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Structural behavior of strengthened bridge deck specimens under fatigue loading
Engineering Structures 26 (2004) 2219–2230 www.elsevier.com/locate/engstruct
Structural behavior of strengthened bridge deck specimens under fatigue loading Jongsung Sim, Hongseob Oh Department of Civil and Environmental Engineering, Hanyang University, 1271, Sa1-dong, Ansan 425-791, South Korea Received 7 March 2004; received in revised form 4 August 2004; accepted 11 August 2004
Abstract The deterioration of concrete bridge decks that have been directly damaged by traffic loads affects their durability, safety, and function. It is therefore necessary to strengthen the damaged concrete structures. Even though there have been many experiments performed to investigate the static behavior of strengthened structures, few experiments or analyses have considered their fatigue behavior. In this study, fatigue tests were conducted on bridge decks strengthened using various fiber-reinforced polymer plastics, such as carbon fiber sheet, glass fiber sheet, and grid-type carbon fiber reinforced plastic. All of the strengthened specimens were shown to have an improved resistance to crack propagation and better stress distributions. The Weibull distribution was adopted to analyze the fatigue life of the decks. The fatigue life limits of the strengthened bridge decks were determined at higher stress levels, and the grid-type carbon reinforced plastic specimens proved to be the most effective. # 2004 Elsevier Ltd. All rights reserved. Keywords: Bridge deck; Fatigue life; Fiber reinforced polymer plastic; Structural strengthening; Weibull distribution
1. Introduction Reinforced concrete bridge decks receive traffic loads directly. Structural damage can increase, such as residual deformation and numerous cracks, which eventually decreases the life of the deck as well as its load carrying capacity [1–5]. In South Korea, there are many deck panels that have deteriorated after almost 20 years of service and which must now be rehabilitated. Many of these were designed for relatively low traffic loads rather than the heavy traffic (over HS25) found nowadays, and are only 18 cm thick. When such decks are strengthened, the overall structural performance must be improved, including their serviceability and fatigue resistance as well as the load carrying capacity. The flexural strength of a deck can be improved easily by applying external bonding techniques, using materials such as carbon fiber sheet (CFS) Corresponding author. Tel.: +82-31-400-5208; fax: +82-31-4187430. E-mail address: [email protected] (H. Oh).
0141-0296/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2004.08.006
and carbon fiber reinforced plastic (CFRP) attached to the tension side of the concrete. However, it is fairly difficult to rehabilitate the fatigue resistance of a deck because the shear strength that has been decreased by repeated loads must be improved with the flexural strength. Previous research by the authors experimentally verified that the fatigue resistance of a deck that was externally strengthened with CFSs was improved even if no additional sectional enlargements of the deck were made [6]. This result presented the possibility of extending the life cycle of a deck panel without adding deadloads by using either mortar overlay or an additional internal stiffener. Although numerous research programs over the past decade have attempted to understand fatigue response and to establish a fatigue model for concrete subjected to repeated loads, the fatigue failure characteristics of strengthened concrete structures are not yet systematically established on a scientific foundation [7–12]. Much of the research for concrete structures has been limited to either a simple S–N relationship or a mechanical approach, because the analysis is too
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complicated to extend to an entire structural system from either the microscopic element or material points of view. The experimental and theoretical work presented in this paper is the result of successive research programs conducted at the Hanyang University in Korea to verify the structural efficiency of various fiber reinforced polymer (FRP) composites for strengthening concrete structures [6,12,13]. The authors have persisted in developing rehabilitation techniques for deteriorated concrete structures for the past decade [6,12,14]. A recent focus has been how to achieve additional benefits by applying FRPs to a deteriorated concrete member, either by extending its fatigue life or enhancing its serviceability. Improvements to both the fatigue and flexural resistance must be considered when rehabilitating a deteriorated concrete bridge deck. The experiments reported in this paper were conducted to find structural differences and efficiencies between slabs strengthened with various FRPs and subjected to cyclic loading [13]. We also attempted to verify the theoretical S–N relationship of strengthened deck panels through a probabilistic approach based on the test results. In this paper, CFS, glass fiber sheet (GFS) and gridtype carbon fiber reinforced plastic (GCFRP) were used as the strengthening materials.
2. Experimental program 2.1. Materials The concrete used in the specimens consisted of ordinary Portland cement, natural sand, and crushed coarse aggregate with a maximum size of 25 mm. The mixture had a 28-day cylinder strength of about 22.5 MPa. Deformed bars, 15.9 mm in diameter with an average yield strength of 300 MPa, were used in the slab panels and beams. The shear reinforcement of the girders consisted of 9.35-mm diameter closed stirrups. The material properties are listed in Table 1.
2.2. Test program For the experimental test program, a prototype deck panel with dimensions of 160 240 cm was selected to simulate a real bridge deck supported by two girders, as referenced in [13]. In order to determine the dimension of deck specimen, 3-dimensional non-linear finite element analyses in which various dimensions of deck considered to simulate either the deformation or deterioration of real bridge deck were carried out before the physical experiments. As a result, the selected dimension of deck from the FE analysis was similar to the real deck size used in Korea. The concrete slab was modeled with eight-node solid elements, reinforcing bars with beam elements, and the CFS was represented by membrane elements with stiffness properties only in the appropriate directions [15–19]. Both beam and membrane elements were assumed to be perfectly bonded to the concrete. The material properties were obtained experimentally. The rubber supports were simulated by spring elements with a hyperelastic material law. The slab thickness was 18 cm, which is the same as that of secondary bridge decks in Korea. The tensile rebar spacing in the transverse direction was 10 cm and the reinforcement spacing in the longitudinal direction was 15 cm. The specimen details and strengthening methods are depicted in Figs. 1 and 2. The CFS and GFS materials were bonded to the prototype deck panel in an upside-down position. Each fiber sheet was attached to the epoxy-coated surface by pressing it into the epoxy. The GCFRP material was first fixed to the concrete surface in an upside-down position using 2.5-cm length anchor bolts spaced every 50 cm. Then, the repair mortar suggested by the manufacturer was overlayed on the concrete surface. The 12 specimens listed in Table 2 were subjected to cyclic loads to investigate their fatigue failure characteristics. CON means the unstrengthened reference panel. The stress level of each specimen, except CON40 and GFS-40 designed to verify the structural response in service state, was designed to assess the endurance limit of deck specimens and compare the
Table 1 Physical properties of materials Thickness or diameter Concrete Rebar Epoxy Carbon fiber sheet Glass fiber sheet GCFRP Mortar for GCFRP
13 mm 0.11 mm 1.3 mm 4.0 mm
Yield strength (MPa)
Ultimate strength (MPa)
– 300 – – – –
22.5 400 88.3 3500 450 1170 27.0
Elastic modulus (MPa) 0:232 105 1:96 105 0:07 105 2:31 105 0:227 105 1:00 105 0:14 105
Ultimate strain
– – – 0.015 0.02 0.0117 –
J. Sim, H. Oh / Engineering Structures 26 (2004) 2219–2230
Fig. 1.
