally obtained Gfc and Gfn data. To generate design factors, an established
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
57
Fig. 12. Evaluation of Monte-Carlo sampling at 150 freeze–wet–dry cycles: (a) comparison to experimental data; (b) assessment of safety factor.
approach (i.e., second-moment criteria) was employed. Direction cosines and associated design parameters may be defined in [33].
COV
G
Gfn fn ffi aGfn ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
ðCOVGfn Gfn Þ þ ðCOVGfc Gfc Þ2
aGfc
COVGfc Gfc ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðCOVGfn Gfn Þ2 þ ðCOVGfc Gfc Þ2
ð23Þ
ð24Þ
U ¼ 1 aGfn bCOVGfn
ð25Þ
c ¼ 1 aGfc bCOVGfc
ð26Þ
where aGfn and aGfc are the direction cosines of the control fracture energy (Gfn) and the interfacial capacity (Gfc), respectively; U is the strength reduction factor; and c is the live load factor; and b is the safety index. Fig. 12b compares the variation of the safety factors with the magnitude of the standard deviation, including the safety factor obtained using the provision of ACI440.2R-08 [11]. This
observation implies that the present approach is reasonably safe for design and practice. 7.2. Reduction factor for interface deterioration To generate strength reduction factors (u) for the design of CFRP–concrete interface subjected to freezing environment, three categories were specified as per the mean annual freeze–thaw (FT) days: Severe (150 < FT 6 250), Moderate (75 < FT 6 150), and Mild (0 < FT 6 75). The map shown in Fig. 13 was created using a climate database of almost 30 years in the US [34]. The concept of safety index (b) is widely used to adjust the level of safe performance of structural members. The acceptable safety indices for new and existing structures are 3.5 and 2.5, respectively [35,36]; therefore, the upper limit of b was set to 2.5 for this research. The lower bound of b may be typically assumed to be 1.5 [30]. The following condition was accordingly specified in this research program for the convenience of developing design factors: Mild (b = 1.5), Moderate (b = 2.0), and Severe (b = 2.5). These configurations were linked with actual freezing environment as per the
Fig. 13. Mapping of average freeze–thaw cycles per year ([34]: used with permission).
58
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
(a)
(b)
Fig. 14. Results of Monte Carlo simulation for freeze–wet–dry cycles: (a) reduction factor (u) with a safety index of 2.5; (b) safety factor (c/u) with a safety index of 2.5.
Table 3 Proposed environmental factors for cold climate regions.
Factor
Severe (b = 2.5)
Moderate (b = 2.0)
Mild (b = 1.5)
0.75
0.80
0.85
mean annual freeze–thaw (FT) days (Fig. 13). In so doing, strength reduction factors (u) for the design of the CFRP–concrete interface subjected to such aggressive environmental conditions can be estimated. Fig. 14a shows the variation of the reduction factor (u) in the Monte-Carlo simulation with b = 2.5. A trend of convergence was achieved in all categories with the increased number of random samples. The safety factors (c/u) of each category exceeded the ACI440.2R-08 limit, as shown in Fig. 14b, confirming that the computed u factors could be safely used for design and practice. Table 3 summarizes the proposed reduction factors for the design of CFRP–concrete interface in a freezing service environment. It is worthwhile to note that the u factors are independent of the strength of FRP materials because the contribution of the coefficient of variation in FRP-strength is not significant on the variation of design parameters [10].
influenced the probability of deterioration; however, such an effect might not be critical in practice as per the assessment of the existing design proposals. Refined environmental reduction factors were proposed for climatic regions where freezing environment existed in order to address the risk of interface deterioration in service, ranging from 0.75 to 0.85 depending upon the severity of a freeze–thaw condition. No reduction factors would be necessary for the interface deterioration induced by wet–dry.
Acknowledgments The writers gratefully acknowledge the support of North Dakota State University and the National Science Foundation through North Dakota Experimental Program to Simulate Competitive Research with a Grant Number of EPS-0814442. Mr. Jason Haley and Dr. Scott Sheridan at Kent State University have generously provided a GIS map used for this study. All findings described here are those of the writers and do not necessarily represent the opinion of the funding agencies. References
8. Summary and conclusions This paper has addressed the effect of aggressive environments on the performance of CFRP–concrete interface. An experimental program was conducted with 53 specimens, followed by probabilistic investigations to generate design parameters for practice. The following is concluded. The effect of freeze–wet–dry was noticeable on the deterioration of CFRP–concrete interface, while that of wet–dry was not significant. Both of these environments increased the statistical uncertainty of the interface, represented by the increased coefficient of variation in the interfacial fracture energy. Constant cold temperature exposure at 30 °C for 2000 h also decreased the interfacial capacity. Empirical deterioration models were proposed. The characteristics of the CFRP–concrete interface changed when associated with environmental cycling, including stress redistribution along the interface. Further research was recommended to quantify the spatial properties of failure surface, sliding friction, and damage mapping depending upon the level of interface deterioration. The probability distribution of the interfacial capacity was found to be normal. A variable coefficient of variation was recommended for durability investigations rather than a constant value. The control interfacial fracture energy (Gfn) significantly
[1] Bakis CE, Bank LC, Brown VL, Cosenza E, Davalos JF, Lesko JJ, et al. Fiberreinforced polymer composites for construction-state-of-the-art review. J Compos Constr 2002;6(2):73–87. [2] Teng JG, Lu XZ, Ye LP, Jiang JJ. Recent research on intermediate crack-induced debonding in FRP-strengthened RC beams. In: 4th international conference on advanced composite materials in bridges and structures, Calgary, AB, Canada; 2005 [CD-ROM]. [3] Smith ST, Teng JG. Interfacial stresses in plate beams. Eng Struct 2001;23(7):571–857. [4] Wan B, Sutton MA, Petrou MF, Harries KA, Li N. Investigation of bond between fiber reinforced polymer and concrete undergoing global mixed mode I/II loading. J Eng Mech 2004;130(12):1467–75. [5] Karbhari VM, Abanilla MA. Design factors, reliability, and durability prediction of wet layup carbon/epoxy used in external strengthening. Composites Part B 2007;38:10–23. [6] Wu Z, Kim YJ, Diab H, Wang X. Recent development in long-term performance of FRP composites and FRP–concrete interface. Adv Struct Eng 2010;13(5):891–903. [7] Green MF, Bisby LA, Beaudoin Y, Labossiere P. Effect of freeze–thaw cycles on the bond durability between fibre reinforced polymer plate reinforcement and concrete. Can J Civ Eng 2000;27:949–59. [8] Boyajian DM, Ray I, Davalos JF. Freeze–thaw cycling under a calcium chloride environment: effects on CFRP strengthened concrete structures. Int J Mater Prod Technol 2007;28(1/2):89–102. [9] Ouyang Z, Wan B. Nonlinear deterioration model for bond interfacial fracture energy of FRP–concrete joints in moist environments. J Compos Constr 2009;13(1):53–63. [10] Atadero RA, Karbhari VM. Calibration of resistance factors for reliability based design of externally-bonded FRP composites. Composites Part B 2008;39:665–79. [11] ACI. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures (ACI-440.2R-08). American Concrete Institute, Farmington Hills, MI; 2008.
