fatigue analysis and life prediction of bridges with structural health monitoring data

International Journal of Fatigue 23 (2001) 4553www.elsevier.com/locate/ijfatigue

Fatigue analysis and life prediction of bridges with structuralhealth monitoring data Part I: methodology and strategy

Z.X. Li 1,*, T.H.T. Chan, J.M. KoDepartment of Civil and Structural Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong

Received 20 September 1999; received in revised form 4 April 2000; accepted 9 June 2000

Abstract

This paper is aimed at developing a methodology and strategy for fatigue damage assessment and life prediction of bridge-decksections of existing bridges with online structural health monitoring data. A fatigue damage model based on the continuum damagemechanics (CDM) is developed for evaluating accumulative fatigue damage of existing bridges. A structural model for the fatiguestress analysis of bridge-deck structures is proposed, in which structures are modeled by elastic members and welded connectionswith possible accumulative damage. Based on the proposed model, an analytical approach for evaluating the fatigue damage andservice life of bridge-deck sections based on strain history data from an online structural health monitoring system and the CDMfatigue model are suggested. The updating of the representative block of cycles of the local stress by online monitoring data in thefuture is included in the computational approach. In order to compare results of fatigue damage and service life prediction evaluatedby the CDM fatigue damage model, a modified PalmgrenMiner rule is developed for the same fatigue problem. 2001 ElsevierScience Ltd. All rights reserved.

Keywords: Structural health monitoring; Fatigue damage; Life prediction; Bridge-deck section; Representative block of cycles; Continuumdamage mechanics

1. Introduction

Structural health monitoring has been accepted as ajustified effort for long-span bridges which are criticalto a regions economic vitality, such as the Tsing MaBridge, the Kap Shui Mun Bridge and the Ting KauBridge in Hong Kong and others. While instrumentationsystems, Wind And Structural Health Monitoring Sys-tem (WASHMS) [1,2], are being installed on thesebridges, a common concerned problem is how to takefull advantage of the real-time monitoring data for effec-tive and reliable health assessment of the structures. Asan important part of structural health, durability of thebridge structures is mainly dominated by the fatiguebehavior of the critical elements of the bridge. On theother hand, fatigue design of bridges according to the

* Corresponding author. College of Civil Engineering, SoutheastUniversity, 2 Si Pai Lou, Nanjing, 210018, Peoples Republic ofChina. Tel.: +86-25-3793384; fax: +86-25-7712719.

E-mail address: [email protected] (Z.X. Li).1 On leave from Southeast University, Nanjing, 210018, P.R. China.

0142-1123/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.PII: S0142- 11 23 (00)00 06 8- 2

code [3] is limited by design loading which may have asignificant effect on the service of bridges. All of thesesuggest that the fatigue analysis is significant for thesafety of these bridges.

There have been a lot of researches on fatigue damageanalysis and life prediction theories [46]. The basicconcept and relative law of cumulative fatigue damagewere proposed by Miner [7] in 1945. His linear rule nowis applied to almost all of the fatigue design. However,the life prediction based on this rule is often unsatisfac-tory for fatigue under variable-amplitude loading [5],since the following effects on fatigue damage accumu-lation are not considered in Miners rule: (1) load cyclesbelow the fatigue limit which can propagate micro-cracks if the cracks are initiated by load cycles withamplitude higher than the fatigue limit; (2) the loadsequence effect. After the work by Miner, many differentfatigue damage models have been developed, whichinclude: (1) the works as an improvement of Minersrule, such as the double linear damage rule [8], the dam-age curve approach, refined double linear damage rule[9] and the double damage curve approach [10]; (2)

46 Z.X. Li et al. / International Journal of Fatigue 23 (2001) 4553

fatigue damage theories based on plastic strain energyor total strain energy [1115]; and (3) fatigue damagetheory based on the new subject of mechanics, con-tinuum damage mechanics [1621], which is speciallysuitable for the period of fatigue crack initiation,although it is still at the primary stage of laboratorystudy. A little work on bridge fatigue damage evaluationhas been made in recent years. For example, Zhao [22]used a linear elastic fracture mechanics-based reliabilitymodel which was updated through non-destructiveinspections to evaluate the fatigue damage of steelbridges; Zheng et al. [23] experimentally investigated thefatigue life of the steel of an old bridge by using speci-mens cut from the chords of the old riveted steel bridge;Agerskov and Nielsen [24] studied the fatigue damageaccumulation in steel highway bridges under randomloading by experiments and the analysis based on frac-ture mechanics; Enright and Frangopol [25] applied thetime-variant reliability methods [26] and Monte Carlosimulation to reliably predict the service life of deterior-ating highway bridges. There has not been any relevantwork found on fatigue analysis for large cable-supportedbridges with structural health monitoring systems. It hasbecome a significant problem to be studied with thedevelopment of the structural health monitoring systemfor large complicated structures.

