research article simplified reliability estimation for optimum...

Research ArticleSimplified Reliability Estimation for OptimumStrengthening Ratio of 30-Year-Old Double T-Beam RailwayBridge by NSM Techniques

Minkwan Ju1 Hongseob Oh2 and Jong-Wan Sun3

1 Department of Civil Engineering Kangwon National University 1 Joonang-ro Kangwon Samcheok 245-711 Republic of Korea2Department of Civil Engineering Gyeongnam National University of Science and Technology 150 Chilam-dong Jinju Gyeongnam660-758 Republic of Korea

3 Research Division G3Way Co Yangjae-dong Seocho Seoul 20-32 Republic of Korea

Correspondence should be addressed to Hongseob Oh opera69cholcom

Received 25 November 2013 Revised 3 March 2014 Accepted 4 March 2014 Published 11 May 2014

Academic Editor Ting-Hua Yi

Copyright copy 2014 Minkwan Ju et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This study is to develop simplified reliability estimation for optimum strengthening ratio of T-beam railway bridge strengthenedby CFRP strip Until now strengthening design has been usually proceeded to satisfy the target load-carrying capacity by using thedeterministic parameter of nominal property for concrete or FRP For the optimum strengthening design however it is requiredthat reliability-based strengthening design should be applied to effectively determine the amount of strengthening material andmake sure of the safety of the structure As applying the reliability-based strengthening ratio more reliable strengthening designusing CFRP strip is possible as well as having a structural redundancy The reliability-based strengthening design methodologysuggested in this study is able to contribute the optimum strengthening design for a concrete structure strengthened by CFRP strip

1 Introduction

FHWA 2009 [1] reported that many existing reinforced con-crete bridges especially superstructures have consistentlyexperienced deteriorations with significant loss of load-carrying capacity As the national budget is decreased forthe new construction the repair and strengthening needshave beenmajor consideration inmaintenance field of infras-tructure In the last decade the conventional strengtheningmaterials have been replaced with fiber reinforced polymer(FRP) materials for strengthening of the deteriorated con-crete structures Among these FRP strengthening materialforms FRP laminate and sheet are widely applied on thesurface of the structure to be strengthened by the externallybonded reinforcing (EBR) technique For this strengtheninghowever the previous researches have raised several kinds ofproblems that the EBR technique cannot sufficiently transfertensile strength of the FRP materials to concrete memberdue to their premature debonding [2] Near surface mounted(NSM) strengthening technique has many advantages for

improving the structural capacity over a conventional ERBstrengthening less site installation work better bondingand structural performance and more effective mainte-nance point of view For these reasons many experimentalresearches have suggested that NSM-FRP strengthening isone of themost reliable strengthening techniques for concretestructures [3ndash5] Although EBR technique needs additionalexternal protection against either the fire attack or an unex-pected collision the NSM strengthening technique providesbetter protection in disaster situations than conventional EBR[6] methods

Also NSM using FRP strips has substantially betterbond resistance because it can be embedded in an adhesiveentirely within the narrow groove of the substrate concreteThis advantage of FRP strips for bonding performance waspreviously demonstrated by Soliman et al [7] In amonotonicload test theNSMCFRP strip demonstrated better anchoragethan the EBR CFRP strips [8 9]

Although many studies for FRP strengthening havebeen conducted previously there are few studies to suggest

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 734016 10 pageshttpdxdoiorg1011552014734016

2 Mathematical Problems in Engineering

24 15 15 15 27 15 18 15 24 24 15 15 15 27 15 18 15 15

90

L-18 S-1820

Length (m)Wheel load (kN)

220

220

24 15 15 15 27 15 18 15 24 24 15 15 15 27 15 18 15 15L-22

20S-22

2203kNm

2420

9

2420

9

440

3

440

3

440

3

440

3

220

220

220

220

110

440

3

440

3

440

3

440

3

220

220

220

230

110

180

180

180

180

120

120

120

120

90 180

180

180

180

120

120

120

120

60kNm

Figure 1 Standard train load in Korea (LS-18 LS-22)

the strengthening guideline such as a strengthening ratioby applying a probabilistic and reliability analysis Thisis important because of the uncertainty for material andstructural point of view on the FRP strengthening methodA parametric study of GFRP rebar for design factors suchas cross-sectional dimension GFRP and concrete strength[10] is conducted Another research is carried out a reli-ability assessment of an FRP-strengthened concrete beamby Chinese codes [11] A parametric study on the effects ofinfluencing factors on average reliability level shows that loadeffect ratio and concrete strength are the first two dominantinfluencing factors among all design variables For designconcepts the conventional ultimate strength design (USD)method is changed to limit state design after 2015 in KoreaTherefore safety and reliability for all structures will beregarded widely as well as the strengthening of concretestructures

This study aims to propose the reliability-based determi-nation procedure on the strengthening ratio of a deterioratedconcrete girder with CFRP strips which has advantages forthe full composite performance with concrete members Thetarget bridge in this study is a double T-beam railway bridgeoriginally designed by LS-18 (an old type of design load fora railway bridge in Korea) Therefore it is required that thetarget bridge should satisfy the present design load (LS-22)and enhance the design speed with the high speed era in thefuture In order to assess the optimal strengthening ratio forthe target bridge in this study the CFRP strip strengtheningmethod was analytically applied to the target bridge

NSM strengthening technique is more effective forenhancing flexural capacity of railway bridge in case vibrationof train traffic due to its superior bond performance Thegoal of this study was to calculate the reliability-basedstrengthening ratio of the concrete beams strengthened byNSM using CFRP strips by applying the reliability indexfor bridge design FE analysis on the deteriorated and thenstrengthened bridge was performed using the design railwayload in the Korea railway specification FEM analysis wasalso used to estimate the amount of steel reinforcements ofthe target bridge due to the absence of structural designinformation of this aged bridge To consider the structural

uncertainties of the strengthening method the probabilityand reliability analysis were performed with Monte Carlosimulation (MCS) Finally the reliability-based strengthen-ing ratio which satisfies the reliability index for the structuraldesign (120573 = 35) is estimated with the structural redundancyfor the target design strength Finally it is suggested thatthe strengthening procedure of the applied probabilistic andreliability approach is a reasonable strengthening designmethod