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59 [12] Wieghaus KT, Atadero RA. Effect of existing structure and FRP uncertainties on the reliability of FRP-based repair. J Compos Constr 2011;15(4):635–43. [13] Harries KA, Aidoo J. Debonding and fatigue-related strain limits for externally bonded FRP. J Compos Constr 2006;10(1):87–90. [14] Kim YJ, Heffernan PJ. Fatigue behavior of structures strengthened with fiber reinforced polymers: state-of-the-art. J Compos Constr 2008;12(3):246–56. [15] MBrace. MBrace saturant: epoxy encapsulation resin. Amherst, NY: Watson Bowman Acme Corp; 2003. [16] Kong A, Fam A, Green MF. Freeze–thaw behavior of FRP-confined concrete under sustained load, Fiber-reinforced Polymer Reinforcement for Concrete Structures (FRPRCS-7). ACI-SP 2005;230:705–22. [17] Degussa. MBrace™ saturant composite strengthening system resin. Shanghai Master Builder Co. Ltd.; 2006. [18] Chen JF, Teng JG. Anchorage strength models for FRP and steel plates bonded to concrete. J Struct Eng 2001;127(7):784–91. [19] Karbhari VM, Rivera J, Dutta PK. Effect of short-term freeze–thaw cycling of composite confined concrete. J Compos Constr 2000;4(4):191–7. [20] Saenz N, Pantelides CP. Short and medium term durability evaluation of FRPconfined circular concrete. J Compos Constr 2006;10(3):244–53. [21] USGS. Northern prairie wildlife research center. United States Geological Survey, Jamestown, ND; 2010.. [22] ACI. Building code requirements for structural concrete and commentary (ACI318). Farmington Hills, MI: American Concrete Institute; 2011. [23] Ebeling CE. An introduction to reliability and maintainability engineering, 2nd ed. Long Grove, IL: Waveland Press, Inc.; 2010. [24] Ayyub BM, Assakkaf IA, Beach JE, Melton WM, Nappi N, Conley JA. Methodology for developing reliability-based load and resistance factor design (LRFD) guidelines for ship structures. Naval Eng J 2008;114(2):23–41. [25] Melchers RE. Structural reliability analysis and prediction, 2nd ed. Chichester: John Wiley and Sons; 1999. [26] Li CQ. Time-dependent reliability analysis of the serviceability of corrosion affected concrete structures. Int J Mater Struct Reliab 2005;3(2):105–16. [27] Lu XZ, Teng JG, Ye LP, Jiang JJ. Bond-slip models for FRP sheets/plates bonded to concrete. Eng Struct 2005;27:920–37. [28] Bizindavyi L, Neale KW. Transfer lengths and bond strengths for composites bonded to concrete. J Compos Constr 1999;3(4):153–60.
59
[29] Yao J, Teng JG, Chen JF. Experimental study on FRP-to-concrete bonded joints. Composites Part B 2005;36:99–113. [30] Nowak AS. Calibration of LRFD bridge code. J Struct Eng 1995;121(8):1245–51. [31] Devroye L. Non-uniform random variate generation. New York, NY: SpringerVerlag; 1986. [32] Dai S-H, Wang M-O. Reliability analysis in engineering applications. New York, NY: Van Nostrand Reinhold; 1992. [33] Ang AH-S, Tang WH. Probability concepts in engineering planning and design. New York, NY: John Wiley and Sons; 1984. [34] Haley JS. Climatology of freeze–thaw days in the conterminous United States: 1982–2009. MS thesis. Kent, OH: Kent State University; 2011. [35] AASHTO. Manual for condition evaluation of bridges (2003 interim revisions). 2nd ed. Washington, DC: American Association of State Highway and Transportation Officials; 2003. [36] AASHTO. LRFD bridge design specifications. 5th ed. Washington, DC: American Association of State Highway and Transportation Officials; 2010. [37] Neubauer U, Rostasy FS. Design aspects of concrete structures strengthened with externally bonded CFRP plates. In: Proceedings of 7th international conference on structural faults and repairs, vol. 2, Edinburgh, Scotland; 1997. p. 109–18. [38] JSCE. Recommendations for upgrading of concrete structures with use of continuous fiber sheets. Tokyo, Japan: Japan Society of Civil Engineers Concrete Engineering Series, 41; 2001. [39] Ueda T, Dai J, Sato Y. A nonlinear bond stress–slip relationship for FRP sheet– concrete interface. In: Proceedings of 6th international symposium on latest achievement of technology and research on retrofitting concrete structures; 2003. p. 113–20. [40] Ulaga T, Vogel T, Meier U. Bilinear stress–slip bond model: theoretical background and significance. In: Proceedings of 6th international symposium on FRP reinforcement for concrete structures (FRPRCS-6), vol. 1; 2003. p. 153–62. [41] CNR. Guide for the design and construction of externally bonded FRP systems (CNR-DT 200/2004). Rome, Italy: National Research Council; 2004. [42] Dai J-G, Ueda T, Sato Y. Development of the nonlinear bond stress–slip model of fiber reinforced plastics sheet–concrete interfaces with a simple method. J Compos Constr 2005;9(1):52–62.
Contents lists available at SciVerse ScienceDirect
Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
A probabilistic investigation into deterioration of CFRP–concrete interface in aggressive environments Yail J. Kim a,⇑, Mozahid Hossain b, Jun Zhang c a
Department of Civil Engineering, University of Colorado Denver, Denver, CO 80217, USA Department of Civil and Environmental Engineering, University of South Carolina, Columbus, SC, USA c Department of Industrial and Manufacturing Engineering, North Dakota State University, Fargo, ND, USA b
h i g h l i g h t s " Performance of CFRP–concrete interface is examined. " Probability-based models predict experimental findings. " Design recommendations are presented.