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Details of specimen (unit: cm).
structural response with deck specimens strengthened with other materials and receiving similar loads. The stress level means the ratio of applied load in fatigue test to ultimate strength of each specimen. Loading at a rate of 2 Hz was repeatedly applied to the slab center. LVDTs were used to record the slab deflections. Concrete strain gauges were attached to the compressive deck surface of the slabs and steel strain gauges were bonded to the main reinforcement to measure the strain variation of the deck.
3. Test results and discussion 3.1. Failure patterns Typical failure patterns of the deck panel are depicted in Fig. 3, and the number of loading cycles and the failure phenomena of the specimens according to their damage state are summarized in Table 3. From the static test results, initial one-way cracks in the deck panel developed parallel to the girder, and then propagated into two-directional cracks due to the stress redistribution as the loads increased [13]. Crack propagation in the deck panels subjected to repeated loading appeared in different patterns according to the stress levels. The failure patterns of deck panels that received
Fig. 2.
Strengthening details. (a) CFS and GFS; (b) GCFRP.
relatively lower stresses were dominated by the effect of initial macro cracks at their midpoints. The failure patterns of deck panels that received higher stresses were similar to those of the decks that received monotonic loads. The angle of the failure surface of the higher stressed panels was greater than that of the lower stressed panels.
Table 2 Stress level CON Stress level (%) Loads (kN)
40 260
CFS 70 450
90 580
60 440
GFS 70 510
80 590
40 280
GCFRP 60 420
80 560
60 430
70 500
80 570
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Fig. 3.
Typical fatigue failure pattern.
Complete debonding failures of the decks two-directionally strengthened with FRP sheets did not occur because the sheets distributed the principle tensile stresses well and kept the flexural cracks relatively small. The propagated flexural cracks branched out into numerous hairline cracks because of the distributed tensile stress. Under cyclic loading, all of the specimens strengthened with FRP sheets failed eventually in a punching shear mode. For example, the CFS-70 specimen finally collapsed after the transverse sheets ruptured. The crack patterns of decks strengthened with GCFRPs propagated in a significantly more dense pattern than those of the decks strengthened with other sheet materials. The crack spacing was related to the grid spacing of the FRPs, as depicted in Fig. 3. Entire mortar overlays came off from the concrete surface at
the midpoint during the fatigue test. Then, the deck panels failed due to punching shear and detached completely from the mortar overlay. The panel GCFRP-60 failed abruptly when a concrete girder collapsed prior to the failure of the deck slab. 3.2. Compliance The variation of the compliance of each specimen was compared to evaluate the fatigue damage. This is illustrated in Fig. 4. The compliance for all specimens except GFS-80 stabilized after the initial loading cycles of about 10 cycles. Panel CON-90 showed a sudden increase in the compliance caused by a static failure at higher loads. The compliance of panel GFS-80 increased continuously during the initial loading cycle because of either a slip or partial debonding of the FRPs due to the relatively higher stress level, while the
Punching after rebar’s 710 yield 20,023
864,408
70
80
501,982
60
Static failure after 1 106 90,074
1367
19,836
Punching after rebar’s 732 yield
Punching failure
669
80
70
60
80
60
Static failure after 1 106 466,611
Punching and interface debonding
40
68,834 10
Punching after rebar’s 633 yield
Static failure after 1 106
90
70
40
Failure pattern
b
Two directional cracks
Two directional cracks
Minor cracks
Two directional cracks
One directional cracks
Minor cracks
Two directional cracks Crack width ¼ 0:2 mm Rebar strain reaches 0.002
One directional cracks Crack width ¼ 0:1 mm
Minor cracks
Two directional cracks
One directional cracks
One directional cracks
Initial statea
Fatigue test Nf
Failure pattern
Ultimate loads (kN)
Static test
Psudo-static damage that occurs between the 1st and 10th cycles. Stabilized fatigue damage from 0.1 to 0.85 cycles of Nf. c Fatigue failure between the 1000th and 5000th cycles. d Punching shear failure. e Diagonal crack. f Delamination of sheet. g Fracture of sheets.
a
GCFRP
CFS
GFS
CON
Series
Table 3 Test results
Rebar strain reaches 0.025
Two directional cracks Rebar strain reaches 0.002 Continuous crack propagation Separation of mortar in mid-span Rebar strain reaches 0.002 Continuous crack propagation
Two directional cracks Rebar strain reaches 0.002 Two directional cracks Partial DE and kinking of sheets Rebar strain reaches 0.0025 Continuous crack propagation Rebar strain reaches 0.0045
DRe of girder DEf and kinking of sheets Rebar strain reaches 0.005 DR of girder DE and kinking of sheets Rebar strain reaches 0.0065
Two directional cracks at 205 cycles
Two directional cracks Infinitesimal crack propagation after 105 cycles Rebar strain reaches 0.015 Two directional cracks Rebar strain reaches 0.0023 –
Steady stateb
PS and Full separation of overlayed mortar
PS after collapse of girder PS
PS
PS due to static loading FRg in only transverse direction and SP
PS
PS due to static loading PS
PS
PSd
PS due to static loading
Final statec
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Fig. 4.
Compliance of test deck panels. (a) CON; (b) GFS; (c) CFS; (d) GCFRP.
compliance of the other specimens was decreased slightly by the stabilized stress redistribution. Considering the stress level, the compliances of all of the strengthened specimens were relatively small compared to those of the unstrengthened reference deck panels, which indicates that the effect of crack control introduced by the strengthening material was sufficient. The GCFRP specimens were more efficient than the other strengthened deck panels. The compliance of the strengthened deck panels suddenly increased as the fatigue failure state was reached. 3.3. Variation of displacement and dissipated energy Cumulative displacements of the specimens are depicted in Fig. 5. The initial displacements of panels GFS-60, CFS-60, and GCFRP-60, which contained a 60% stress level and are not shown, were similar to that of panel CON-70, which received almost the same amount of loading as the strengthened specimens. As the number of loading cycles increased, the cumulative
displacements of panel CON-70 were larger than those of the strengthened panels. Other strengthened specimens with a stress level of 80% (not shown in the figures) had greater structural stiffness as compared to the unstrengthened deck panel with the same load, Whereas the structural stiffness of the GCFRP panel series was relatively low compared to those strengthened with CFSs. these deck panels failed due to a more ductile mode, except for panel GCFRP-60. The GFSs delaminated from the concrete during the fatigue test, while the CFS panel series developed only minor debonding problems in the mid-span of the deck. The energy dissipated from each strengthened panel is illustrated in Fig. 6. Concrete as an inelastic material develops residual deformation and has a different of the ascent curve and descent curve in load–displacement curve. Therefore, the discrepancy between the area of ascent curve and the area of descent curve under load–displacement curve at each load cycle can be defined as dissipated energy. The dissipated energies of the strengthened panels with CFS and GCFRP were
J. Sim, H. Oh / Engineering Structures 26 (2004) 2219–2230
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Fig. 5. Cumulative displacement. (a) CON-70; (b) GFS-60; (c) CFS-60; (d) GCFRP-70.