2 Estimation of the Unknown Property ofTarget Bridge

The target bridge is a simply supported railway bridge inKorea which was built for the design load of LS-18 in 1982 InDesign Specification of Railway ofKorea [15] standard designload is categorized as LS-18 restricted to 120 kmhr and LS-22for high speed railway as depicted in Figure 1 Actual speedand dynamic behavior on the LS-18 train weremonitored andanalyzed by [16]

Figures 2 and 3 show the typical cross-section andlongitudinal view of the RC T bridge

There are some recent diagnosis techniques [17ndash19] Forthis bridge conventional inspection method was appliedSome of deterioration defects such as cracks efflorescencesteel corrosion and concrete segregation were visualized byinspection Whereas the compressive strength of concrete is408MPa the strength of steel rebar is not verified from thefield inspection

To evaluate the requirement of strengthening amount aload-carrying capacity or flexural stiffness for the structuralcondition in service mode should be investigated Due tothe characteristics of this railway bridge dynamic tests forstructural evaluation were performed using in-field moni-toring data for the train loads passing the target point [16]with structural stiffness as the main indicator of structuralcondition For this acceleration data was monitored andcompared with an RC bridge with a similar span length andsize According to Hwang et al [16] the acceleration of thetarget bridge was shown to be over 04 g (1 g is 980 cms2 gal)

Mathematical Problems in Engineering 3

Waterproof mortar

540420350 1520 100 20

8020 2070 7080 80

260

1515

1025

135

95

CL

Figure 2 A cross-section of the target bridge (unit m)

B(T) Haseo-cheon

Centrifugalreinforced

concrete pileempty 300 times 900

FL

H middot W middot L = 10645

L middot W middot L = 10445

Mokpo direction



Daejeondirection

900 900 900 900122 122 1223956

250

140

300

120

90times4

(Southbound lane) 108 km 13

680 L

=3956

Figure 3 A longitudinal view of the target bridge

when the train passed In Europe it is recommended thatthe acceleration should be under 035 g for the preventionof turbulence on the railway in service [20 21] Thus high-level acceleration in service is considered proof of structuralperformance degradation and the appropriate strengtheningmeans to satisfy the serviceability limit are required Tosolve the vibration problem strengthening by FRP compositecan enhance the structural stiffness [22 23] For anotherstrengthening need structural condition was recorded asC-grade after an in-depth inspection conducted in 2003[24] During the bridgersquos 30 years of service time structuralmaterials such as concrete and steel reinforcement havepossibly deteriorated Therefore the target bridge should betreated with structural upgrade maintenance In this studyFRP strip strengthening of the deteriorated target bridge

is an effective strategy and the strengthening ratiomdashthemost significant factor for the strengthening designmdashwillbe suggested through a reliability analysis of material andstructural uncertainties using a reliability index

To assess the amount of adequate strengthening ratio tosatisfy the requirement the unknown reinforcement ratio ofsteel rebar should be reasonably estimated Structural analysison the target bridge without the steel rebar was initiallyperformed to calculate external flexuralmoment subjected byLS-18 design loadsThe structuralmodeling and analysis wereconducted by commercial FEA program [25] The bridgemodel was built by plate and solid elements the dead load likegravel rail was excepted Figure 4 shows the analysis resultsof external flexural moments for dead and live loads Thedesign load factors for dead and live loads were based on the


MIDASCivilPostprocessorBeam forceMoment-120574

179960e + 002

160096e + 002

122768e + 002

141032e + 002

103703e + 002

046392e + 001

655749e + 001

465107e + 001

274455e + 001

000000e + 000

minus106820e + 001

minus297452e + 001

Scale factor =40289E + 002

CB dead allMax 0Min 26File railroadUnit kNmiddotm

X minus0516Y minus0766Z 0383

View-directionDate 4132012

(a) Bending moment diagram for a factored dead loadMIDASCivilPostprocessorBeam forceMoment-120574

Scale factor =

Max 10Min 3File railroadUnit kNmiddotm


View-direction

500095e + 002

514061e + 002

447227e + 002

300393e + 002

313559e + 002

246725e + 002

179891e + 002

112057e + 002

462233e + 001

000000e + 000

minus874446e + 001

minus154279e + 002

119743E + 002Ctall live all

Date 4132012

(b) Bending moment diagram for a factored live load

Figure 4 FE analyses for dead and live loads

design specification of railway of Korea and were 14 and 20respectively

The design flexural moment by FE analysis was calculatedas 7610 kNsdotm With this moment capacity the area of steelrebar can be estimated as 1718mm2 by the moment equi-librium equation for the rectangular beam with an effectivewidth of slab

3 Limit State Function and Safety Index

31 Limit State Function The conventional performancefunction for flexural capacity of the bridge cross-sectionconsists of 119877119863 and 119871 where 119877 is strength resistance or loadcarrying capacity119863 is dead load effect and119871 is live load effectincluding impact [26] For consideration of the limit state thelimit state model to express railway by Cho et al [27] wasadapted and followed as

119892 (sdot) = 119877 minus (119878119863+ 119878119871) (1)

where 119877 is structural resistance and 119878119863and 119878119871are dead and

live load effect respectively 119877 119878119863 and 119878

119871are reexpressed as

follows119877 = 119877

119899sdot 119863119865sdot 119873119877

119878119863= 119862119863sdot 119863119899sdot 119873119863

119878119871= 119862119871sdot 119871119899sdot 119870119878(1 + 119894) sdot 119873