Fatigue life can be considered to consist of two per-iods: the fatigue crack initiation and the crack growthperiod. The fatigue crack initiation covers the initiationand growth of the small cracks in the micro-range size,which cannot be detected by eye or non-destructiveinspection. For the health of a new bridge to be moni-tored in order to determine the need for reinforcing orrepairing by the administration, the first period shouldbe a major part of the research. The Miners rule usedin many fatigue design guides has the advantage of sim-plicity with mathematical elegance, making them attract-ive to practising structural engineers. However, thisapproach does not directly associate fatigue damage withits physical mechanism such as fatigue crack initiationand growth. Fatigue tests on different materials[17,20,21] have shown that a nonlinear fatigue modelbased on continuum damage mechanics (CDM) is morereliable than the linear Miners model. Now further stud-ies are needed for developing a new approach based ona CDM fatigue model for accurately evaluating the stateof fatigue for existing structures. This paper aims todevelop a methodology and strategy for fatigue damageassessment and life prediction of the bridge-deck sectionbased on online structural health monitoring data and afatigue damage model based on the continuum damagemechanics. A structural model for the fatigue analysisof steel bridge decks is proposed, in which the structureis modeled by elastic members and welded connectionswith possible initiated cracks described by a damagevariable. The model allows the process of fatigue

initiation at the connections of the bridge-deck sectionto be analyzed by a CDM fatigue damage model. Theservice life prediction for steel bridge decks based onthe online straintime history of the bridge under thecurrent volume of traffic could be modified by updatingthe representative block of the local stress history by thefuture online data, which will be included in the compu-tational approach.

As mentioned above, the Miners rule has been popu-lar in fatigue design of steel bridges. However, it can beshown that a fatigue damage model based on CDM hasclear physical meaning and precise modeling for a dam-aged structure. In order to compare results of fatiguedamage evaluated by the CDM fatigue damage model, amodified PalmgrenMiner rule is developed for the samefatigue problem.

2. Models for fatigue analysis of bridge-decksections

2.1. Structural model for fatigue stress analysis

Bridge members usually react to service stress farbelow design critical stress in the way of elastic defor-mation. Still there exist local failures, usually brittle, inthe presence of the notches or some type of geometricdiscontinuities such as holes, grooves and welded con-nections where the stresses are locally elevated. Bridge-deck sections are constructed by connecting many plates,beams and bars by welding, rivets or some other way.Fatigue cracks in a bridge are likely to appear at thelocation of these connections. Therefore, the bridge-decksection should be one of the main parts of the fatigueanalysis for a bridge. Structurally the deck section of theTsing Ma Bridge is a hybrid arrangement combiningboth truss and box form [2]. As shown in Fig. 1, twolongitudinal trusses to the full depth of the deck at26 m centers act in conjunction with the steel orthotropicdecks of the upper and lower carriageways to providethe vertical bending stiffness. Plan diagonal bracings atthe upper and lower levels enable the trusses to providelateral bending stiffness. Cross frames of Vierendeelform are provided at 4.5 m centers with every fourthframe being supported from suspenders. A stainless steelcladding along the outer edges of the deck is providedin order to control air flow across the deck. The finalexternal appearance of the Tsing Ma Bridge deck istherefore of a box with faired edges having continuousgaps along the top and bottom surface.

Bridge fatigue is a high-cycle fatigue problem wherestress fluctuations are low so that the deformation in thestructure is elastic except at notches and welds wherelocal stresses are concentrated. Therefore the material inthe vicinity of welds would be locally yielded and plasticor micro-plastic deformation generates there. For accur-

47Z.X. Li et al. / International Journal of Fatigue 23 (2001) 4553

Fig. 1. A deck section of the Tsing Ma Bridge.

ate evaluation of fatigue stress, fatigue crack initiationand growth in the vicinity of welds should be properlymodeled and coupled into the structural model of abridge-deck section. Fatigue damage in the region offatigue crack initiation and growth of cracks in micro-scale can be well modeled by the CDM concept andtheory. The structural model for fatigue damage analysistherefore consists of elastic deformed members in whichstresses are below the elastic limit of the material, andwelded connections where fatigue cracks in micro-scaleinitiate and grow. The deformation of elastic memberswill follow the constitutive law of elasticity, while thedeformation in the vicinity of welds follows the consti-tutive equations of damaged material. As an example ofsuch a structural model, a part of the bridge-deck sectionconsidered, a typical longitudinal truss, is shown in Fig.2. All vertical posts, diagonal bracings, top and bottomchords are non-damage members, and welds at connec-tions of these members are critical locations of fatiguedamage.