larger than those of the CON and GFS panels. The dissipated energy decreased slightly as the number of loading cycles increased. However, as inferred from panel GCFRP-60 in Fig. 6, the energy dissipated at the fatigue failure state increased rapidly due to the major cracks at the failure surfaces. Although it is not shown in the figure, the energy released by the deck panels in the first loading cycle was 25% of the total dissipated energy. From the compliance and energy dissipation relationships, CFSs and GCFRPs were more effective at dispersing cracks and preventing macro-cracks from forming as compared to GFSs.
4. Probabilistic approach 4.1. Weibull distribution The fatigue characteristics of the bridge deck specimens strengthened with FRPs were evaluated based on the fatigue test results and a probabilistic analysis. In the probabilistic analysis, the Weibull distribution was adopted to evaluate the failure probability and hazard
function of each specimen [15]. The Weibull distribution is widely applied in fatigue analysis because it explains the physical phenomenon of the fatigue response well [10,16–18]. The probability density function (PDF) and cumulative distribution function (CDF) obtained using the Weibull distribution are defined by Eqs. (1) and (2) as follows: " # k n n0 k1 n n0 k PDF : fN ðnÞ ¼ exp u n0 u n0 u n0 ðn n0 Þ
" # n n0 k CDF : FN ðnÞ ¼ 1 exp u n0
ð1Þ ðn n0 Þ
ð2Þ
where u is a scaling parameter or characteristic life at stress level S, k is a shape parameter, n is the fatigue life, and n0 is the minimum fatigue life. Previous researches have shown that n0 ¼ 0 is appropriate to predict the fatigue response [21,22]. In this study, parameters k and u were obtained from the S–N relationship of the fatigue test.
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Fig. 6. Variation of energy dissipation. (a) CON; (b) GFS; (c) CFS; (d) GCFRP.
The hazard function, which represents the fatigue characteristics of a given concrete member, increases harmonically with the accumulation of fatigue damage [17]. The hazard function indicates the probability that the member will collapse between time (0, t) and (t, tþdt). It can be written as [18–20]: LðtÞ Lðt þ DtÞ 1 d hðtÞ ¼ lim ¼ LðtÞ Dt!0 DtLðtÞ LðtÞ dt f ðtÞ ð3Þ ¼ LðtÞ where f(t) is the probability density function. Therefore, the hazard function for the Weibull distribution can be obtained by substituting Eqs. (1) and (2) into Eq. (3) as follows:
n n0 hN ðnÞ ¼ k u n0
k1 ðn n0 Þ
ð4Þ
In the test results, the stress level (S) and fatigue life (Nf) were displayed as Nf SA ¼ B, and parameters k and u were calculated from Eq. (5) [21], p2 k ¼ 2; 6s 2
0:5772 þ lnðB SA Þ lnu ¼ k
ð5Þ
where s is the standard deviation of ln(Nf), k is a
Weibull distribution shape parameter, and A and B are experimental constants. s, k, A, and B were calculated from the test results and are listed in Table 4. Sample moments of the expected fatigue life may also be used to estimate the distribution parameters. It can be shown that the moments of the Weibull distribution can be written as follows: 1 0:5772 1 ¼ B SA exp C 1þ ð6Þ E½N ¼ uC 1 þ k k k where E[ ] indicates an expected value and C( ) represents the gamma function. The design fatigue life (ND) should be selected such that there is only a small probability that a fatigue failure will occur. Once the distribution function has been determined, the design fatigue life corresponding to an acceptable value can be selected subsequent to an acceptable P½N < ND ¼ 1 pf , where pf is the probTable 4 Distribution parameters of test panels
k A B s
CON
GFS
CFS
GCFRP
2.827 30.279 1.795 0.454
1.399 25.126 2.633 0.917
1.325 33.254 1.962 0.968
2.702 38.948 1.392 0.475
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Table 5 Characteristic parameters and expected life cycles S
E[N]
U
Pf 0.01
0.05
0.10
CON
0.9 0.7 0.4
18.404 60,731 4:15 1012
18.526 61,132 4:18 1012
7.822914 15,781.9 3:61 1011
13.92398 28,090.17 6:42 1011
17.96156 36,235.55 8:28 1011
GFS
0.8 0.6 0.4
698 1,424,233 6:58 1010
707 1,446,295 6:68 1010
22.25777 30,667.96 8:15 108
71.37167 98,339.74 2:61 109
119.4009 164,517 4:37 109
CFS
0.8 0.7 0.6 0.4
4660 395,249 66,543,827 4:77 1013
5065 429,562 72,320,813 5:19 1013
83.8796 7113.948 1,197,699 8:59 1011
286.9674 24,338.11 4,097,548 2:94 1012
494.0124 41,897.9 7,053,901 5:06 1012
9116 1,653,753 669,721,341 4:8 1015
10,250 1,859,595 753,081,472 5:4 1015
1120 221,359 89,644,131 7:27 1014
2230 404,633 1:64 1018 1:33 1015
2911 528,142 2:14 1018 1:74 1015
0.8 0.7 GCFRP 0.6 0.4
Fig. 7. S–N relationship. (a) CON; (b) GFS; (c) CFS; (d) GCFRP.