119871

(2)

where 119877119899is estimated nominal strength of undamaged

structures (flexural moment or shear force) 119863119865is damage

coefficient 119873119877is uncertain parameter when 119877

119873and 119863

119865are

estimated119862119863and119862

119871are the effect factor of flexural moment

and shear force for dead and live loads 119863119899and 119871

119899are the

nominal dead and live loads respectively 119870119878is the response

ratio (CalculationMeasure) 119894 is the impact factor and 119873119863

and119873119871are the calibration factors of 119862

119863and 119862

119871 respectively

119873119877can be calculated by PsdotMsdotFsdotD P for uncertainties of

estimation for analytical modelM formaterial strength F forfabrication andD for damage factors In this study structural


h d2 d1

d998400

be

c

120576s120576f

120576998400c

120576cu

fsff

Cc

C998400s

085f998400c

1205731c

Figure 5 Compatibility diagram of strain and strength of the cross-section for strengthening

failure denotes the state when the theoretical flexural capacityis reached Failure occurs if the function119892 is less than or equalto zero

As depicted in Figure 5 the resistancemoment (119872119899) used

in this reliability analysis is calculated by (3) to (6) accordingto the recommendations from ACI Committee 440 [28] andBank [29] In this study the damage factor 119863

119891was newly

applied in the steel rebar terms in (5)

1198621+ 1198622= 1198791+ 1198792 (3)

08511989110158401198881205731119887119890119888 + 11986010158401199041198911015840119904= 119860119904119891119904+ 119860119891119891119891

(4)

119872119899= 119863119891119860119904(1198891minus1205731119888

2) + 120595frb119860119891119891119891 (119867 minus

1205731119888

2) (5)

119872119906ge Φ119872

119899 (6)

where 119860119904is area of tensile steel bar (mm2) 119891

119904is tensile

stress of steel bar (400MPa) ℎ is total height (1250mm)1198891is effective depth of tensile steel bar (1200mm) 119889

2is

effective depth of CFRP strip (1220mm) 1198891015840 is effective depthof compressive steel bar (50mm) 119860

119891is area of CFRP strip

(mm2) 119891119891is effective strength of CFRP strip (119891fuave minus 3120590

MPa) 120595frp is environmental reduction factor (085) Φ isstrength reduction factor (085) 1198911015840

119888is compressive strength

of concrete (41MPa) and 119887119890is effective width of rectangular

beam (1900mm) 119863119891means the damage factor assumed in

the reliability analysis (Table 4)In the case of failure mode of a concrete beam externally

bonded with CFRP materials except in a premature failurecase the following four failure modes are classified represen-tatively

(1) steel yielding and concrete compressive failure beforeCFRP rupture

(2) steel yielding and CFRP rupture after concrete com-pressive failure

(3) CFRP rupture and concrete compressive failurebefore steel yielding

(4) concrete compressive failure before steel yielding andCFRP rupture

Among the Cases 1sim4 Cases 3 and 4 are typicaloverstrengthening failure which leads to brittle failure ofstrengthening beams Cases 1 and 2 however would resultin ductile failure rather than that of Cases 3 and 4 For rea-sonable failure cases Case 1) is more suitable for preventingthe brittle failure because concrete compressive failure is lessbrittle than that of CFRP strip Balanced failure means thata strengthened concrete member fails simultaneously withconcrete compressive failure and CFRP rupture

Structural safety can be conveniently calculated withrespect to the reliability index 120573 as follows

120573 =120583119892

120590119892

(7)

The variables 120583119892and 120590

119892are the terms of the mean and stan-

dard deviation of the performance function 119892 respectivelyThe reliability index for flexural capacity after strengtheningis calculated based on the effective cross-section of the targetbridge with the amount of CFRP strip required to satisfy thestrength for NSM strengthening In this study the reliabilityindex is computed by the Rackwitz-Fiessler algorithm [30]

32 Computational Uncertainty Factors (119870119904) The computa-

tional uncertainties 119870119904 are adapted to be considered in pre-

dicting resistance The statistics for randomness are definedbased on analytical results or test results Some analytical andtest results are introduced by a literature review of previousresearch papers for reliability analysis [10] In this study itis assumed that statistics of the computational uncertaintyfactor in concrete crushing mode are effective to estimatethe strengthening ratio by reliability analysisThus from datafrom a total of 91 specimens 1061 of mean value and 009 ofstandard deviation resulted The following equation denotesthe computational uncertainties in this analysis

119870119904=119872119880exp

119872119880pre

(8)

33 Damage Factor Cho et al [31] have theoretically definedthat the damage factor is the ratio of stiffness for a non-damaged structure to a damaged structure For quantitative


Select the target structure forNSM strengthening

Constitute the limit state function

Calculate the external moment

Define of material and structural uncertainty

Calculate the resistance moment and perform reliability analysis

Determine the strengthening ratio of CFRP strip

Reassuming the CFRP

strengthening ratio

No

Yes

120573 = 35

Figure 6 A procedure for determining the reliability-based strengthening ratio of CFRP strip with a target reliability index of 35

approaches it can be calculated by using the ratio of powerof natural frequency for a damaged structure to that fora nondamaged structure In actual state however it is notasserted that this ratio can directly represent the degreeof damage Estimating the damage factor is hard to bedetermined without the plentiful history data so that thedamage factor in this study is assumed by previous research[29] Therefore the average of damage factor is ranged from06 to 09 anduncertainty of damage factor is considered from01 to 03 of coefficient of variation With this statistical datathe probability and reliability analysis are carried out and aresult of sensitive analysis for the variation of damage factoris discussed

4 Characteristics of Random Variables

For reliability analyses the statistics of random variables aredefined in advance There are three variables considered inthis analysis external load for dead and live ones materialstrength of concrete steel rebar and CFRP strip and designof cross-section

In the reliability analysis for structural safety it is essentialthat the load effect must be considered by combining thevariability of loads dead and live loads A related study wasconducted and suggested the load and resistance factors forRC concrete design [32] Table 1 shows the statistics of theload effect for dead and live load for reliability analysis [33]Among these mean value is the external moment resulting

from FE analysis to the target bridge and load factor is basedon the KR specification