a r t i c l e
i n f o
Article history: Received 28 April 2012 Received in revised form 17 November 2012 Accepted 22 November 2012 Available online 3 January 2013 Keywords: Bond Durability Fiber reinforced polymer Interface Probability
a b s t r a c t This paper presents a probabilistic investigation into the deterioration of CFRP–concrete interface subjected to aggressive environments. A total of 53 single-lap shear specimens are exposed to freeze– wet–dry, wet–dry, and constant cold temperature conditions, 7 of which are unconditioned control specimens. Test parameters include the number of environmental cycles up to 150 and the degree of temperature as low as 30 °C for 2000 h. Upon completion of the planned environmental cycling, the residual capacity of the CFRP-interface (i.e., local interfacial fracture energy) is evaluated. The effect of freeze– wet–dry and constant cold temperature exposure is noticeable on the deterioration of the interface, whereas that of wet–dry is negligible. Probability distribution of the interfacial capacity is found to be normal and statistical uncertainty increases with the number of environmental cycles. Refined design factors are suggested using a Monte-Carlo simulation to ensure the sustainable performance of CFRP-retrofit systems for climatic regions with which freezing environment is associated. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction The performance of constructed reinforced concrete members may be improved by carbon fiber reinforced polymer (CFRP) composites. Structural retrofit is readily implemented on site by bonding CFRP sheets to the tensile soffit of a member, thereby enhancing load-carrying capacity or serviceability [1]. Epoxy adhesives are a commonly used bonding agent for such an application. Despite the promising track-record of CFRP-retrofit, deterioration of CFRP–concrete interface needs further examinations because premature debonding of the CFRP can significantly influence the efficacy of the retrofit. The research community has been struggling with a number of issues with regard to bond of CFRP, including the sources of deterioration and failure mechanisms [2]. Elastic solutions provided an understanding of stress-development and propagation [3], while fracture mechanics approaches were suc⇑ Corresponding author. Tel.: +1 303 352 3653. E-mail address: [email protected] (Y.J. Kim). 0950-0618/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.conbuildmat.2012.11.101
cessful in determining the capacity of CFRP–concrete interface [4]. One of the major challenges to be addressed is the long-term durability of externally-bonded CFRP [5,6]. A number of experimental programs have been conducted to examine the behavior of CFRP–concrete interface exposed to aggressive conditions such as freeze–thaw or moist environments [7–9]. Most design provisions currently available are based on deterministic investigations and do not explicitly take into account uncertainty that could be associated with long-term effects on site [10]. The emphasis of major design guidelines such as ACI440.2R [11] is primarily on precluding the failure of a CFRP-retrofit system, rather than on providing performance-based refined recommendations (e.g., progressive deterioration of a CFRP system under longterm loads and corresponding in situ performance depending upon the intensity of such loads). Some research has adopted probabilistic approaches to examine the failure of externally bonded CFRP [10,12], whereas limited effort is made on the probability of interface deterioration that requires more attention from a service perspective. This paper presents a probability-based investigation into
50
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
the performance of CFRP–concrete interface subjected to aggressive environments. A single-lap shear test was conducted and experimental results were probabilistically modeled to provide design recommendations, including refined resistance factors. 2. Research significance Recent research has reported the provisions of ACI440.2R [11] need to be refined [13,14]. The reason is that their applicable ranges are not object-specific when externally bonded CFRP materials are subjected to progressive deterioration, such as fatigue and environmental damage. For example, a single environmental reduction factor of 0.85 is given to CFRP systems exposed to aggressive environments, regardless of the period of exposure and the degree of aggressiveness. Such an approximation may be a convenient means for design and practice, whereas the actual behavior of CFRP systems with time is questionable and cannot be adequately projected. Of interest is the performance of CFRP– concrete interface in service, rather than debonding failure, because deterioration of the interface is dominantly observed on site. Most existing experimental research is concerned with qualitative examinations on the deterioration of CFRP–concrete interface when subjected to environmental load. The applicability of individual research results is, therefore, limited to actual design and practice. The challenge associated with prognosticating the long-term performance of CFRP bonded to a concrete substrate is that interface deterioration is stochastic in nature. Accordingly, refined design factors have not been readily available. To overcome such an impediment, a probabilistic approach was taken in this research program. A combined experimental and modeling study was conducted to generate refined design factors for CFRP-retrofit in aggressive environment (i.e., cold regions). The methodology proposed here has significant potential for developing refined design factors in various long-term loading conditions (e.g., fatigue and creep) that are vulnerable to the in situ performance of CFRP–concrete interface. 3. Experimental program 3.1. Details of materials and test specimens The unidirectional CFRP sheet used here had a tensile modulus of 227 GPa and corresponding strength of 3800 MPa with an equivalent thickness of 0.165 mm [15]. Tested CFRP coupons (15 mm wide 200 mm long) showed an average tensile modulus of 231 GPa with corresponding strength of 3590 MPa. Concrete was manually mixed in the laboratory, including a 5.5% air-entrainer. The water-to-cement ratio was 0.45. The use of air-entrainer is particularly important for concrete exposed to aggressive environment to preclude disintegration of the constituents [16]. The specified compressive strength was 20 MPa, while the average 28-day strength tested was 23 MPa. A two-part epoxy adhesive was used to bond the CFRP to concrete. The epoxy had a strength of 54 MPa and a tensile modulus of 3 GPa [17]. Concrete blocks (100 mm wide 50 mm deep 150 mm long) were cast and cured, and a single layer of precut CFRP sheet (75 mm wide 250 mm long) was bonded to the substrate of the concrete with the bonding agent, as shown in Fig. 1. It is important to note that the bond length of the CFRP (100 mm) exceeded the effective length ranging from 52 mm to 57 mm according to existing expressions [11,18] beyond which no further increase in strength of the CFRP–concrete interface would be achieved. Prior to bonding the sheet, the concrete surface was roughened using 80-grit sand paper and a water-jet. The prepared specimens were cured for a minimum of 1 week at room temperature. Seven specimens were tested to serve as control, whereas 46 specimens were conditioned as described below. 3.2. Test protocol To examine the effect of aggressive environments on the behavior of CFRP–concrete interface, a three-phase test protocol was designed (Fig. 1b). The first phase was freeze–wet–dry: one cycle of freeze–wet–dry included 16 h of freezing at 30 °C, 4 h of submerging in a water bath, and 4 h of drying at room temperature (25 °C). An environmental chamber equipped with a digital temperature adjustment function was used to simulate cold temperature. The fraction of such simulation hours was determined based on literature concerning the durability of CFRP in
cold region environment [7,16,19]. The second phase was wet–dry: one cycle of wet–dry was 16 h of submerging in a water bath and 8 h of drying at room temperature. These two phases were repeated up to 150 cycles, determined from previous research [7,20]. A comparison between the first and second phases would provide the effect of freezing on the behavior of the CFRP–concrete interface. The last phase was constant cold temperature: test specimens were subjected to four different temperatures at 0 °C, 10 °C, 20 °C, and 30 °C for 2000 h (3 months). The purpose of the third phase was to study the effect of a continued cold temperature condition that was frequently observed in cold climate regions. The simulated hours of the constant cold temperature exposure were determined based on the temperature of cold regions in the US typically showing about 3 months of sub-zero temperatures per winter [21]. It is worthwhile to note that refined durability investigations may improve the predictive response of CFRP-strengthened members even though accelerated durability tests are dominantly used to examine the long-term behavior of such members. Table 1 summarizes test specimens and environmental conditions. The identification code of each specimen indicates the type of exposure (R = control; FWD = freeze–wet–dry; WD = wet–dry; and CT = constant temperature), the number of environmental cycles and repetition (e.g., Specimen WD3100 means the specimen was the third repetition for 100 cycles of wet–dry), and temperature (e.g., Specimen CT-30-4 was subjected to 30 °C and was the fourth repetition). 3.3. Test set-up and instrumentation Upon completion of the planned environmental conditioning, all specimens were monotonically loaded until failure occurred at a rate of 2.5 mm/min using an MTS 810 hydraulic testing machine. A custom-made loading frame allowed a stable loading environment for the single-lap shear test (Fig. 1c). The clamping area of the CFRP was 38 mm 50 mm. The displacement and applied load were measured from the stroke of the loading-head and a built-in load cell, respectively. Strain gages were bonded along the CFRP at 20 mm on center to monitor the progression of CFRP-debonding when loaded. All test data were recorded by a data acquisition system.