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Table 6 S–N relationship and endurance limit S–N relationship CON GFS CFS GCFRP
Test P Test P E P E P
S S S S S S S S
¼ 1:00930 0:06300 log10 ðN f Þ ¼ 0:97039 0:04865 log10 ðN f Þ ¼ 1:01285 0:06800 log10 ðN f Þ ¼ 0:98149 0:05517 log10 ðN f Þ ¼ 1:00451 0:05551 log10 ðN f Þ ¼ 0:97378 0:04407 log10 ðN f Þ ¼ 1:00299 0:04971 log10 ðN f Þ ¼ 0:96587 0:03806 log10 ðN f Þ
ability of failure. Noting that pf ¼ P½N < ND , the design fatigue life corresponding to a permissible probability pf can be determined from the following relation: ND ¼ u ln
1 1 pf
1=k ð7Þ
Endurance limit (%)
Loads (kN)
P/T
63.0 67.8 60.5 65.0 67.0 70.9 70.5 73.8
403.2 433.9 426.8 458.6 492.6 521.2 502.3 525.6
1.0 1.08 1.0 1.06 1.0 1.06 1.0 1.05
The required mean fatigue life for a given stress level can be obtained from Eq. (8), 1 E½N ð8Þ E½N ffi ND C 1 þ ðpf Þ1=k ; ND ¼ k U where U should be included as a safety factor and used a value 1.0 for analysis. The calculated values of E[ ]
Fig. 8. Fracture probability.
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Fig. 9. Hazard function. (a) CON; (b) GFS; (c) CFS; (d) GCFRP.
and pf are summarized in Table 5. In Table 5, last three columns below pf denote the life cycles at each pf. 4.2. Analysis of fatigue life The fatigue life, as described in the previous sections, was analyzed using Eqs. (5) and (6). The following relations were obtained. Unstrengthend deck panel : Nf S30:279 ¼ 1:795 25:126
ð9Þ
¼ 2:633
ð10Þ
CFS panel : Nf S33:254 ¼ 1:962
ð11Þ
GFS panel : Nf S
GCFRP panel : Nf S
38:948
¼ 1:392
ð12Þ
Usually, the endurance limit of a reinforced concrete structure subjected to fatigue loading is about 60–70% of the ultimate static loads when the number of loading cycles is between 1 106 and 3 106 [23]. The strengthened deck panels exhibited more effective fatigue resistance than did the unstrengthened deck panel. Also, at relatively low stress levels, the fatigue life of the deck panels strengthened with either CFSs or
GCFRPs was extended as compared to that of the deck panels strengthened with GFSs. The failure loads of the unstrengthened damaged deck, panel CON-40, that was monotonically loaded after 1 106 cycles, were about 10% less than the ultimate static strength of the undamaged reference deck panel. However, the failure loads of the strengthened deck, panel GFS-40, that was also statically loaded after 1 106 cycles, were similar with the ultimate strength of undamaged strengthened deck with GFS. The damage accumulation of the strengthened deck was smaller than that of the unstrengthened deck. S–N relationships based on the test results and probabilistic analyses are depicted in Fig. 7 and summarized in Table 6. The discrepancies between the tests and analyses were about 5–8%. The endurance limits calculated from the probabilistic approach were similar to the test results. 4.3. Failure probability and hazard function Figs. 8 and 9 show the failure probability and hazard function. The variances in the fatigue life of the
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unstrengthened deck and the strengthened deck with GFSs (not shown here) were smaller than those of the other strengthened decks. For the fatigue life obtained after 1 106 cycles at a 70% stress level, the fracture probability of the strengthened deck with GCFRPs was the smallest at about 17%. However, the probabilities for the strengthened panels with CFSs and GFSs were about 93% and 100%, respectively. From this result, CFRPs and CFSs are more appropriate strengthening materials for decks that are subjected to lower stress level while in service. The hazard function expresses the damage accumulation due to fatigue loading. The fracture probability of strengthened decks with GCFRPs was small as compared to that of the other strengthened decks when the number of loading cycles increased at lower stress levels, but the fracture probability suddenly increased at high stress level. This result suggests that GCFRPs are more brittle material in response to fatigue loads because mortar overlay enclosed GCFRPs were abruptly delaminated from concrete surface, Whereas either CFSs or GFSs with which decks were two directionally strengthened, have a more stabilized bond-slip relationship, leading to a ductile failure. The initial hazard function of the CFS specimens was relatively high at lower stress level, but the increment rate of the hazard function slowed down as the number of loading cycles increased. From the above results, GCFRP is an effective strengthening material when stress levels are relatively lower, whereas CFS works better when strengthening decks that are subjected to relatively higher stress level.
5. Conclusions Strengthening concrete bridge deck panels with various FRP materials can substantially increase fatigue life. The strengthening effect in fatigue loading was mainly influenced by the bonding characteristics between the strengthening material and the concrete surface. The compliance of strengthened decks when materials delaminated from the concrete either due to stress concentration or damage accumulation increased abruptly. The S–N relationship obtained from the tests and probabilistic analyses was used to predict the fatigue life of the decks. A probabilistic approach based on the Weibull distribution yielded appropriate results when compared with the actual fatigue responses of the deck specimens. The fatigue behavior of decks strengthened using GCFRPs and CFSs was more effective than that of the deck strengthened by GFSs. Therefore, the choice of strengthening material should depend on whether the purpose of the strengthening is to extend the fatigue life or to raise the design traffic loads of the bridge deck.