The statistics of resistance-related variables such as 1198911015840119888 ℎ

and 119889 listed in Table 2 are adopted from Ellingwood [32]Also included in Table 2 are the statistics of the strength ofCFRP strip (119891fu) for Barros and Fortes [34] and of the width(119887) of T-beam for Oh et al [13] In the case of the nominalvalue of ℎ and 119889 the real dimension of the cross section inthe target bridge is used For steel rebar statistics from manyof tensile tests are summarized in Table 3 [35] As comparedwith Grade series by ASTM A 165 SD30 SD35 and SD40rebar considered in the reliability analysis showed relativelybetter coefficient of variation The probability distributionwas considered as normal type In this study statistics ofSD40 in Korea were adopted in reliability analysis

5 Reliability-Based Strengthening Ratio ofCFRP Strip

51 Target Safety Index in Reliability Analysis This studyis to calculate the reliability-based strengthening ratio ofCFRP strip to the existing railway bridge which has struc-tural uncertainties Therefore it is important to define howmuch structural safety should be acquired This is simplydetermined by using the reliability index or the target safetyfactor 120573 in the load and resistance analysis Previous studyhas shown that 120573 values of 25sim30 and 30sim35 were used


Table 1 Result of FEM analysis for external railway load

Probability distribution MeanNominal Mean COVa Load factorDead load Normal 105 1800 kNsdotm 01 14Live load Lognormal 100 5808 kNsdotm 02ndash04 20aCOV coefficient of variation

Table 2 Statistics of random design variables (I)

Design variable Nominal value Mean value Standard deviation Probability distribution119891119888

1015840 (MPa) 4134 4616 194 Normal119891fu (MPa)a mdash 2790 857 Normal119887 (mm)b 1900 119887 + 094 60 Normalℎ (mm)c 1250 ℎ minus 305 635 Normal119889 (mm)c 1200 119889 minus 470 1270 NormalaISO 527-3 (1997)[12] bOh et al (1993) [13] ccross-sectional dimension of the target bridge

Table 3 Statistics of random design variables (II)

MeanNominal COV Average strength Number of data Standard deviation Probability distributionSD 30a 120 0064 3600 822 2304 NormalSD 35a 113 0038 3955 80 1503 NormalSD 40a 109 0048 4360 773 2093 NormalGrade 40b 113 0116 3170 mdash 3672 NormalGrade 60b 112 0098 4725 mdash 4631 NormalaKS D 3504bASTM A 615 Standard Specification for Deformed and Plain Carbon Steel Bars for Concrete Reinforcement-AASHTO No M 31 [14]

for tension failure and compression failure respectively [36]Kulicki et al [37] proposed the target or code-specifiedreliability indices obtained from reliability analysis of a groupof 175 existing actual bridges designed by either ASD or LFDmethod and then suggested the range of values using the newload and resistance factors From this research AASHTOaltered the reliability index to 35 when either a higher levelof safety or taking more risk was appropriate [38] Accordingto the recent research [39] the target beta for beam is 35for flexural strength of RC beams constructed with lightweight and normal weight concrete In this study the targetreliability index is determined with 35 and a reliability-basedstrengthening ratio satisfying the probability index 120573 = 35will be calculated

52 Result of Reliability Analysis To evaluate the reliability-based strengthening ratio of the target bridge the probabilitydistribution between the external load and structural resis-tance from the limit state function was analyzed A safetymargin was used and 120573

119879= 35 of target reliability index was

specified by AASHTO [38] Figure 6 is a process to calculatestrengthening ratio of CFRP strip by reliability analysis witha reliability index of 35 FEM analysis should be conductedto determine the external moment for dead and live loadsStructural resistance is affected as when strengthening ratioof CFRP strip is variedTherefore iteration process is neededuntil safety margin of 35 of the strengthening bridge againstexternal load is acquired

0

00005

0001

00015

0002

00025

0003

00035

0004

00045

Prob

abili

ty d

ensit

y

0 500 1000 1500 2000 2500 3000Flexural moment (kNmiddotm)

Q(LS-18)Q(LS-22)R for LS-18Case1 (120588cfrp = 00001)

Case2 (120588cfrp = 0000108)Case3 (120588cfrp = 0000114)Case4 (120588cfrp = 0000122)Case5 (120588cfrp = 0000130)

LS-22

R for LS-18

LS-18

Strengthening effect at 120573T = 35

Figure 7 Probability distribution curves for external load andresistance

Figure 7 is the probability distribution curves for externalload and resistance resulted from the reliability analysisFor external loads the probability distribution of LS-22was additionally considered to investigate the how muchthe strengthening effect of CFRP strips can decrease theprobability of failure compared LS-22 design load 119876 meansthe external load and 119877 is for the resistance moment


Table 4 Sensitive analysis for damage factor standard deviation of damage factor and live load effect

Damage factor Standard deviation COV 120588CFRP at 120573119879 = 35 Live load moment Standard deviation COVCase 1 07 014 02 0000128 2904 8712 03Case 2 08 016 02 0000114 2904 8712 03Case 3 09 018 02 0000102 2904 8712 03Case 4 08 008 01 0000048 2904 8712 03Case 5 08 016 02 0000114 2904 8712 03Case 6 08 024 03 0000196 2904 8712 03Case 7 08 016 02 0000095 2904 5808 02Case 8 08 016 02 0000114 2904 8712 03Case 9 08 016 02 0000137 2904 11616 04

320

330

340

350

360

370

0000100 0000108 0000114 0000122 0000130

Reliability-based strengthening ratio

120573

120588cfrp

Figure 8 Critical strengthening ratio of CFRP strip strengthenedby NSM

0

000005

00001

000015

00002

000025

0 01 02 03 04 05 06 07 08 09 1Applied parametric value

Degree of sensitive for COV of Degree of sensitive for COV of live load factorDegree of sensitive for average value of

120588cf

rp

Df

Df

Figure 9 Sensitive analysis for COV and average value of 119863119891and

COV of live load factor

Strengthening effect is denoted as a case series FEM analysiswas performed to calculate the external moment for LS-18and LS-22 design railway load For probability distribution ofLS-22 which is the present design load of railway in Korea

probability characteristics for LS-18 were used in the sameway In order to acquire the reliability-based strengtheningratio for 120573