4. Probability modeling for interface deterioration 4.1. Interfacial fracture energy Extensive effort has been made on examining the interfacial fracture energy of CFRP materials bonded to a concrete substrate (i.e., the energy required to fracture CFRP–concrete interface). Table 2 summarizes selected expressions to predict the fracture capacity of CFRP–concrete interface. Typical parameters considered include the properties of constituents (tensile or compressive strength, tensile modulus, and thickness) and geometric configurations (CFRP-bond width). Given all of these equations have been empirically developed, a comprehensive assessment may be necessary to identify their dissimilarity, if any. The tensile strength of concrete for the expressions shown pffiffiffiffi in Table 2 was consistently assumed here using fr ¼ 0:62 fc0 where fc0 is the compressive strength of concrete in MPa, which is equivalent to the modulus of rupture available in ACI-318 [22]. 4.2. Fundamental properties To predict the performance of CFRP–concrete interface subjected to aggressive environments, a probabilistic approach was employed. Of interest was the probability of interface deterioration. For modeling convenience, interfacial fracture energy was classified into two categories: Gfc and Gfn are the mean capacities of the conditioned and control specimens, respectively. The local interfacial fracture energy can be measured from the area of the shear stress versus CFRP–slip relationship of a single-lap test specimen (Fig. 1). The local shear stress and corresponding slip may be experimentally determined using Eqs. (1) and (2), respectively.
s ¼ Ef t f s¼
Z
x2 x1
e2 e1
x2 x1
eðxÞdx
ð1Þ
ð2Þ
51
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
(a)
(b)
(c)
(d)
(e)
(f)
Fig. 1. Specimen details and test set-up: (a) schematic of the test and instrumentation; (b) test protocols; (c) single-lap shear test; (d) freezing inside environmental chamber (30 °C); (e) wet; (f) drying at room temperature (25 °C).
Table 1 Test specimens. ID
R1 R2 R3 R4 R5 R6 R7 FWD1-25 FWD2-25 FWD3-25 FWD4-25 FWD1-50 FWD2-50 FWD3-50 FWD4-50 FWD1-100 FWD2-100 FWD3-100 FWD4-100 FWD1-150 FWD2-150 FWD3-150 FWD4-150 WD1-25 WD2-25 WD3-25 WD4-25
Env. effect
None None None None None None None 25 cycles 25 cycles 25 cycles 25 cycles 50 cycles 50 cycles 50 cycles 50 cycles 100 cycles 100 cycles 100 cycles 100 cycles 150 cycles 150 cycles 150 cycles 150 cycles 25 cycles 25 cycles 25 cycles 25 cycles
Pu (kN)
17.3 15.2 17.6 13.5 20.0 18.0 17.3 19.2 17.2 17.4 12.5 13.5 17.0 16.2 15.1 16.7 7.0 18.9 15.2 10.7 16.4 15.7 13.5 15.9 14.7 19.2 14.5
Local interfacial fracture energy (N/mm) Gfc
Ave
S
0.26 0.20 0.27 0.23 0.26 0.30 0.24 0.29 0.30 0.23 0.18 0.16 0.32 0.22 0.20 0.20 0.09 0.27 0.23 0.14 0.21 0.27 0.18 0.23 0.18 0.29 0.25
0.25
0.03
0.25
0.06
0.23
0.07
0.20
0.08
0.20
0.05
0.24
0.05
ID
Env. effect
WD1-50 WD2-50 WD3-50 WD4-50 WD1-100 WD2-100 WD3-100 WD1-150 WD2-150 WD3-150 CT0-1 CT0-2 CT0-3 CT0-4 CT-10-1 CT-10-2 CT-10-3 CT-10-4 CT-20-1 CT-20-2 CT-20-3 CT-20-4 CT-30-1 CT-30-2 CT-30-3 CT-30-4
50 cycles 50 cycles 50 cycles 50 cycles 100 cycles 100 cycles 100 cycles 150 cycles 150 cycles 150 cycles 0 °C 0 °C 0 °C 0 °C 10 °C 10 °C 10 °C 10 °C 20 °C 20 °C 20 °C 20 °C 30 °C 30 °C 30 °C 30 °C
Pu (kN)
6.3 13.9 14.1 16.1 13.0 17.3 20.0 17.2 15.6 17.6 16.2 17.1 18.1 10.5 14.1 15.5 13.0 16.4 18.0 19.1 18.2 17.0 13.6 12.3 15.0 15.8
Local interfacial fracture energy (N/mm) Gfc
Ave
S
0.09 0.20 0.16 0.23 0.13 0.34 0.29 0.20 0.19 0.27 0.34 0.25 0.29 0.20 0.21 0.32 0.23 0.31 0.22 0.25 0.27 0.21 0.14 0.18 0.21 0.23
0.17
0.06
0.25
0.11
0.22
0.04
0.27
0.06
0.27
0.06
0.24
0.03
0.19
0.04
Env. effect = environmental effect; Ave = average; S = standard deviation; Pu = ultimate load; su = maximum average shear stress; Gfc = interfacial fracture energy.
where s is the local shear stress; Ef and tf are the tensile modulus and thickness of the CFRP, respectively; s is the local slip of the CFRP; and e(x) is the strain increment at arbitrary locations based on e1 and e2 at the locations of x1 and x2. For this research, the post-peak energy of test specimens was ignored because interfacial
failure was brittle. The design margin index (g) is a convenient tool to assess the existing design expressions (Table 2):
g¼
ðGfci Gfd Þ Gfci
ð3Þ
52
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
be required to determine the cycle-dependent interfacial fracture energy, Gfc(N). For the convenience of probabilistic investigations, the probability distribution of Gfc(N) and Gfn(N) is transformed to standard normal so that g(Gfc, Gfn) becomes g(U, N) where U is the standard normal random variables, as shown in
Table 2 Existing interfacial fracture energy for design (Gfd in N/mm). Reference
Model
Neubauer and Rostasy [37] JSCE [38] Ueda et al. [39]
Gfd ¼ 0:204f r Gfd ¼ 0:5 N=mm 0:352 fc0:236 ðEp tp Þ0:023 Gfd ¼ 0:446 Gtaa
Ulaga et al. [40]
Gfd ¼ 0:045fc rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2b =bc pffiffiffiffiffiffiffi Gfd ¼ 0:03 1þb f=400 fc fr
CNR [41]
gðU; NÞ ¼ ½Gfc ðNÞ þ rfc ðNÞU fc ðNÞ ½Gfn ðNÞ þ rfn ðNÞU fn ðNÞ
2=3
The gradient of the initial random variable U0 is defined as
f
Dai et al. [42] Lu et al. [27]
ð10Þ
Gfd ¼ 0:514fc0:236 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffi 2:25b =b Gfd ¼ 0:308b2w fr in which bw ¼ 1:25þbf =bcc f
fr = Compressive strength of concrete; fr = tensile strength of concrete; bf = width of bonded FRP; fc = width of concrete substrate.