Acknowledgements This work was supported by the Post-doctoral Fellowship Program of the Korea Science and Engineering Foundation (KOSEF). References [1] Sonoda K, Horikawa T. Fatigue strength of reinforced concrete slab under moving loads. IABSE Reports 1982;37:455–62. [2] Schla¨fli M, Bru¨hwiler E. Fatigue of existing reinforced concrete bridge deck slabs. Engineering Structures 1998;20(11):991–8. [3] Mufti AA, Jaeger LG, Bakht B, Wegner LD. Experimental investigation of fibre-reinforced concrete deck without internal steel reinforcement. Canadian Journal of Civil Engineering 1993;20(3):398–406. [4] Takeshi H. An outline of repairing and strengthening of RC deck slabs. Bridge and Foundation Engineering 1994;26(8):105–8. [5] Fang IK, Worley JA, Burns NH, Klinger RE. Behavior of isotropic R/C bridge decks on steel girders. Journal of the Structural Engineering 1990;116(3):659–78. [6] Oh H, Sim J, Meyer C. Experimental assessment of bridge deck panels strengthened with carbon fiber sheets. Composites Part B: Engineering 2003;34(6):527–38. [7] Holmen JO. Fatigue of concrete by constant and variable amplitude loading. Fatigue of Concrete Structures, Special Publications ACI SP-75. Detroit, 1982, 71–110. [8] Paskova T, Meyer C. Low-cycle fatigue of plain and fiber-reinforced concrete. ACI Materials Journal 1997;94(4):273–85. [9] Freudenthal AM. Prediction of fatigue failure. Journal of Applied Physics 1968;21(12):47–69. [10] Oh B-H. Fatigue-life distributions of concrete for various stress levels. ACI Materials Journal 1991;88(2):122–8. [11] Tepfers R. Tensile fatigue strength of plain concrete. Journal of ACI 1979;79:919–33. [12] Kujawski D, Elyin FA. Cumulative damage theory of fatigue crack initiation and propagation. International Journal of Fatigue 1984;6(2):83–8. [13] Sim J. Evaluation of repair and rehabilitation efficiency of concrete bridge deck. Research Report, Korea Highway Corporation, Seoul, Korea, 2000 [in Korean]. [14] Sim J, Shim J-W, Oh H, Lee K-M. Fatigue loading effect on the concrete bridge deck specimen strengthened by carbon fiber sheet. Proceedings of the 8th EASEC International Conference, Singapore 2001. 2001 [Paper No. 1529]. [15] Weibull W. Fatigue—testing and analysis of results. Oxford, England: Pergamon Press; 1961. [16] Collins JA. Failure of materials in mechanical design. New York: John Wiley & Sons Inc; 1981. [17] Singh SP, Kaushik SKF. Fatigue strength of steel fiber reinforced concrete in flexure. Cement and Concrete Composites 2003;25(7):779–86. [18] Freudenthal AM, Gumbel EJ. On the statistical interpretation of fatigue test. Proceedings of the Royal Society of London: London, England 1953;216:309–22. [19] Achintya A, Sankaran MP. Probability, reliability, and statistical methods engineer design. New York: John Wiley & Sons Inc; 1999. [20] Roberts EM. Structural reliability analysis and prediction. New York: John Wiley & Sons Inc; 1999. [21] Kapur KC, Lamberson LR. Reliability in engineering design. New York: John Wiley & Sons Inc; 1997. [22] Yao JPT. Fatigue reliability and design. Journal of the Structural Division, ASCE 1974;100(ST9). [23] ACI Committe 215. Consideration for design of concrete structures subject to fatigue loading. ACI 1986;215R-1–25.
Structural behavior of strengthened bridge deck specimens under fatigue loading Jongsung Sim, Hongseob Oh Department of Civil and Environmental Engineering, Hanyang University, 1271, Sa1-dong, Ansan 425-791, South Korea Received 7 March 2004; received in revised form 4 August 2004; accepted 11 August 2004
Abstract The deterioration of concrete bridge decks that have been directly damaged by traffic loads affects their durability, safety, and function. It is therefore necessary to strengthen the damaged concrete structures. Even though there have been many experiments performed to investigate the static behavior of strengthened structures, few experiments or analyses have considered their fatigue behavior. In this study, fatigue tests were conducted on bridge decks strengthened using various fiber-reinforced polymer plastics, such as carbon fiber sheet, glass fiber sheet, and grid-type carbon fiber reinforced plastic. All of the strengthened specimens were shown to have an improved resistance to crack propagation and better stress distributions. The Weibull distribution was adopted to analyze the fatigue life of the decks. The fatigue life limits of the strengthened bridge decks were determined at higher stress levels, and the grid-type carbon reinforced plastic specimens proved to be the most effective. # 2004 Elsevier Ltd. All rights reserved. Keywords: Bridge deck; Fatigue life; Fiber reinforced polymer plastic; Structural strengthening; Weibull distribution
1. Introduction Reinforced concrete bridge decks receive traffic loads directly. Structural damage can increase, such as residual deformation and numerous cracks, which eventually decreases the life of the deck as well as its load carrying capacity [1–5]. In South Korea, there are many deck panels that have deteriorated after almost 20 years of service and which must now be rehabilitated. Many of these were designed for relatively low traffic loads rather than the heavy traffic (over HS25) found nowadays, and are only 18 cm thick. When such decks are strengthened, the overall structural performance must be improved, including their serviceability and fatigue resistance as well as the load carrying capacity. The flexural strength of a deck can be improved easily by applying external bonding techniques, using materials such as carbon fiber sheet (CFS) Corresponding author. Tel.: +82-31-400-5208; fax: +82-31-4187430. E-mail address: [email protected] (H. Oh).
0141-0296/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2004.08.006
and carbon fiber reinforced plastic (CFRP) attached to the tension side of the concrete. However, it is fairly difficult to rehabilitate the fatigue resistance of a deck because the shear strength that has been decreased by repeated loads must be improved with the flexural strength. Previous research by the authors experimentally verified that the fatigue resistance of a deck that was externally strengthened with CFSs was improved even if no additional sectional enlargements of the deck were made [6]. This result presented the possibility of extending the life cycle of a deck panel without adding deadloads by using either mortar overlay or an additional internal stiffener. Although numerous research programs over the past decade have attempted to understand fatigue response and to establish a fatigue model for concrete subjected to repeated loads, the fatigue failure characteristics of strengthened concrete structures are not yet systematically established on a scientific foundation [7–12]. Much of the research for concrete structures has been limited to either a simple S–N relationship or a mechanical approach, because the analysis is too
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complicated to extend to an entire structural system from either the microscopic element or material points of view. The experimental and theoretical work presented in this paper is the result of successive research programs conducted at the Hanyang University in Korea to verify the structural efficiency of various fiber reinforced polymer (FRP) composites for strengthening concrete structures [6,12,13]. The authors have persisted in developing rehabilitation techniques for deteriorated concrete structures for the past decade [6,12,14]. A recent focus has been how to achieve additional benefits by applying FRPs to a deteriorated concrete member, either by extending its fatigue life or enhancing its serviceability. Improvements to both the fatigue and flexural resistance must be considered when rehabilitating a deteriorated concrete bridge deck. The experiments reported in this paper were conducted to find structural differences and efficiencies between slabs strengthened with various FRPs and subjected to cyclic loading [13]. We also attempted to verify the theoretical S–N relationship of strengthened deck panels through a probabilistic approach based on the test results. In this paper, CFS, glass fiber sheet (GFS) and gridtype carbon fiber reinforced plastic (GCFRP) were used as the strengthening materials.
2. Experimental program 2.1. Materials The concrete used in the specimens consisted of ordinary Portland cement, natural sand, and crushed coarse aggregate with a maximum size of 25 mm. The mixture had a 28-day cylinder strength of about 22.5 MPa. Deformed bars, 15.9 mm in diameter with an average yield strength of 300 MPa, were used in the slab panels and beams. The shear reinforcement of the girders consisted of 9.35-mm diameter closed stirrups. The material properties are listed in Table 1.