119879= 35 the range of probability parameters was

roughly considered then the final 5 cases for 120588cfrp from 00001to 000013 were analyzed Each probability distribution curveis illustrated in Figure 7 Figure 8 is the result of reliability-based strengthening ratio According to the result of thestrengthening effect by probability distribution the targetbridge strengthened by the CFRP strip strengthening ratioresulting from the reliability analysis could be sufficientlysafe against the LS-22 present design railway load As thestrengthening ratio of CFRP strip that could satisfy 120573

119879= 35

it was with 120588cfrp = 0000114

53 Sensitive Analysis for Three Important ParametersFigure 9 shows the result of sensitive analysis for three param-eters such as damage factor standard deviation of damagefactor and live load effect The CFRP strip strengtheningratio resulting from the reliability analysis is plotted withthree important parameters The purpose of this process isto identify how sensitively the strengthening ratio will beaffected when the three parameters are varied independentlyThe determination of the variation ranges of the parameterswas considered to simply but effectively apply the sensitivecharacteristics For live loads and damage factor there weresimilar degrees of sensitivity Variation of COV of damagefactor however was more sensitive than that of the otherparameters Itmight be concluded that COVof damage factorlargely affected to estimate the reliability-based strengtheningusing about the CFRP strip For more reliable estimation ofdamage factor many of structural diagnosis data should beanalyzed in future Table 4 summarizes the input parametersused in the sensitive analysis

6 Conclusions

This study suggested the reliability-based strengthening ratiofor 30-year-old railway bridge using CFRP strips Conclu-sions are as follows

(1) In previous strengthening schemes it has beenuncertain to determine how much the strengthen-ing effect should be required The methodology forthe reliability-based strengthening ratio can improve


these problems of the previous strengtheningmethodThe target reliability index for CFRP strip strengthen-ing is considered as 35 according to AASHTO spec-ification As using the reliability-based strengtheningratio in this studymore effective strengthening designto concrete structure having a specified strength-ening target as well as reflecting the structural andmaterial uncertainties is possible

(2) In the result of a sensitive analysis variation of COVfor damage factor mostly affected to the reliability-based strengthening ratio of CFRP strip Thereforedamage factor should be studied more properly onthe target bridge This may be possible by analyzingthe database for long-term safety inspection historyand its reasonable quantification Stabilization andnormalization processes of the damage factor are alsorequired

(3) One of the important factors for determining thesafety margin against the resistance is external loadeffect In order to improve the reliability-basedstrengthening ratio of CFRP strip in this study uncer-tainties for external load of a railway bridge should beanalytically and experimentally verified This can besolved by analyzing the acquired data from long-termmonitoring then the reliability of the strengtheningratio of CFRP strip will be promoted

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was supported by Korea Institute of EnergyTechnology Evaluation and Planning (0000000015513) andResearch grant from Gyeongnam National University ofScience and Technology

References

[1] FHWA Bridge Programs NBI data 2009 httpwwwfhwadotgovbridgenbi

[2] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening Con-crete Structures (ACI 4402R-08) American Concrete InstituteFarmington Hills Mich USA 2008

[3] J M de Sena Cruz and J A O De Barros ldquoBond between near-surface mounted carbon-fiber-reinforced polymer laminatestrips and concreterdquo Journal of Composites for Construction vol8 no 6 pp 519ndash527 2004

[4] T Hassan and S Rizkalla ldquoInvestigation of bond in concretestructures strengthened with near surface mounted carbonfiber reinforced polymer stripsrdquo Journal of Composites forConstruction vol 7 no 3 pp 248ndash257 2003

[5] S M Soliman E El-Salakawy and B Benmokrane ldquoFlexuralbehavior of concrete beams strengthened with near surfacemounted FRP barsrdquo in Proceedings of 4th International confer-ence on FRP composites in civil engineering (CICE rsquo08) 2008

[6] J P Firmo J R Correia and P Franca ldquoFire behaviour ofreinforced concrete beams strengthened with CFRP laminatesprotection systems with insulation of the anchorage zonesrdquoComposites Part B Engineering vol 43 no 3 pp 1545ndash15562012

[7] S M Soliman E El-Salakawy and B Benmokrane ldquoBondperformance of near-surface-mounted FRP barsrdquo Journal ofComposites for Construction vol 15 no 1 pp 103ndash111 2011

[8] THassan and S Rizkalla ldquoFlexural strengthening of prestressedbridge slabs with FRP systemsrdquo PCI Journal vol 47 no 1 pp76ndash93 2002

[9] J R Yost S P Gross and D W Dinehart ldquoNear surfacemounted CFRP reinforcement for structural retrofit of concreteflexural membersrdquo in Proceedings of the 4th InternationalConference on Advanced Composite Materials in Bridges andStructures Calgary Canada 2004

[10] Z He and F Qiu ldquoProbabilistic assessment on flexural capacityof GFRP-reinforced concrete beams designed by guideline ACI4401R-06rdquo Construction and Building Materials vol 25 no 4pp 1663ndash1670 2011

[11] Z He and L Jiang ldquoFlexural reliability assessment of FRP-strengthened reinforced concrete beams designed by ChineseCECS-146 Guidelinerdquo Pacific Science Review vol 9 no 1 pp123ndash133 2007

[12] International Organization for Standardization ldquoDetermina-tion of tensile properties-part 5 test conditions for unidirec-tional fibre reinforced plastic compositesrdquo ISO 527-5 Interna-tional Organization for Standardization Geneva Switzerland1997

[13] B H Oh C K Koh S W Baik H J Lee and S H HanldquoRealistic reliability analysis of reinforced concrete structuresrdquoJournal of Korea Society of Civil Engineering vol 13 no 2 pp121ndash133 1993 (Korean)

[14] Steel bars for concrete reinforcement KS D 3504 KoreanIndustrial Standards 2011 (Korean)

[15] KR Network Design Specification of Railway Railway BridgeKorea Rail Network Authority Seoul Republic of Korea 2004(Korean)

[16] S K Hwang J T Oh J S Lee et al Performance Enhancementof Railway System-Track amp Civil Development of the DesignSpecification for Improving Dynamic Characteristics of RailwayBridges Korea Railway Research Institute Seoul Republic ofKorea 2003 (Korean)