rgðU 0 ðNÞÞ ¼
@gðU; NÞ @gðU; NÞ ¼ ðrfc ðNÞ; rfn ðNÞÞ ; @U fc @U fn
ð11Þ
Assuming the initial random variable U0(N) = (0, 0) for Ufc(N) and Ufn(N)
gðU 0 ðNÞÞ ¼ Gfc ðNÞ Gfn ðNÞ
ð12Þ
The norm of vector rg(U0(N)) is calculated by where Gfci is the interfacial fracture energy of the ith test specimen and Gfd is the design fracture energy. The bias factor (k) can provide the degree of conservatism of the design interfacial fracture energy:
Gfci k¼ Gfd
ð4Þ
The probability distribution of test specimens may be assumed to be normal if the median positioning associated with a leastsquare fit (Eq. (5)) tends to be linear with respect to corresponding z scores (Eq. (6)) [23].
FðGfc Þ ¼
i 0:3 n þ 0:4
ð5Þ
krgðU 0 ðNÞÞk ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi r2fc ðNÞ þ r2fn ðNÞ
ð13Þ
The ratio of the gradient of the performance function to corresponding norm, a0, is shown in
a0 ¼
rgðU 0 ðNÞÞ krgðU 0 ðNÞÞk 0
1
rfc ðNÞ rfn ðNÞ B C ¼ @qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ; qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA 2 2 2 2 rfc ðNÞ þ rfn ðNÞ rfc ðNÞ þ rfn ðNÞ
ð14Þ
The norm of the initial random variable, b0, is then:
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi U 2fc0 þ U 2fn0
where i is the ith test specimen of n ordered residual interfacial fracture energy (Gfc).
b0 ¼ kU 0 ðNÞk ¼
zi ¼ U1 ½FðGfc Þ
The most probable point within the probabilistic domain, U, may be found using
ð6Þ
where U is the standard normal distribution. Once the distribution of the test specimens is found to be normal, the probability distribution of the interfacial fracture energy can be expressed as
1 1 Gfc Gfci f ðGfc Þ ¼ pffiffiffiffiffiffiffi exp 2 rfc r 2p
b ¼ kU k
ð17Þ
The probability of interface deterioration is calculated using
Pr ¼ UðbÞ or UðbÞ
4.3. Formulation of first-order reliability method The first-order reliability method (FORM) may be used to prognosticate the progressive deterioration of CFRP–concrete interface with environmental cycles, given that interface deterioration is fundamentally stochastic. The benefit of using such a method includes that a probability formulation can be done with only the mean and corresponding standard deviation of a random variable [24]. The following briefly describes the FORM method, while further details and theoretical background may be available in any reliability textbook or papers [25,26]. A linear performance function of CFRP–concrete interface is expressed as
ð8Þ
where Gfc(N) and Gfn(N) are the interfacial fracture energy and corresponding control capacity at an environmental cycle N, respectively. Taking into account practical significance in design, Gfn(N) may be assumed to be constant irrespective of the number of environmental cycles. Based on Eq. (8), the probability of interface deterioration is defined as
PrðNÞ ¼ PrðgðGfc ; Gfn Þ 6 0Þ ¼ PrðGfc ðNÞ 6 Gfn ðNÞÞ
ð16Þ
The norm of the U will be the reliability index, b, as shown in
ð7Þ
where rfc is the standard deviation of the Gfc.
gðGfc ; Gfn Þ ¼ Gfc ðNÞ Gfn ðNÞ
rgðU 0 Þ U ¼ a0 b0 þ krgðU 0 Þk
ð15Þ
ð9Þ
where Pr(N) is the probability of interface deterioration at an arbitrary environmental cycle N. A regression analysis of test data may
ð18Þ
where U(b or b) is the cumulative density function of the standard normal distribution. It is worthwhile to note that U(b) is used when Gfc(N) is greater than Gfn(N), which could happen in experimental investigations, and U(b) is used for an opposite case. 5. Test results 5.1. Residual capacity of CFRP–concrete interface Table 1 provides the single-lap shear test results with and without environmental conditioning. The average shear stress versus displacement behavior of selected specimens is given in Fig. 2. The mean failure load of the control specimens was 17.0 kN with a standard deviation of 2.1 kN. The measured interfacial fracture energy (i.e., area under average shear stress versus CFRP–slip curve) was 0.25 N/mm, on average, and corresponding coefficient of variation was 0.12. It should be noted that the experimental local shear stress versus slip (Fig. 3) was typically bilinear as is for the case of other test programs [27]. The failure load and interfacial fracture energy of the specimens subjected to freeze–wet–dry decreased with cycles, as shown in Table 1; for example, an average decrease of 20.0% in the facture energy was measured for the specimens exposed to 150 cycles of freeze–wet–dry when compared
53
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
others because of an outlier specimen (the CFRP was wet-lay-up and thus bond between the CFRP and concrete substrate was not ideal). The degree of constant cold temperature affected interfacial strength. The specimens exposed to 30 °C for 2000 h exhibited a decrease of 29.6% in the average interfacial fracture energy when compared with those subjected to 0 °C. The increased brittleness of the interface with lowering temperature is believed to accelerate the dislocation of the interface constituents. All test specimens showed typical interfacial shear failure, as shown in Fig. 1c. 5.2. Variation of interfacial fracture energy
Fig. 2. Average shear stress versus displacement response.
A regression analysis was conducted to provide empirical equations forming the base of the probabilistic investigation. All measured interfacial fracture energies with environmental effects shown in Table 1 were fitted using a logarithmic term (i.e., the average coefficient of determination of the interfacial fracture energy was 0.48). The predictive equations for the interfacial capacity of the specimens subjected to freeze–wet–dry and wet–dry cycles (Gfc(N)) are shown in Eqs. (19) and (20), respectively.