2.2. Test program For the experimental test program, a prototype deck panel with dimensions of 160 240 cm was selected to simulate a real bridge deck supported by two girders, as referenced in [13]. In order to determine the dimension of deck specimen, 3-dimensional non-linear finite element analyses in which various dimensions of deck considered to simulate either the deformation or deterioration of real bridge deck were carried out before the physical experiments. As a result, the selected dimension of deck from the FE analysis was similar to the real deck size used in Korea. The concrete slab was modeled with eight-node solid elements, reinforcing bars with beam elements, and the CFS was represented by membrane elements with stiffness properties only in the appropriate directions [15–19]. Both beam and membrane elements were assumed to be perfectly bonded to the concrete. The material properties were obtained experimentally. The rubber supports were simulated by spring elements with a hyperelastic material law. The slab thickness was 18 cm, which is the same as that of secondary bridge decks in Korea. The tensile rebar spacing in the transverse direction was 10 cm and the reinforcement spacing in the longitudinal direction was 15 cm. The specimen details and strengthening methods are depicted in Figs. 1 and 2. The CFS and GFS materials were bonded to the prototype deck panel in an upside-down position. Each fiber sheet was attached to the epoxy-coated surface by pressing it into the epoxy. The GCFRP material was first fixed to the concrete surface in an upside-down position using 2.5-cm length anchor bolts spaced every 50 cm. Then, the repair mortar suggested by the manufacturer was overlayed on the concrete surface. The 12 specimens listed in Table 2 were subjected to cyclic loads to investigate their fatigue failure characteristics. CON means the unstrengthened reference panel. The stress level of each specimen, except CON40 and GFS-40 designed to verify the structural response in service state, was designed to assess the endurance limit of deck specimens and compare the
Table 1 Physical properties of materials Thickness or diameter Concrete Rebar Epoxy Carbon fiber sheet Glass fiber sheet GCFRP Mortar for GCFRP
13 mm 0.11 mm 1.3 mm 4.0 mm
Yield strength (MPa)
Ultimate strength (MPa)
– 300 – – – –
22.5 400 88.3 3500 450 1170 27.0
Elastic modulus (MPa) 0:232 105 1:96 105 0:07 105 2:31 105 0:227 105 1:00 105 0:14 105
Ultimate strain
– – – 0.015 0.02 0.0117 –
J. Sim, H. Oh / Engineering Structures 26 (2004) 2219–2230
Fig. 1.
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Details of specimen (unit: cm).
structural response with deck specimens strengthened with other materials and receiving similar loads. The stress level means the ratio of applied load in fatigue test to ultimate strength of each specimen. Loading at a rate of 2 Hz was repeatedly applied to the slab center. LVDTs were used to record the slab deflections. Concrete strain gauges were attached to the compressive deck surface of the slabs and steel strain gauges were bonded to the main reinforcement to measure the strain variation of the deck.
3. Test results and discussion 3.1. Failure patterns Typical failure patterns of the deck panel are depicted in Fig. 3, and the number of loading cycles and the failure phenomena of the specimens according to their damage state are summarized in Table 3. From the static test results, initial one-way cracks in the deck panel developed parallel to the girder, and then propagated into two-directional cracks due to the stress redistribution as the loads increased [13]. Crack propagation in the deck panels subjected to repeated loading appeared in different patterns according to the stress levels. The failure patterns of deck panels that received
Fig. 2.
Strengthening details. (a) CFS and GFS; (b) GCFRP.
relatively lower stresses were dominated by the effect of initial macro cracks at their midpoints. The failure patterns of deck panels that received higher stresses were similar to those of the decks that received monotonic loads. The angle of the failure surface of the higher stressed panels was greater than that of the lower stressed panels.
Table 2 Stress level CON Stress level (%) Loads (kN)
40 260
CFS 70 450
90 580
60 440
GFS 70 510
80 590
40 280
GCFRP 60 420
80 560
60 430
70 500
80 570
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Fig. 3.
Typical fatigue failure pattern.
Complete debonding failures of the decks two-directionally strengthened with FRP sheets did not occur because the sheets distributed the principle tensile stresses well and kept the flexural cracks relatively small. The propagated flexural cracks branched out into numerous hairline cracks because of the distributed tensile stress. Under cyclic loading, all of the specimens strengthened with FRP sheets failed eventually in a punching shear mode. For example, the CFS-70 specimen finally collapsed after the transverse sheets ruptured. The crack patterns of decks strengthened with GCFRPs propagated in a significantly more dense pattern than those of the decks strengthened with other sheet materials. The crack spacing was related to the grid spacing of the FRPs, as depicted in Fig. 3. Entire mortar overlays came off from the concrete surface at
the midpoint during the fatigue test. Then, the deck panels failed due to punching shear and detached completely from the mortar overlay. The panel GCFRP-60 failed abruptly when a concrete girder collapsed prior to the failure of the deck slab. 3.2. Compliance The variation of the compliance of each specimen was compared to evaluate the fatigue damage. This is illustrated in Fig. 4. The compliance for all specimens except GFS-80 stabilized after the initial loading cycles of about 10 cycles. Panel CON-90 showed a sudden increase in the compliance caused by a static failure at higher loads. The compliance of panel GFS-80 increased continuously during the initial loading cycle because of either a slip or partial debonding of the FRPs due to the relatively higher stress level, while the
Punching after rebar’s 710 yield 20,023
864,408
70
80
501,982
60
Static failure after 1 106 90,074
1367
19,836
Punching after rebar’s 732 yield
Punching failure
669
80
70
60
80
60
Static failure after 1 106 466,611
Punching and interface debonding
40
68,834 10
Punching after rebar’s 633 yield
Static failure after 1 106
90
70
40
Failure pattern
b
Two directional cracks
Two directional cracks
Minor cracks
Two directional cracks
One directional cracks
Minor cracks
Two directional cracks Crack width ¼ 0:2 mm Rebar strain reaches 0.002
One directional cracks Crack width ¼ 0:1 mm
Minor cracks
Two directional cracks
One directional cracks
One directional cracks
Initial statea
Fatigue test Nf
Failure pattern
Ultimate loads (kN)
Static test
Psudo-static damage that occurs between the 1st and 10th cycles. Stabilized fatigue damage from 0.1 to 0.85 cycles of Nf. c Fatigue failure between the 1000th and 5000th cycles. d Punching shear failure. e Diagonal crack. f Delamination of sheet. g Fracture of sheets.
a
GCFRP
CFS
GFS
CON
Series
Table 3 Test results
Rebar strain reaches 0.025
Two directional cracks Rebar strain reaches 0.002 Continuous crack propagation Separation of mortar in mid-span Rebar strain reaches 0.002 Continuous crack propagation
Two directional cracks Rebar strain reaches 0.002 Two directional cracks Partial DE and kinking of sheets Rebar strain reaches 0.0025 Continuous crack propagation Rebar strain reaches 0.0045
DRe of girder DEf and kinking of sheets Rebar strain reaches 0.005 DR of girder DE and kinking of sheets Rebar strain reaches 0.0065
Two directional cracks at 205 cycles
Two directional cracks Infinitesimal crack propagation after 105 cycles Rebar strain reaches 0.015 Two directional cracks Rebar strain reaches 0.0023 –
Steady stateb
PS and Full separation of overlayed mortar
PS after collapse of girder PS
PS
PS due to static loading FRg in only transverse direction and SP
PS
PS due to static loading PS
PS
PSd
PS due to static loading
Final statec
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Fig. 4.
