Deterioration of concrete bridge decks affects their durability, safety, and function. It is therefore necessary to conduct structural rehabilitation of damaged concrete decks by strengthening them with fiberreinforced polymer. Of the recent studies on the strengthened structures, most have focused on static behavior; only a few studies have investigated fatigue behavior. Accurate analysis of fatigue in concrete deck performance requires a more realistic simulated moving load. This study developed a theoretical liveload model to reflect the effect of moving vehicle loads, based on a statistical approach to the measurement of real traffic loads over various time periods in Korea. It assessed the fatigue life and strengthening effect of bridge decks strengthened with either carbon fiber sheets or grid carbon fiber polymer plastic using probabilistic and reliability analyses. It used extrapolations and simulations to derive maximum load effects for time periods ranging from 1 day to 75 years. Limited fatigue tests were conducted and probabilistic and reliability analyses were carried out on the strengthened concrete bridge deck specimens to predict the extended fatigue life. Analysis results indicated that strengthened concrete decks provide sufficient resistance against increasing truck loads during the service life of a bridge.
Upgrading existing concrete structures has been an important issue over the last 30 years. Many studies have focused on developing new technologies to strengthen and retrofit deteriorated structures [
Many researchers have investigated structural performance, such as the ultimate limit and serviceability limit of strengthened material, but few have focused on the service life cycle or durability of the strengthened structure. Strengthening of a concrete structure is mainly intended to improve loadcarrying capacity or serviceability. Concrete gradually fails due to fatigue loads, but under service loading states rather than ultimate loading states [
Improving loadcarrying capacity and serviceability are undoubtedly important design factors, but extended service life is also important. If the strengthening method used to reinforce a structure ensures the required performance, does it also ensure improved structural performance over its lifecycle? It is important to confirm the longterm performance of a reinforced structure in addition to its loadcarrying capacity and serviceability [
Many assessments of the fatigue performance of strengthened concrete have been limited to laboratories, where tests are conducted under pulsating loading conditions. In the case of bridge deck panels, one main cause of deterioration is deck fatigue failure caused by excessive repeated heavy traffic loads. Continuous static and fatigue tests have verified the failure mechanisms for bridge decks strengthened with fiberreinforced polymers (FRPs), and simplified flexural and punching shear design procedures and semiempirical fatigue life cycle assessment techniques have been proposed based on the cumulated damage theory [
This study developed a semiempirical methodology for fatigue analysis, using a liveload model derived from probabilistic analysis of real traffic data in South Korea and previously obtained fatigue test results. The proposed live traffic model was then tested based on real Korean traffic conditions. Probabilistic approaches and reliability analyses based on restricted test results for the strengthened concrete bridge decks were also applied to verify the strengthening effect and to predict the extended fatigue life. This information is especially important because investigations of bridge deck fatigue performance conducted under laboratory or real bridge deck conditions provide limited data and invariably involve large uncertainties and extensive variations in results.
To predict the fatigue life of a bridge, the fatigue analysis should apply the axle loads that pass over the bridge. Land load data can be used to simulate fatigue conditions, including traffic jams, over long periods, but these data are rare and generally not used for fatigue analysis of a bridge structure [
Banpo Bridge consists of steel box girder and concrete deck.
The Banpo Bridge is classified as a Class 2 bridge by the Korean Highway Bridge Design Specification DB18 [
Detailed specification of standard truck loads in Korea.
Bridge grade  Load grade  Total truck load 1.8 W (kN)  Front axle load 0.1 W (kN)  Rear axle load 0.4 W (kN) 

Class 1  DB24  432  24  96 
Class 2  DB18  324  18  72 
Class 3  DB13.5  243  13.5  54 
The scheme of standard design truck in Korea.
Yoon [
Actual truck axle loads [
Truck  Axle loads 

(a) Axle loads in the normal state  
TT3 ( 
58.4 kN 
84.1 kN  
84.0 kN  


ST5 ( 
49.4 kN 
65.2 kN  
65.7 kN  
82.2 kN  
68.1 kN  


(b) Axle loads in an overloaded state  
TT3 ( 
58.4 kN 
133.9 kN  
84.0 kN  


ST5 ( 
49.4 kN 
65.2 kN  
112.4 kN  
82.2 kN  
68.1 kN 
Various truck types considered for liveload model [
Type T2
Type TT3
Type ST4
Type ST5
Type ST6
Type FT5
Figure
Probability frequency of a TT3 truck.
Axle loads in the normal state
Axle loads in an overloaded state
This study used the average daily truck traffic (ADTT) on the Banpo Bridge provided by the Korean Ministry of Construction and Transportation [
Average daily truck traffic (ADTT) of Banpo Bridge.
Passenger vehicle  Bus  Truck  