Gfc ðNÞ ¼ 0:0302 ln ðNÞ þ 0:3444 6 Gfn
for FWD
ð19Þ
Gfc ðNÞ ¼ 0:0058 ln ðNÞ þ 0:1961 6 Gfn
for WD
ð20Þ
where N is the number of environmental cycle (N > 0). Average differences between the tested interfacial capacities and the predicted values using Eqs. (19) and (20) were 2.3% and 13.2%, respectively. The coefficient of variation of these two test categories was fitted as well:
GfcCOV ðNÞ ¼ 0:0479 ln ðNÞ þ 0:0971 for FWD
ð21Þ
GfcCOV ðNÞ ¼ 0:0323 ln ðNÞ þ 0:1598 for WD
ð22Þ
Fig. 3. Local shear stress versus slip of control (Specimen R4).
with that of the control. The average coefficient of variation in the interfacial fracture energy of the freeze–wet–dry specimens was 248.8% greater than that of the control specimen. This increase illustrates that experimental uncertainty (i.e., dispersion of test data) has increased due to the environmental conditioning: bond between the CFRP and concrete deteriorated in a non-uniform manner. Contrary to the freeze–wet–dry test, there was no obvious trend in decreasing the interfacial capacity of the wet–dry test specimens. The coefficient of variation was, however, influenced by the wet–dry environment: an average increase of 246.5% was noticed when compared to the coefficient of variation of the control specimens. This observation implies that the wet–dry effect might not be sufficient to influence the capacity of the CFRP–concrete interface; however, such an effect can increase experimental uncertainty from a statistical point of view. It should be noted that the average capacity of the WD-50 category was lower than that of
The margin of error in the predicted coefficient of variation was 15.0% and 36.9% for Eqs. (21) and (22), respectively, on average. Such relatively large differences in comparison to the case of the interfacial fracture energy (Eqs. (19) and (20)) are attributed to the limited number of the test specimens; however, these fitted coefficients of variation were acceptable (to be discussed in Section 6.1). 5.3. Strain development Fig. 4 shows the development of strains along the bonded CFRP sheet (only selected specimens are given here since other specimens demonstrated similar behavior). As checked in Section 3, the bonded length was sufficient to transfer the applied load from the CFRP to concrete substrate without premature peeling failure. Due to stress concentrations, higher strains near the loaded-end
Fig. 4. Strain development: (a) control (Specimen R4); (b) freeze–wet–dry at 150 cycles (Specimen FWD4-150).
54
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
were recorded prior to the initiation of CFRP-debonding (i.e., a sudden increase in strain reading). When the applied load increased, the debonded region shifted towards the free-end of the specimens and the CFRP–concrete interface eventually failed. Conspicuous debonding of the CFRP was not observed within service load levels irrespective of the environmental effects (up to 150 cycles of freeze–wet–dry and wet–dry, and 2000 h of continued cold temperature exposure). Once CFRP-debonding was noticed, its development was rapid. The measured strains at the tip of the CFRP were slightly lower than those of other locations because of stress re-distribution associated with experimental uncertainty such as non-uniform debonding of the CFRP and the presence of aggregates on the concrete surface. Other experimental programs reported a similar trend [28,29]. Although the environmental conditioning did not significantly influence the debonding strain of CFRP (all test data are not shown here for brevity), it was obvious that such conditioning altered debonding characteristics of the CFRP (Fig. 4). The empirical predictors shown in Eqs. (19) and (20) confirm these qualitative observations. 6. Predicted probability 6.1. Probabilistic response To implement the probability modeling described previously, the control interfacial fracture energy (Gfn) serving as a limit for interface deterioration was first evaluated. Fig. 5a compares the existing design models (Table 2) with the control specimens tested in this research program. The design margin index (Eq. (3)) is presented in Fig. 5b, based on the average Gfn value of 0.25 N/mm.
Most of the models were conservative, while the degree of conservatism varied from 0.28 to 4.38 as per the design margin index. Fig. 6 shows the effect of the environmental exposure on the bias factors of the test specimens (Eq. (4)). The bias factors were positioned between 0.28 and 0.44. This observation indicates that the experimental capacity of the CFRP–concrete interface exceeded the design capacity even though a trend of deterioration was noticed, in particular when associated with cold temperature exposure. The design interfacial capacity was estimated using the average Gfd value of the design equations available in Table 2 (Gfd = 0.61 N/mm). The probability distribution of the test specimens was determined based on the normality test (Fig. 7a). Significant linearity was observed in all cases with an average coefficient of determination (R2) of 0.976. It was, therefore, reasonable to conclude that the test data were normally distributed from a probability perspective. Such an observation supports the adequacy of the probability study presented here even though the number of the test specimens was limited; in other words, the normal probability distribution function will virtually cover all possible test results within the investigation range given in this research program (regardless of the number of test specimens). After generating probability distribution functions using Eq. (7), corresponding cumulative distributions were obtained (Fig. 7b). Fig. 8 compares the fitted coefficient of variation (Eqs. (21) and (22)). This comparison confirms the adequacy of the current probabilistic study. Although the present research accepted a variable coefficient of variation with environmental cycles (Eqs. (21) and (22)), such a statistical parameter is frequently assumed to be constant for simplicity [30].
Fig. 5. Evaluation of proposed design equations for local interfacial fracture energy, Gfd (Dai = Dai et al. [42]; Ueda = Ueda et al. [39]; JSCE = JSCE [38]; CNR = CNR [41]; Exp = present experimental data of control specimens): (a) parametric comparison between experiment and models; (b) design margin index with averaged experimental capacity.
Fig. 6. Bias factor for interfacial fracture energy with averaged experimental capacity per test category: (a) freeze–wet–dry and wet–dry; (b) constant temperature for 2000 h.
55
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
(a)
(b)
Fig. 7. Validation of probability distribution: (a) normality test; (b) cumulative distribution of selected cycles in freeze–wet–dry.
Fig. 8. Evaluation of coefficient of variation for probability modeling.
Prior to conducting an extensive probability simulation, a sensitivity analysis was carried out to examine how sensitive the
(a)
(c)
fracture energy and the coefficient of variation would be when the number of environmental cycles increased. Fig. 9a and b shows the experimental variation of the averaged interfacial fracture energy and coefficient of variation, respectively, for each environmental condition. The interfacial fracture energy and the coefficient of variation varied within a range of less than 0.3 N/mm (Fig. 9a) and 0.3 (Fig. 9b), respectively. The probability of deterioration of the CFRP–concrete interface subjected to freeze– wet–dry (more critical than wet–dry) was prognosticated (Eq. (18)) with possible variation ranges of the control fracture energy (Fig. 9c) and the coefficient of variation (Fig. 9d). The Gfn value was a significant factor influencing the probability of interface deterioration within the investigation range studied here, as shown in Fig. 9c. Such an observation, however, was not a critical concern because the variation of Gfn might not be significant in practice. Table 1 supports the consistency of the measured control fracture energy (Gfn). An increase in the coefficient of variation increased the uncertainty of interface deterioration, including the change of the predicted probability curve (Fig. 9d). This observation indicates
(b)
(d)
Fig. 9. Sensitivity analysis of interfacial fracture energy: (a) averaged experimental interfacial fracture energy (Gfc); (b) averaged experimental coefficient of variation (COV); (c) effect of control fracture energy (Gfn) based on freeze–wet–dry with standard deviation of 0.03 N/mm; (d) effect of COV with Gfn = 0.25 N/mm based on freeze–wet–dry.