Compliance of test deck panels. (a) CON; (b) GFS; (c) CFS; (d) GCFRP.
compliance of the other specimens was decreased slightly by the stabilized stress redistribution. Considering the stress level, the compliances of all of the strengthened specimens were relatively small compared to those of the unstrengthened reference deck panels, which indicates that the effect of crack control introduced by the strengthening material was sufficient. The GCFRP specimens were more efficient than the other strengthened deck panels. The compliance of the strengthened deck panels suddenly increased as the fatigue failure state was reached. 3.3. Variation of displacement and dissipated energy Cumulative displacements of the specimens are depicted in Fig. 5. The initial displacements of panels GFS-60, CFS-60, and GCFRP-60, which contained a 60% stress level and are not shown, were similar to that of panel CON-70, which received almost the same amount of loading as the strengthened specimens. As the number of loading cycles increased, the cumulative
displacements of panel CON-70 were larger than those of the strengthened panels. Other strengthened specimens with a stress level of 80% (not shown in the figures) had greater structural stiffness as compared to the unstrengthened deck panel with the same load, Whereas the structural stiffness of the GCFRP panel series was relatively low compared to those strengthened with CFSs. these deck panels failed due to a more ductile mode, except for panel GCFRP-60. The GFSs delaminated from the concrete during the fatigue test, while the CFS panel series developed only minor debonding problems in the mid-span of the deck. The energy dissipated from each strengthened panel is illustrated in Fig. 6. Concrete as an inelastic material develops residual deformation and has a different of the ascent curve and descent curve in load–displacement curve. Therefore, the discrepancy between the area of ascent curve and the area of descent curve under load–displacement curve at each load cycle can be defined as dissipated energy. The dissipated energies of the strengthened panels with CFS and GCFRP were
J. Sim, H. Oh / Engineering Structures 26 (2004) 2219–2230
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Fig. 5. Cumulative displacement. (a) CON-70; (b) GFS-60; (c) CFS-60; (d) GCFRP-70.
larger than those of the CON and GFS panels. The dissipated energy decreased slightly as the number of loading cycles increased. However, as inferred from panel GCFRP-60 in Fig. 6, the energy dissipated at the fatigue failure state increased rapidly due to the major cracks at the failure surfaces. Although it is not shown in the figure, the energy released by the deck panels in the first loading cycle was 25% of the total dissipated energy. From the compliance and energy dissipation relationships, CFSs and GCFRPs were more effective at dispersing cracks and preventing macro-cracks from forming as compared to GFSs.
4. Probabilistic approach 4.1. Weibull distribution The fatigue characteristics of the bridge deck specimens strengthened with FRPs were evaluated based on the fatigue test results and a probabilistic analysis. In the probabilistic analysis, the Weibull distribution was adopted to evaluate the failure probability and hazard
function of each specimen [15]. The Weibull distribution is widely applied in fatigue analysis because it explains the physical phenomenon of the fatigue response well [10,16–18]. The probability density function (PDF) and cumulative distribution function (CDF) obtained using the Weibull distribution are defined by Eqs. (1) and (2) as follows: " # k n n0 k1 n n0 k PDF : fN ðnÞ ¼ exp u n0 u n0 u n0 ðn n0 Þ
" # n n0 k CDF : FN ðnÞ ¼ 1 exp u n0
ð1Þ ðn n0 Þ
ð2Þ
where u is a scaling parameter or characteristic life at stress level S, k is a shape parameter, n is the fatigue life, and n0 is the minimum fatigue life. Previous researches have shown that n0 ¼ 0 is appropriate to predict the fatigue response [21,22]. In this study, parameters k and u were obtained from the S–N relationship of the fatigue test.
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Fig. 6. Variation of energy dissipation. (a) CON; (b) GFS; (c) CFS; (d) GCFRP.
The hazard function, which represents the fatigue characteristics of a given concrete member, increases harmonically with the accumulation of fatigue damage [17]. The hazard function indicates the probability that the member will collapse between time (0, t) and (t, tþdt). It can be written as [18–20]: LðtÞ Lðt þ DtÞ 1 d hðtÞ ¼ lim ¼ LðtÞ Dt!0 DtLðtÞ LðtÞ dt f ðtÞ ð3Þ ¼ LðtÞ where f(t) is the probability density function. Therefore, the hazard function for the Weibull distribution can be obtained by substituting Eqs. (1) and (2) into Eq. (3) as follows:
n n0 hN ðnÞ ¼ k u n0
k1 ðn n0 Þ
ð4Þ
In the test results, the stress level (S) and fatigue life (Nf) were displayed as Nf SA ¼ B, and parameters k and u were calculated from Eq. (5) [21], p2 k ¼ 2; 6s 2
0:5772 þ lnðB SA Þ lnu ¼ k
ð5Þ
where s is the standard deviation of ln(Nf), k is a
Weibull distribution shape parameter, and A and B are experimental constants. s, k, A, and B were calculated from the test results and are listed in Table 4. Sample moments of the expected fatigue life may also be used to estimate the distribution parameters. It can be shown that the moments of the Weibull distribution can be written as follows: 1 0:5772 1 ¼ B SA exp C 1þ ð6Þ E½N ¼ uC 1 þ k k k where E[ ] indicates an expected value and C( ) represents the gamma function. The design fatigue life (ND) should be selected such that there is only a small probability that a fatigue failure will occur. Once the distribution function has been determined, the design fatigue life corresponding to an acceptable value can be selected subsequent to an acceptable P½N < ND ¼ 1 pf , where pf is the probTable 4 Distribution parameters of test panels
k A B s
CON
GFS
CFS
GCFRP
2.827 30.279 1.795 0.454
1.399 25.126 2.633 0.917
1.325 33.254 1.962 0.968
2.702 38.948 1.392 0.475
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Table 5 Characteristic parameters and expected life cycles S
E[N]
U
Pf 0.01
0.05
0.10
CON
0.9 0.7 0.4
18.404 60,731 4:15 1012
18.526 61,132 4:18 1012
7.822914 15,781.9 3:61 1011
13.92398 28,090.17 6:42 1011
17.96156 36,235.55 8:28 1011
GFS
0.8 0.6 0.4
698 1,424,233 6:58 1010
707 1,446,295 6:68 1010
22.25777 30,667.96 8:15 108
71.37167 98,339.74 2:61 109
119.4009 164,517 4:37 109
CFS
0.8 0.7 0.6 0.4
4660 395,249 66,543,827 4:77 1013
5065 429,562 72,320,813 5:19 1013
83.8796 7113.948 1,197,699 8:59 1011
286.9674 24,338.11 4,097,548 2:94 1012
494.0124 41,897.9 7,053,901 5:06 1012
9116 1,653,753 669,721,341 4:8 1015
10,250 1,859,595 753,081,472 5:4 1015
1120 221,359 89,644,131 7:27 1014
2230 404,633 1:64 1018 1:33 1015
2911 528,142 2:14 1018 1:74 1015
0.8 0.7 GCFRP 0.6 0.4
Fig. 7. S–N relationship. (a) CON; (b) GFS; (c) CFS; (d) GCFRP.