Suppose the macro-plastic strain does not exist inmembers of a steel bridge on the preliminary stage ofservice, and the only irreversible strain is micro-plasticwhich will be considered later in the fatigue damagemodel. The fatigue damage in the vicinity of welds iscoupled into the material constitutive law using the con-cept of effective stress [18]. Therefore, the constitutiveequation for the proposed model of bridge structure canbe written as:

Fig. 2. A typical longitudinal truss.

eij5Cijklskl for non-damage members (1)where eij and skl are the rate of strain and stress tensor,respectively, Cijkl is a tensor of elastic compliance. Ifdamage in the material is described by introducing a sca-lar variable, D, the deformation behavior of damagedmaterial is modeled as follows:

eij5Cijklskl in the vicinity of welds (2)where skl is a tensor of effective stresses that can beexpressed as follows [27]:

sij5ksijl1- D2

k- sijl1- hD (3)

in which the McCauley bracket ,x. yields x for x.0and 0 for x,0, and 0#h#1 is associated with closingof micro-cracking when the local stress state is com-pressive.

The above model can be used not only to analyzefatigue damage of steel structures, but also for finiteelement modeling of damaged structures to calculate thestressstrain response and the state of damage if theevolution law of the damage variable is provided.Further explanation of the structural model and strategyfor finite element modeling of a bridge-deck section willbe reported in a separate paper on the fatigue analysisof steel bridges by the finite element method.

2.2. Local model for high-cycle fatigue damage

The damage evolution model for the high-cyclefatigue damage problem must be written in terms ofstress since the irreversible strain involved in the fatiguedeformation is only micro-plastic, which is not measur-able and difficult to calculate. Based on the theory ofthermodynamics and potential of dissipation, a generaldamage model can be written as a function of theaccumulated plastic or micro-plastic strain, the strainenergy density release rate and current state of damage[17]. The micro-plastic strain, usually neglected in a lowcycle fatigue problem, and its accumulation must be con-sidered when high-cycle fatigue damage occurred in theelastic range, even if macro-plastic strain does not exist.


Therefore, the damage evolution equation here is writ-ten as:

D =Rvs2eq|seq- seq|b

B(1 - D)a kseql

D =0if

s$sfs,sf

(4)

where B, a and b are constants of material, sf is thestress limit to fatigue, seq is Von Mises equivalent stressdefined by:

seq5F32sDijsDijG1/2 (5)in which sDij is the deviatoric stress tensor. In Eq. (4),s* is the damage equivalent stress which, for damage,acts as the Von Mises equivalent stress used in plasticity,and in the case of a one-dimension problem, it isgiven by:

s5s if s$0; s5S 1- D1- hDD1/2|s| if s,0 (6)and Rv is a triaxial function to express the influence ofthe triaxial ratio of the stress state, and in pure bilateralconditions (h=1) this function reduces to:

Rv5FsseqG2

523(11n)13(122n)FsHseqG

2

(7)

In the one-dimensional case, Eq. (4) becomes:

D =s2|s- s|bB(1 - D)aksl

D =0if

s$sfs,sf

(8)

in which s=sm is the mean stress.Eq. (4) or Eq. (8) is a general constitutive model for

high cycle fatigue, which is valid for any kind of load-ing. It has to be integrated over time for each cycle ifthe cycles are different in magnitude of stress range andmean stress. The identification of the coefficients B, aand b in the model needs the Woehler curve for uniaxialperiodic fatigue and the measurement of damageobtained by means of a strain controlled fatigue test.

3. Methodology and strategy of fatigue analysis

3.1. Fatigue analysis approach on the basis of onlinemonitoring data

With the above model for fatigue analysis, the assess-ment procedure for the fatigue of a bridge can bedescribed as follows:

1. Global structural analysis by the finite element com-

putations to determine the components of nominalstress corresponding to fatigue and extreme loadsgenerated by cyclic loading.

2. Local stress analysis to determine the hot-spot stressconcentration factors and the degree of the localiz-ation, i.e. the proportion of the localized stress to totalstress relevant to the location where cracks or micro-cracks may be generated.

3. Determination of stress spectrum to generate the hot-spot stress range and mean stress histogram for thelocation where fatigue cracks may occur.