56
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
(a)
(b)
(c)
(d)
Fig. 10. Probable frequency of occurrence: (a) freeze–wet–dry; (b) wet–dry; (c) cumulative distribution of freeze–wet–dry; (d) cumulative distribution of wet–dry.
that the coefficient of variation is related to the uncertainty of interface deterioration; however, existing approaches usually assumes a constant coefficient of variation for simplicity [30]. 6.2. Effect of environments Fig. 10 exhibits the effect of environmental cycles on the probability distribution of the interfacial capacity (Gfc). The predicted probability distribution of the freeze–wet–dry shifted to the left with an increasing cycle, indicating that the interfacial fracture energy decreased due to the deterioration of the CFRP–concrete interface (Fig. 10a). The contribution of freeze–wet–dry was significantly greater than that of wet–dry, as shown in Fig. 9a and b. The capacity in wet–dry, however, did not show such a trend until 150 cycles were reached (Fig. 10b). The variation range in the cumulative distribution of freeze–wet–dry was also noticeable in comparison to that of wet–dry, as shown in Fig. 10c and d, respectively.
Fig. 11. Comparison between freeze–wet–dry and wet–dry effects for probability of interface deterioration.
The probability of deterioration of the CFRP–concrete interface subjected to these two environmental conditions is shown in Fig. 11. For the interface exposed to freeze–wet–dry, a gradual increase in the probability of deterioration was noticed after 15 cycles and approached unity when 60 cycles were exceeded. It should be noted that the horizontal line in the freeze–wet–dry at a probability of deterioration of 0.5 was generated due to the boundary condition shown in Eq. (19). This observation implies that CFRP–concrete interface will surely deteriorate in a freeze– wet–dry environment. Noticeable evidence of interface deterioration, however, was not observed up to 150 cycles in the case of wet–dry (Fig. 10).
7. Design recommendation 7.1. Monte Carlo simulation A Monte Carlo simulation was conducted to help develop design recommendations for the deterioration of CFRP–concrete interface subjected to freezing weather. The simulation complemented the limited experimental data through usage of a prescribed set of interfacial fracture energy within a possible probability domain. Random values were generated for the conditioned (Gfc) and control (Gfn) capacities, based on the inverse transformation method [31]. It is worthwhile to note that the random sampling with variable Gfn can broaden the applicable range of the design factors even though Gfn may not significantly vary in practice. The ranges of data sampling for trial-simulations were l ± 3r for Gfc and Gfn, where l and r are the mean and standard deviation, respectively. The sampling range of l ± 3r can cover 99.73% of all possible values in a normally distributed parameter [32]. A typical sampling region is shown in Fig. 12a, including the experimentally obtained Gfc and Gfn data. To generate design factors, an established
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
57
Fig. 12. Evaluation of Monte-Carlo sampling at 150 freeze–wet–dry cycles: (a) comparison to experimental data; (b) assessment of safety factor.
approach (i.e., second-moment criteria) was employed. Direction cosines and associated design parameters may be defined in [33].
COV
G
Gfn fn ffi aGfn ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2
ðCOVGfn Gfn Þ þ ðCOVGfc Gfc Þ2
aGfc
COVGfc Gfc ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðCOVGfn Gfn Þ2 þ ðCOVGfc Gfc Þ2
ð23Þ
ð24Þ
U ¼ 1 aGfn bCOVGfn
ð25Þ
c ¼ 1 aGfc bCOVGfc
ð26Þ
where aGfn and aGfc are the direction cosines of the control fracture energy (Gfn) and the interfacial capacity (Gfc), respectively; U is the strength reduction factor; and c is the live load factor; and b is the safety index. Fig. 12b compares the variation of the safety factors with the magnitude of the standard deviation, including the safety factor obtained using the provision of ACI440.2R-08 [11]. This
observation implies that the present approach is reasonably safe for design and practice. 7.2. Reduction factor for interface deterioration To generate strength reduction factors (u) for the design of CFRP–concrete interface subjected to freezing environment, three categories were specified as per the mean annual freeze–thaw (FT) days: Severe (150 < FT 6 250), Moderate (75 < FT 6 150), and Mild (0 < FT 6 75). The map shown in Fig. 13 was created using a climate database of almost 30 years in the US [34]. The concept of safety index (b) is widely used to adjust the level of safe performance of structural members. The acceptable safety indices for new and existing structures are 3.5 and 2.5, respectively [35,36]; therefore, the upper limit of b was set to 2.5 for this research. The lower bound of b may be typically assumed to be 1.5 [30]. The following condition was accordingly specified in this research program for the convenience of developing design factors: Mild (b = 1.5), Moderate (b = 2.0), and Severe (b = 2.5). These configurations were linked with actual freezing environment as per the
Fig. 13. Mapping of average freeze–thaw cycles per year ([34]: used with permission).
58
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59
(a)
(b)
Fig. 14. Results of Monte Carlo simulation for freeze–wet–dry cycles: (a) reduction factor (u) with a safety index of 2.5; (b) safety factor (c/u) with a safety index of 2.5.
Table 3 Proposed environmental factors for cold climate regions.
Factor
Severe (b = 2.5)
Moderate (b = 2.0)
Mild (b = 1.5)
0.75
0.80
0.85
mean annual freeze–thaw (FT) days (Fig. 13). In so doing, strength reduction factors (u) for the design of the CFRP–concrete interface subjected to such aggressive environmental conditions can be estimated. Fig. 14a shows the variation of the reduction factor (u) in the Monte-Carlo simulation with b = 2.5. A trend of convergence was achieved in all categories with the increased number of random samples. The safety factors (c/u) of each category exceeded the ACI440.2R-08 limit, as shown in Fig. 14b, confirming that the computed u factors could be safely used for design and practice. Table 3 summarizes the proposed reduction factors for the design of CFRP–concrete interface in a freezing service environment. It is worthwhile to note that the u factors are independent of the strength of FRP materials because the contribution of the coefficient of variation in FRP-strength is not significant on the variation of design parameters [10].
influenced the probability of deterioration; however, such an effect might not be critical in practice as per the assessment of the existing design proposals. Refined environmental reduction factors were proposed for climatic regions where freezing environment existed in order to address the risk of interface deterioration in service, ranging from 0.75 to 0.85 depending upon the severity of a freeze–thaw condition. No reduction factors would be necessary for the interface deterioration induced by wet–dry.