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Table 6 S–N relationship and endurance limit S–N relationship CON GFS CFS GCFRP
Test P Test P E P E P
S S S S S S S S
¼ 1:00930 0:06300 log10 ðN f Þ ¼ 0:97039 0:04865 log10 ðN f Þ ¼ 1:01285 0:06800 log10 ðN f Þ ¼ 0:98149 0:05517 log10 ðN f Þ ¼ 1:00451 0:05551 log10 ðN f Þ ¼ 0:97378 0:04407 log10 ðN f Þ ¼ 1:00299 0:04971 log10 ðN f Þ ¼ 0:96587 0:03806 log10 ðN f Þ
ability of failure. Noting that pf ¼ P½N < ND , the design fatigue life corresponding to a permissible probability pf can be determined from the following relation: ND ¼ u ln
1 1 pf
1=k ð7Þ
Endurance limit (%)
Loads (kN)
P/T
63.0 67.8 60.5 65.0 67.0 70.9 70.5 73.8
403.2 433.9 426.8 458.6 492.6 521.2 502.3 525.6
1.0 1.08 1.0 1.06 1.0 1.06 1.0 1.05
The required mean fatigue life for a given stress level can be obtained from Eq. (8), 1 E½N ð8Þ E½N ffi ND C 1 þ ðpf Þ1=k ; ND ¼ k U where U should be included as a safety factor and used a value 1.0 for analysis. The calculated values of E[ ]
Fig. 8. Fracture probability.
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Fig. 9. Hazard function. (a) CON; (b) GFS; (c) CFS; (d) GCFRP.
and pf are summarized in Table 5. In Table 5, last three columns below pf denote the life cycles at each pf. 4.2. Analysis of fatigue life The fatigue life, as described in the previous sections, was analyzed using Eqs. (5) and (6). The following relations were obtained. Unstrengthend deck panel : Nf S30:279 ¼ 1:795 25:126
ð9Þ
¼ 2:633
ð10Þ
CFS panel : Nf S33:254 ¼ 1:962
ð11Þ
GFS panel : Nf S
GCFRP panel : Nf S
38:948
¼ 1:392
ð12Þ
Usually, the endurance limit of a reinforced concrete structure subjected to fatigue loading is about 60–70% of the ultimate static loads when the number of loading cycles is between 1 106 and 3 106 [23]. The strengthened deck panels exhibited more effective fatigue resistance than did the unstrengthened deck panel. Also, at relatively low stress levels, the fatigue life of the deck panels strengthened with either CFSs or
GCFRPs was extended as compared to that of the deck panels strengthened with GFSs. The failure loads of the unstrengthened damaged deck, panel CON-40, that was monotonically loaded after 1 106 cycles, were about 10% less than the ultimate static strength of the undamaged reference deck panel. However, the failure loads of the strengthened deck, panel GFS-40, that was also statically loaded after 1 106 cycles, were similar with the ultimate strength of undamaged strengthened deck with GFS. The damage accumulation of the strengthened deck was smaller than that of the unstrengthened deck. S–N relationships based on the test results and probabilistic analyses are depicted in Fig. 7 and summarized in Table 6. The discrepancies between the tests and analyses were about 5–8%. The endurance limits calculated from the probabilistic approach were similar to the test results. 4.3. Failure probability and hazard function Figs. 8 and 9 show the failure probability and hazard function. The variances in the fatigue life of the
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unstrengthened deck and the strengthened deck with GFSs (not shown here) were smaller than those of the other strengthened decks. For the fatigue life obtained after 1 106 cycles at a 70% stress level, the fracture probability of the strengthened deck with GCFRPs was the smallest at about 17%. However, the probabilities for the strengthened panels with CFSs and GFSs were about 93% and 100%, respectively. From this result, CFRPs and CFSs are more appropriate strengthening materials for decks that are subjected to lower stress level while in service. The hazard function expresses the damage accumulation due to fatigue loading. The fracture probability of strengthened decks with GCFRPs was small as compared to that of the other strengthened decks when the number of loading cycles increased at lower stress levels, but the fracture probability suddenly increased at high stress level. This result suggests that GCFRPs are more brittle material in response to fatigue loads because mortar overlay enclosed GCFRPs were abruptly delaminated from concrete surface, Whereas either CFSs or GFSs with which decks were two directionally strengthened, have a more stabilized bond-slip relationship, leading to a ductile failure. The initial hazard function of the CFS specimens was relatively high at lower stress level, but the increment rate of the hazard function slowed down as the number of loading cycles increased. From the above results, GCFRP is an effective strengthening material when stress levels are relatively lower, whereas CFS works better when strengthening decks that are subjected to relatively higher stress level.
5. Conclusions Strengthening concrete bridge deck panels with various FRP materials can substantially increase fatigue life. The strengthening effect in fatigue loading was mainly influenced by the bonding characteristics between the strengthening material and the concrete surface. The compliance of strengthened decks when materials delaminated from the concrete either due to stress concentration or damage accumulation increased abruptly. The S–N relationship obtained from the tests and probabilistic analyses was used to predict the fatigue life of the decks. A probabilistic approach based on the Weibull distribution yielded appropriate results when compared with the actual fatigue responses of the deck specimens. The fatigue behavior of decks strengthened using GCFRPs and CFSs was more effective than that of the deck strengthened by GFSs. Therefore, the choice of strengthening material should depend on whether the purpose of the strengthening is to extend the fatigue life or to raise the design traffic loads of the bridge deck.
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