[17] H S Shang T H Yi and L S Yang ldquoExperimental studyon the compressive strength of big mobility concrete withnondestructive testing methodrdquo Advances in Materials Scienceand Engineering vol 2012 Article ID 345214 6 pages 2012

[18] TH YiHN Li andHM Sun ldquoMulti-stage structural damagediagnosis method based on ldquoenergy-damagerdquo theoryrdquo SmartStructures And Systems vol 12 no 3-4 pp 345ndash361 2013

[19] H S Shang T H Yi and X X Guo ldquoStudy on strength andultrasonic of air-entrained concrete and plain concrete in coldenvironmentrdquo Advances in Materials Science and Engineeringvol 2014 Article ID 706986 7 pages 2014

[20] Korea High Speed Rail Construction Authority (KHRC)ldquoBridge designmanual (BRDM)rdquo Technical Report KoreaHighSpeed Rail Construction Authority (KHRC) Pusan Public ofKorea 1995 (Korean)

[21] International Union of Railway UIC Code 776-1R Loads to BeConsidered in Railway Bridge Design International Union ofRailway Paris France 4th edition 1994


[22] M Abdessemed S Kenai A Bali and A Kibboua ldquoDynamicanalysis of a bridge repaired by CFRP experimental andnumerical modellingrdquoConstruction and BuildingMaterials vol25 no 3 pp 1270ndash1276 2011

[23] G Zanardo H Hao Y Xia and A J Deeks ldquoStiffness assess-ment through modal analysis of an RC slab bridge before andafter strengtheningrdquo Journal of Bridge Engineering vol 11 no 5pp 590ndash601 2006

[24] Korea Infrastructure Safety and Technology corporation(KISTEC) A Database of Maintenance History KoreaInfrastructure Safety and Technology corporation (KISTEC)Gyeonggi-do Republic of Korea 2003 (Korean)

[25] MIDAS IT MIDAS Civil Program Manual MIDAS ITGyeonggi Republic of Korea 2009

[26] S W Tabsh and A S Nowak ldquoReliability of highway girderbridgesrdquo Journal of Structural Engineering ASCE vol 117 no 8pp 2372ndash2388 1991

[27] H N Cho K H Kwak and S J Lee ldquoReliability-based safetyand capacity evaluation of high-speed railway bridgesrdquo Journalof Computational Structural Engineering Institute in KoreaCOSEIK vol 10 no 3 pp 133ndash143 1997 (Korean)

[28] ACI Committee 440 Guide for the Design and Constructionof Externally Bonded FRP Systems for Strengthening ConcreteStructures American Concrete Institute Farmington HillsMich USA 2008

[29] L C Bank Composites for Construction-Structural Design withFRP Materials John Wiley amp Sons New York NY USA 2006

[30] R Rackwitz and B Flessler ldquoStructural reliability under com-bined random load sequencesrdquo Computers and Structures vol9 no 5 pp 489ndash494 1978

[31] H N Cho H H Choi S Y Lee and J W Sun ldquoMethodologyfor reliability-based assessment of capacity-rating of plate girderrailway bridges using ambient measurement datardquo Journal ofKorea Society of Steel Construction vol 15 no 2 pp 187ndash1962003 (Korean)

[32] B Ellingwood Reliability Bases of Load and Resistance Factorsfor Reinforced Concrete Design National Bureau of StandardsBuilding Science Series 110 Washington DC USA 1978

[33] US Department of CommreceNational Bureau of StandardsldquoDevelopment of a probability based load criteria for Amer-ican National Standard A58rdquo NBS Special Publication 577US Department of CommreceNational Bureau of StandardsGaithersburg Md USA 1980

[34] J A O Barros and A S Fortes ldquoFlexural strengthening ofconcrete beamswithCFRP laminates bonded into slitsrdquoCementand Concrete Composites vol 27 no 4 pp 471ndash480 2005

[35] S H Kim H K Cho H W Bae and H S Park ldquoReliabilityevaluation of structures-a case of reinforced concrete buildingsunder dead live and wind loadsrdquo Technical Report KoreaInstitute of Construction Technology 1989 (Korean)

[36] J G MacGregor ldquoLoad and resistance factors for concretedesignrdquo Journal of the American Concrete Institute vol 80 no4 pp 279ndash287 1983

[37] J M Kulicki D R Mertz and W G Wassef ldquoLRFD Designof highway bridgesrdquo NHI Course 13061 Federal HighwayAdministration Washington DC USA 1994

[38] AASHTO Bridge Design Practice American Association ofState Highway and Transportation Officials Washington DCUSA 2011

[39] A S Nowak and A M Rakoczy ldquoReliability-based calibrationof design code for concrete structures (ACI 318)rdquo in Proceeding

of the Anais do 54 Congress Brasileiro do Concreto CBC2012-54CBC pp 1ndash12 2012

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


24 15 15 15 27 15 18 15 24 24 15 15 15 27 15 18 15 15

90

L-18 S-1820

Length (m)Wheel load (kN)

220

220

24 15 15 15 27 15 18 15 24 24 15 15 15 27 15 18 15 15L-22

20S-22

2203kNm

2420

9

2420

9

440

3

440

3

440

3

440

3

220

220

220

220

110

440

3

440

3

440

3

440

3

220

220

220

230

110

180

180

180

180

120

120

120

120

90 180

180

180

180

120

120

120

120

60kNm

Figure 1 Standard train load in Korea (LS-18 LS-22)

the strengthening guideline such as a strengthening ratioby applying a probabilistic and reliability analysis Thisis important because of the uncertainty for material andstructural point of view on the FRP strengthening methodA parametric study of GFRP rebar for design factors suchas cross-sectional dimension GFRP and concrete strength[10] is conducted Another research is carried out a reli-ability assessment of an FRP-strengthened concrete beamby Chinese codes [11] A parametric study on the effects ofinfluencing factors on average reliability level shows that loadeffect ratio and concrete strength are the first two dominantinfluencing factors among all design variables For designconcepts the conventional ultimate strength design (USD)method is changed to limit state design after 2015 in KoreaTherefore safety and reliability for all structures will beregarded widely as well as the strengthening of concretestructures