Acknowledgments The writers gratefully acknowledge the support of North Dakota State University and the National Science Foundation through North Dakota Experimental Program to Simulate Competitive Research with a Grant Number of EPS-0814442. Mr. Jason Haley and Dr. Scott Sheridan at Kent State University have generously provided a GIS map used for this study. All findings described here are those of the writers and do not necessarily represent the opinion of the funding agencies. References
8. Summary and conclusions This paper has addressed the effect of aggressive environments on the performance of CFRP–concrete interface. An experimental program was conducted with 53 specimens, followed by probabilistic investigations to generate design parameters for practice. The following is concluded. The effect of freeze–wet–dry was noticeable on the deterioration of CFRP–concrete interface, while that of wet–dry was not significant. Both of these environments increased the statistical uncertainty of the interface, represented by the increased coefficient of variation in the interfacial fracture energy. Constant cold temperature exposure at 30 °C for 2000 h also decreased the interfacial capacity. Empirical deterioration models were proposed. The characteristics of the CFRP–concrete interface changed when associated with environmental cycling, including stress redistribution along the interface. Further research was recommended to quantify the spatial properties of failure surface, sliding friction, and damage mapping depending upon the level of interface deterioration. The probability distribution of the interfacial capacity was found to be normal. A variable coefficient of variation was recommended for durability investigations rather than a constant value. The control interfacial fracture energy (Gfn) significantly
[1] Bakis CE, Bank LC, Brown VL, Cosenza E, Davalos JF, Lesko JJ, et al. Fiberreinforced polymer composites for construction-state-of-the-art review. J Compos Constr 2002;6(2):73–87. [2] Teng JG, Lu XZ, Ye LP, Jiang JJ. Recent research on intermediate crack-induced debonding in FRP-strengthened RC beams. In: 4th international conference on advanced composite materials in bridges and structures, Calgary, AB, Canada; 2005 [CD-ROM]. [3] Smith ST, Teng JG. Interfacial stresses in plate beams. Eng Struct 2001;23(7):571–857. [4] Wan B, Sutton MA, Petrou MF, Harries KA, Li N. Investigation of bond between fiber reinforced polymer and concrete undergoing global mixed mode I/II loading. J Eng Mech 2004;130(12):1467–75. [5] Karbhari VM, Abanilla MA. Design factors, reliability, and durability prediction of wet layup carbon/epoxy used in external strengthening. Composites Part B 2007;38:10–23. [6] Wu Z, Kim YJ, Diab H, Wang X. Recent development in long-term performance of FRP composites and FRP–concrete interface. Adv Struct Eng 2010;13(5):891–903. [7] Green MF, Bisby LA, Beaudoin Y, Labossiere P. Effect of freeze–thaw cycles on the bond durability between fibre reinforced polymer plate reinforcement and concrete. Can J Civ Eng 2000;27:949–59. [8] Boyajian DM, Ray I, Davalos JF. Freeze–thaw cycling under a calcium chloride environment: effects on CFRP strengthened concrete structures. Int J Mater Prod Technol 2007;28(1/2):89–102. [9] Ouyang Z, Wan B. Nonlinear deterioration model for bond interfacial fracture energy of FRP–concrete joints in moist environments. J Compos Constr 2009;13(1):53–63. [10] Atadero RA, Karbhari VM. Calibration of resistance factors for reliability based design of externally-bonded FRP composites. Composites Part B 2008;39:665–79. [11] ACI. Guide for the design and construction of externally bonded FRP systems for strengthening concrete structures (ACI-440.2R-08). American Concrete Institute, Farmington Hills, MI; 2008.
Y.J. Kim et al. / Construction and Building Materials 41 (2013) 49–59 [12] Wieghaus KT, Atadero RA. Effect of existing structure and FRP uncertainties on the reliability of FRP-based repair. J Compos Constr 2011;15(4):635–43. [13] Harries KA, Aidoo J. Debonding and fatigue-related strain limits for externally bonded FRP. J Compos Constr 2006;10(1):87–90. [14] Kim YJ, Heffernan PJ. Fatigue behavior of structures strengthened with fiber reinforced polymers: state-of-the-art. J Compos Constr 2008;12(3):246–56. [15] MBrace. MBrace saturant: epoxy encapsulation resin. Amherst, NY: Watson Bowman Acme Corp; 2003. [16] Kong A, Fam A, Green MF. Freeze–thaw behavior of FRP-confined concrete under sustained load, Fiber-reinforced Polymer Reinforcement for Concrete Structures (FRPRCS-7). ACI-SP 2005;230:705–22. [17] Degussa. MBrace™ saturant composite strengthening system resin. Shanghai Master Builder Co. Ltd.; 2006. [18] Chen JF, Teng JG. Anchorage strength models for FRP and steel plates bonded to concrete. J Struct Eng 2001;127(7):784–91. [19] Karbhari VM, Rivera J, Dutta PK. Effect of short-term freeze–thaw cycling of composite confined concrete. J Compos Constr 2000;4(4):191–7. [20] Saenz N, Pantelides CP. Short and medium term durability evaluation of FRPconfined circular concrete. J Compos Constr 2006;10(3):244–53. [21] USGS. Northern prairie wildlife research center. United States Geological Survey, Jamestown, ND; 2010.
59
[29] Yao J, Teng JG, Chen JF. Experimental study on FRP-to-concrete bonded joints. Composites Part B 2005;36:99–113. [30] Nowak AS. Calibration of LRFD bridge code. J Struct Eng 1995;121(8):1245–51. [31] Devroye L. Non-uniform random variate generation. New York, NY: SpringerVerlag; 1986. [32] Dai S-H, Wang M-O. Reliability analysis in engineering applications. New York, NY: Van Nostrand Reinhold; 1992. [33] Ang AH-S, Tang WH. Probability concepts in engineering planning and design. New York, NY: John Wiley and Sons; 1984. [34] Haley JS. Climatology of freeze–thaw days in the conterminous United States: 1982–2009. MS thesis. Kent, OH: Kent State University; 2011. [35] AASHTO. Manual for condition evaluation of bridges (2003 interim revisions). 2nd ed. Washington, DC: American Association of State Highway and Transportation Officials; 2003. [36] AASHTO. LRFD bridge design specifications. 5th ed. Washington, DC: American Association of State Highway and Transportation Officials; 2010. [37] Neubauer U, Rostasy FS. Design aspects of concrete structures strengthened with externally bonded CFRP plates. In: Proceedings of 7th international conference on structural faults and repairs, vol. 2, Edinburgh, Scotland; 1997. p. 109–18. [38] JSCE. Recommendations for upgrading of concrete structures with use of continuous fiber sheets. Tokyo, Japan: Japan Society of Civil Engineers Concrete Engineering Series, 41; 2001. [39] Ueda T, Dai J, Sato Y. A nonlinear bond stress–slip relationship for FRP sheet– concrete interface. In: Proceedings of 6th international symposium on latest achievement of technology and research on retrofitting concrete structures; 2003. p. 113–20. [40] Ulaga T, Vogel T, Meier U. Bilinear stress–slip bond model: theoretical background and significance. In: Proceedings of 6th international symposium on FRP reinforcement for concrete structures (FRPRCS-6), vol. 1; 2003. p. 153–62. [41] CNR. Guide for the design and construction of externally bonded FRP systems (CNR-DT 200/2004). Rome, Italy: National Research Council; 2004. [42] Dai J-G, Ueda T, Sato Y. Development of the nonlinear bond stress–slip model of fiber reinforced plastics sheet–concrete interfaces with a simple method. J Compos Constr 2005;9(1):52–62.