Normal state truck  Overloaded state truck  
Sixlane road  121,954  17,510  23,405  3,200 
ADTT  20,326  2,918  3,901  533 
4,434 (4,400) 
It has been studied that the moving and cyclic load can affect reinforced concrete bridge deck more 4 to 7 times than that of static cyclic load. In present, however, only static cyclic load has been adopted for fatigue analysis of the bridge deck. Therefore, the liveload model for fatigue analysis of the bridge deck was developed by using Type I extreme function, based on the wellestablished assumptions by Collins and Nowak [
Parameters
Therefore, the maximum axle load formed as a standard distribution can be determined by generating pseudorandom numbers for the axle load. This study assumed that the values of the coefficient of variation and average nominal ratio for an adopted axle load to an extreme function were 0.25 and 1.24, respectively, based on Collins and Nowak [
Figures
Liveload model (normal state tandem load: 84.0 kN).
Probability density function
Cumulative distribution function
Liveload model (overloaded state tandem load: 133.9 kN).
Probability density function
Cumulative distribution function
The probabilistic analysis revealed that the load effect of a normal state, in which the tandem load was only 84.0 kN, increased to 170.0 kN at 1 day and 281.5 kN at 75 years, respectively, as shown in Figure
Some previous researchers have found that the fatigue life of a deck panel under a moving load is four to seven times less than when it is under a pulsating load and that this has a large effect on real bridge decks [
To assess the static and fatigue behavior of strengthened deck panels, a total of 12 deck specimens were prepared, and carbon fiber sheet (CFS) and grid typed carbon fiberreinforced polymer (GCFRP) were used as strengthening materials. During the experimental test program, a prototype 160 × 240cm (63 × 94.5in) deck panel was used to simulate a real bridge deck supported by two girders, as described in previous studies [
Specimen details (unit: cm).
Deck panels were fabricated using ordinary Portland cement, natural sand, and crushed coarse aggregate with a maximum size of 25 mm (0.984 in). The compressive strength of the concrete was 22.5 MPa (3262.5 psi) after curing for 28 days. Deformed bars with a diameter of 15.9 mm (0.626 in) and average yield strength of 300 MPa (43500 psi) were used in the deck panels and beams. Table
Physical properties of the materials.
Thickness or diameter  Yield strength (MPa)  Ultimate strength (MPa)  Elastic modulus (MPa)  Ultimate strain  

Concrete  —  22.5  0.232 × 10^{5}  —  
Rebar  13 mm  300  400  1.96 × 10^{5}  — 
Epoxy  —  88.3  0.07 × 10^{5}  —  
Carbon fiber sheet  0.11 mm  —  3,500  2.31 × 10^{5}  0.015 
GCFRP (grid typed carbon fiberreinforced)  4.0 mm  —  1,170  1.00 × 10^{5}  0.0117 
Mortar for GCFRP  27.0  0.14 × 10^{5}  — 
The slab thickness was 18 cm (7.09 in), identical to that of secondary bridge decks in Korea. The tensile rebar spacing was 10 cm in the transverse direction, and the reinforcement spacing was 15 cm (5.91 in) in the longitudinal direction. Figures
Strengthening methods.
CFS
GCFRP
In Table
Stress level and test results.
CON  CFS  GCFRP  

Static test  Ultimate loads  633 (kN)  732 (kN)  710 (kN)  
Failure mode  PS^{a}  PS^{a}  PS^{a}  



Stress level (%)  40  70  90  60  70  80  60  70  80 
Loads (kN)  260  450  580  440  510  590  430  500  570  
Number of cyclic loading  10^{6}  68,834  10  10^{6}  90,074  19,836  501,982  864,408  20,023  
Failure mode  PS^{b}  PS^{c}  PS^{c}  PS^{b}  PS^{c}  PS^{c}  PS^{d}  PS^{c}  PS^{c}  
Typical failure pattern 