This study aims to propose the reliability-based determi-nation procedure on the strengthening ratio of a deterioratedconcrete girder with CFRP strips which has advantages forthe full composite performance with concrete members Thetarget bridge in this study is a double T-beam railway bridgeoriginally designed by LS-18 (an old type of design load fora railway bridge in Korea) Therefore it is required that thetarget bridge should satisfy the present design load (LS-22)and enhance the design speed with the high speed era in thefuture In order to assess the optimal strengthening ratio forthe target bridge in this study the CFRP strip strengtheningmethod was analytically applied to the target bridge

NSM strengthening technique is more effective forenhancing flexural capacity of railway bridge in case vibrationof train traffic due to its superior bond performance Thegoal of this study was to calculate the reliability-basedstrengthening ratio of the concrete beams strengthened byNSM using CFRP strips by applying the reliability indexfor bridge design FE analysis on the deteriorated and thenstrengthened bridge was performed using the design railwayload in the Korea railway specification FEM analysis wasalso used to estimate the amount of steel reinforcements ofthe target bridge due to the absence of structural designinformation of this aged bridge To consider the structural

uncertainties of the strengthening method the probabilityand reliability analysis were performed with Monte Carlosimulation (MCS) Finally the reliability-based strengthen-ing ratio which satisfies the reliability index for the structuraldesign (120573 = 35) is estimated with the structural redundancyfor the target design strength Finally it is suggested thatthe strengthening procedure of the applied probabilistic andreliability approach is a reasonable strengthening designmethod

2 Estimation of the Unknown Property ofTarget Bridge

The target bridge is a simply supported railway bridge inKorea which was built for the design load of LS-18 in 1982 InDesign Specification of Railway ofKorea [15] standard designload is categorized as LS-18 restricted to 120 kmhr and LS-22for high speed railway as depicted in Figure 1 Actual speedand dynamic behavior on the LS-18 train weremonitored andanalyzed by [16]

Figures 2 and 3 show the typical cross-section andlongitudinal view of the RC T bridge

There are some recent diagnosis techniques [17ndash19] Forthis bridge conventional inspection method was appliedSome of deterioration defects such as cracks efflorescencesteel corrosion and concrete segregation were visualized byinspection Whereas the compressive strength of concrete is408MPa the strength of steel rebar is not verified from thefield inspection

To evaluate the requirement of strengthening amount aload-carrying capacity or flexural stiffness for the structuralcondition in service mode should be investigated Due tothe characteristics of this railway bridge dynamic tests forstructural evaluation were performed using in-field moni-toring data for the train loads passing the target point [16]with structural stiffness as the main indicator of structuralcondition For this acceleration data was monitored andcompared with an RC bridge with a similar span length andsize According to Hwang et al [16] the acceleration of thetarget bridge was shown to be over 04 g (1 g is 980 cms2 gal)


Waterproof mortar

540420350 1520 100 20

8020 2070 7080 80

260

1515

1025

135

95

CL


B(T) Haseo-cheon



FL



Mokpo direction



Daejeondirection

900 900 900 900122 122 1223956

250

140

300

120

90times4


680 L

=3956







179960e + 002

160096e + 002

122768e + 002

141032e + 002

103703e + 002

046392e + 001

655749e + 001

465107e + 001

274455e + 001

000000e + 000

minus106820e + 001

minus297452e + 001






Scale factor =



View-direction

500095e + 002

514061e + 002

447227e + 002

300393e + 002

313559e + 002

246725e + 002

179891e + 002

112057e + 002

462233e + 001

000000e + 000

minus874446e + 001

minus154279e + 002


Date 4132012







119892 (sdot) = 119877 minus (119878119863+ 119878119871) (1)




follows119877 = 119877

119899sdot 119863119865sdot 119873119877

119878119863= 119862119863sdot 119863119899sdot 119873119863

119878119871= 119862119871sdot 119871119899sdot 119870119878(1 + 119894) sdot 119873

119871

(2)




119873and 119863

119865are




119899are the




119863and 119862

119871 respectively




h d2 d1

d998400

be

c

120576s120576f

120576998400c

120576cu

fsff

Cc

C998400s

085f998400c

1205731c





119891was newly


1198621+ 1198622= 1198791+ 1198792 (3)

08511989110158401198881205731119887119890119888 + 11986010158401199041198911015840119904= 119860119904119891119904+ 119860119891119891119891

(4)

119872119899= 119863119891119860119904(1198891minus1205731119888

2) + 120595frb119860119891119891119891 (119867 minus

1205731119888

2) (5)

119872119906ge Φ119872

119899 (6)


119904is tensile


2is
















120573 =120583119892

120590119892

(7)







119870119904=119872119880exp

119872119880pre

(8)









Reassuming the CFRP

strengthening ratio

No

Yes

120573 = 35























0

00005

0001

00015

0002

00025

0003

00035

0004

00045

Prob

abili

ty d

ensit

y




LS-22

R for LS-18

LS-18







320

330

340

350

360

370

0000100 0000108 0000114 0000122 0000130


120573

120588cfrp


0

000005

00001

000015

00002

000025



120588cf

rp

Df

Df







119879= 35



6 Conclusions









Acknowledgments


References

















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Waterproof mortar

540420350 1520 100 20

8020 2070 7080 80

260

1515

1025

135

95

CL


B(T) Haseo-cheon



FL



Mokpo direction



Daejeondirection

900 900 900 900122 122 1223956

250

140

300

120

90times4


680 L

=3956







179960e + 002

160096e + 002

122768e + 002

141032e + 002

103703e + 002

046392e + 001

655749e + 001

465107e + 001

274455e + 001

000000e + 000

minus106820e + 001

minus297452e + 001






Scale factor =



View-direction

500095e + 002

514061e + 002

447227e + 002

300393e + 002

313559e + 002

246725e + 002

179891e + 002

112057e + 002

462233e + 001

000000e + 000

minus874446e + 001

minus154279e + 002


Date 4132012







119892 (sdot) = 119877 minus (119878119863+ 119878119871) (1)




follows119877 = 119877

119899sdot 119863119865sdot 119873119877

119878119863= 119862119863sdot 119863119899sdot 119873119863

119878119871= 119862119871sdot 119871119899sdot 119870119878(1 + 119894) sdot 119873

119871

(2)




119873and 119863

119865are




119899are the




119863and 119862

119871 respectively




h d2 d1

d998400

be

c

120576s120576f

120576998400c

120576cu

fsff

Cc

C998400s

085f998400c

1205731c





119891was newly


1198621+ 1198622= 1198791+ 1198792 (3)

08511989110158401198881205731119887119890119888 + 11986010158401199041198911015840119904= 119860119904119891119904+ 119860119891119891119891

(4)

119872119899= 119863119891119860119904(1198891minus1205731119888

2) + 120595frb119860119891119891119891 (119867 minus

1205731119888

2) (5)

119872119906ge Φ119872

119899 (6)


119904is tensile


2is
















120573 =120583119892

120590119892

(7)







119870119904=119872119880exp

119872119880pre

(8)









Reassuming the CFRP

strengthening ratio

No

Yes

120573 = 35























0

00005

0001

00015

0002

00025

0003

00035

0004

00045

Prob

abili

ty d

ensit

y




LS-22

R for LS-18

LS-18







320

330

340

350

360

370

0000100 0000108 0000114 0000122 0000130


120573

120588cfrp


0

000005

00001

000015

00002

000025



120588cf

rp

Df

Df







119879= 35



6 Conclusions









Acknowledgments


References

















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











179960e + 002

160096e + 002

122768e + 002

141032e + 002

103703e + 002

046392e + 001

655749e + 001

465107e + 001

274455e + 001

000000e + 000

minus106820e + 001

minus297452e + 001






Scale factor =



View-direction

500095e + 002

514061e + 002

447227e + 002

300393e + 002

313559e + 002

246725e + 002

179891e + 002

112057e + 002

462233e + 001

000000e + 000

minus874446e + 001

minus154279e + 002


Date 4132012







119892 (sdot) = 119877 minus (119878119863+ 119878119871) (1)




follows119877 = 119877

119899sdot 119863119865sdot 119873119877

119878119863= 119862119863sdot 119863119899sdot 119873119863

119878119871= 119862119871sdot 119871119899sdot 119870119878(1 + 119894) sdot 119873

119871

(2)




119873and 119863

119865are




119899are the




119863and 119862

119871 respectively




h d2 d1

d998400

be

c

120576s120576f

120576998400c

120576cu

fsff

Cc

C998400s

085f998400c

1205731c





119891was newly


1198621+ 1198622= 1198791+ 1198792 (3)

08511989110158401198881205731119887119890119888 + 11986010158401199041198911015840119904= 119860119904119891119904+ 119860119891119891119891

(4)

119872119899= 119863119891119860119904(1198891minus1205731119888

2) + 120595frb119860119891119891119891 (119867 minus

1205731119888

2) (5)

119872119906ge Φ119872

119899 (6)


119904is tensile


2is
















120573 =120583119892

120590119892

(7)







119870119904=119872119880exp

119872119880pre

(8)









Reassuming the CFRP

strengthening ratio

No

Yes

120573 = 35























0

00005

0001

00015

0002

00025

0003

00035

0004

00045

Prob

abili

ty d

ensit

y




LS-22

R for LS-18

LS-18







320

330

340

350

360

370

0000100 0000108 0000114 0000122 0000130


120573

120588cfrp


0

000005

00001

000015

00002

000025



120588cf

rp

Df

Df







119879= 35



6 Conclusions









Acknowledgments


References

















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










h d2 d1

d998400

be

c

120576s120576f

120576998400c

120576cu

fsff

Cc

C998400s

085f998400c

1205731c





119891was newly


1198621+ 1198622= 1198791+ 1198792 (3)

08511989110158401198881205731119887119890119888 + 11986010158401199041198911015840119904= 119860119904119891119904+ 119860119891119891119891

(4)

119872119899= 119863119891119860119904(1198891minus1205731119888

2) + 120595frb119860119891119891119891 (119867 minus

1205731119888

2) (5)

119872119906ge Φ119872

119899 (6)


119904is tensile


2is
















120573 =120583119892

120590119892

(7)







119870119904=119872119880exp

119872119880pre

(8)









Reassuming the CFRP

strengthening ratio

No

Yes

120573 = 35























0

00005

0001

00015

0002

00025

0003

00035

0004

00045

Prob

abili

ty d

ensit

y




LS-22

R for LS-18

LS-18







320

330

340

350

360

370

0000100 0000108 0000114 0000122 0000130


120573

120588cfrp


0

000005

00001

000015

00002

000025



120588cf

rp

Df

Df







119879= 35



6 Conclusions









Acknowledgments


References

















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Reassuming the CFRP

strengthening ratio

No

Yes

120573 = 35























0

00005

0001

00015

0002

00025

0003

00035

0004

00045

Prob

abili

ty d

ensit

y




LS-22

R for LS-18

LS-18







320

330

340

350

360

370

0000100 0000108 0000114 0000122 0000130


120573

120588cfrp


0

000005

00001

000015

00002

000025



120588cf

rp

Df

Df







119879= 35



6 Conclusions









Acknowledgments


References

















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















0

00005

0001

00015

0002

00025

0003

00035

0004

00045

Prob

abili

ty d

ensit

y




LS-22

R for LS-18

LS-18







320

330

340

350

360

370

0000100 0000108 0000114 0000122 0000130


120573

120588cfrp


0

000005

00001

000015

00002

000025



120588cf

rp

Df

Df







119879= 35



6 Conclusions









Acknowledgments


References

















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












320

330

340

350

360

370

0000100 0000108 0000114 0000122 0000130


120573

120588cfrp


0

000005

00001

000015

00002

000025



120588cf

rp

Df

Df







119879= 35



6 Conclusions









Acknowledgments


References

















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















Acknowledgments


References

















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article simplified reliability estimation for optimum...

Documents