Note: PS^{a}: punching shear failure after yielding of rebar, PS^{b}: punching shear failure due to static loading, PS^{c}: fatigue punching shear, and PS^{d}: fatigue punching shear failure after girder collapse.
Failure patterns of deck panels subjected to less stress appeared to be dominated by initial microcracking at the midpoint, but the failure patterns of deck panels subjected to more stress were similar to those of decks subjected to monotonic loads. Therefore, when designing real concrete decks, it is also important to consider the stress level to control cracking either by strengthening the pattern or the amount.
The failure surface of panels subjected to more stress had a greater angle than that of panels subjected to less stress. In the case of decks strengthened with FRP sheets, complete debonding could not occur because the FRP sheets distributed tensile stresses and kept flexural cracks relatively small. Major cracks on the sheet branched out into numerous minor cracks, because the FRP reinforcement arrested the cracks. As shown in Table
Loaddisplacement relationship of deck specimens under 70% stress level.
CON70
CFS70
CGFRP70
Fatigue damage in strengthened and traditional RC samples consisting of concrete, rebar, and strengthening material cannot be defined using these strain concepts and a numerical approach based on nonlinear fracture mechanics. The residual life cycle of deteriorated RC bridge deck panels is repeatedly subjected to an unknown number of traffic loads and external aggressive effects, so it is difficult to evaluate them using the local strain concepts applied by other researchers. Here, fatigue damage to deck panels before and after strengthening was evaluated based on the loaddisplacement relationship represented by an overall structural response. Fatigue damage will be defined here as
Figure
Ratio of cumulated deflection to maximum deflection at ultimate strength at cyclic loading.
This study conducted probabilistic fatigue analyses to evaluate the fatigue characteristics of bridge deck specimens strengthened with FRP. This probabilistic analysis applied the Weibull distribution to evaluate the probability of failure and hazard function for the specimens. Oh [
The probability of density function (PDF) and cumulative distribution function (CDF) obtained using the Weibull distribution are defined by
The hazard function, which represents the fatigue characteristics of a given concrete specimen, increases harmonically with accumulated fatigue damage [
A probabilistic coefficient of specimens.
CON  CFS  CGGFP  


2.827  1.325  2.702 

30.279  33.254  38.948 

1.795  1.962  1.392 

0.454  0.968  0.475 
The
The appropriate selection of the design fatigue life (
Table
Axle load for the mixed rate of overloaded trucks (kN).
Mixed rate of overloaded trucks  0%  10%  20%  30%  40%  50%  60%  70%  80%  90%  100% 

Axle loads (kN)  84.0  89.0  94.0  99.0  104.0  109.0  113.9  118.9  123.9  128.9  133.9 
Random variables for reliability analysis.
Variables  Mean  COV  Distribution 

Traffic  4,400  0.20  Normal 
Axle load  1.24 × axle load  0.25  Lognormal 
Figure
Failure probability of test specimens.
CON
CFS
CGFRP
CGFRPstrengthened bridge decks had a 20% probability of failure at a 75year service life and an 80% mixing rate of overloaded trucks; when approaching a failure condition, these decks also had a greater margin of probability of failure than did bridges strengthened with CFS. This probability analysis demonstrated that increased truck loads caused increased rates of damage to bridge decks strengthened with CGFRP, more than for bride decks strengthened with CFS when bridge decks approached failure conditions. CFS and CGFRP specimens had failure probabilities of 98% and 92%, respectively, indicating that both CFS and CGFRP strengthening can provide sufficient safety margins for a 75year service life.
Figure
Reliability indexes of the rate of overloaded trucks to the total trucks.
50%
90%
This study proposed another approach to fatigue design for strengthened structures. The test results and considered variables were limited to the proposed fatigue design technique, so more research will be required for more reliable strengthening of deteriorated concrete structures. The bridge deck reliability index evaluation indicated that both CFS and CGFRP strengthening methods could strengthen bridge decks with increased rates of overloaded trucks. Bridge decks strengthened with CFS or CGFRP extended bridge deck fatigue life by 1.2–1.5 times compared to a nonstrengthened bridge deck. The CGFRP strengthening method resulted in a better reliability index than did the CFS strengthening method with regard to both strengthening and extended fatigue lives. Therefore, CGFRP is a more effective strengthening method than CFS for concrete bridge decks.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by research Grants of Korea Institute of Marine Science & Technology Promotion (PJT200493) and National Research Foundation of Korea (NRF20100024085).