4. Fatigue damage analysis for the crack initiation periodor fatigue crack growth analysis for the crack growthperiod to determine the state of fatigue damage andthe remaining service life of the structure.

It can be seen from the above that the fatigue analysisis firstly based on the stress analysis to get the distri-bution of the stress in structures. The stress analysis isknown to be very difficult for a large complicated struc-ture, such as large cable supported bridges, since thereare too many uncertain conditions remaining in the cal-culation. The development of the structural health moni-toring system provides an efficient way to get an accur-ate evaluation of local stress history for bridge-decksections under actual traffic. As an example of the sys-tem, the WASHMS [1,2] has been installed for the threecable-supported bridges in Hong Kong, which is con-sidered to be the most heavily instrumented bridge pro-ject of the integrated online monitoring system in theworld. The bridge response is monitored by a total ofapproximately 774 sensors, including accelerometers,strain gauges, displacement transducers, level sensors,anemometers, temperature sensors and weigh-in-motionsensors installed permanently on the bridges, and thedata acquisition and processing system. The straingauges were installed to measure stresses at bridge-decksections. As shown in Fig. 3, the locations of straingauges installed for the Tsing Ma Bridge including railtrack sections at Chainage (CH) 24662.50, bridge-decktrough section at CH 24664.75 and deck at tower androcker bearing links at CH 23623.00. The most criticalparts of the cross-frames for fatigue damage have beenidentified during the design of the WASHMS by theFlint and Neill Partnership [28]. Therefore, all thesestrain gauges are supposed to be installed at critical partsof the bridge-deck sections. Then, data measured bythese strain gauges can be used to obtain nominalstresses corresponding to critical parts of the bridge-decksection. The local stresses at hot-spots are then calcu-lated by local stress analysis with the finite elementmethod or conveniently corrected using appropriate cor-rection factors, which is described in the companionpaperPart II [31].

Straintime histories recorded by strain gaugesinstalled at bridge-deck sections now become the most


Fig. 3. Strain gauges layout of the Tsing Ma Bridge.

useful database for online fatigue assessment of thebridge. Based on the measured data from the structuralhealth monitoring system, proposed procedures for thefatigue analysis of bridge-deck sections are suggestedand the flow chart of the procedures is shown in Fig. 4.

Fig. 4. A flow chart of procedures for the fatigue analysis of a bridge-deck section.

3.2. The representative block of cycles of stress attraffic loading

Fatigue damage is dependent on the nature of thestresstime history that is generated by the live load on


the bridge due to traffic. The measured data of straintime history at the gauge locations of the bridge isobserved to be very complicated. Fig. 5 shows part ofstrain histories recorded by a strain gauge in the crossframe at CH 24662.50. It is seen that the straintimehistory consists of complicated cycles with variableamplitude of strain range and varying values of meanstrain. If the original straintime history was directlyused to assess the fatigue by the rain-flow counting pro-cedures, it would be almost impossible to record thestrain from the time the bridge started on service to theend, and to put all of the recorded data into a computerto get the rain-flow counting results. Therefore it isnecessary to analyze the character of recorded straintime history.

The recorded strain is generated by the live load onthe bridge due to the traffic loading, and the traffic ona bridge can be considered as approximately repeatedfrom day to day. The investigation on the particular fea-ture of the straintime history [29] showed that thestraintime history curves are similar from day to day.They have common characteristics in curve shape andmagnitude of cycles, which can be observed fromrecorded strain cyclic histories shown in Fig. 5, threedays straintime history at (a) May 20, (b) May 15 and(c) April 27, 1999.

Based on the above analysis, the real-time straincycles recorded by strain gauges will be modeled as ablock of repeated cycles in the fatigue analysis of bridge-deck sections based on the monitoring data. The original

Fig. 5. Straintime history at (a) May 20, 1999; (b) May 15, 1999; (c) April 27, 1999.

strain history is therefore represented by the block-repeated cycles in which a standard block, defined as arepresentative block of daily cycles, is repeated everyday. The representative block of cycles can be obtainedby statistical analysis of many samples of daily straintime history recorded at the same location. The detailedprocedures for obtaining the representative block ofcycles are shown in Fig. 4.

3.3. Fatigue damage rate generated by therepresentative block of cycles

After obtaining the representative block of cycles ofstrain history, the rain-flow counting method is used todetermine the stress spectrum as shown in the flow chartof the procedures for the fatigue analysis (see Fig. 4). Itgives stress range, relevant mean stress and its cyclecounts in the representative block of cycles of stresstime history. Then the fatigue damage Eq. (4) or Eq. (8)should be integrated for each cycle over time of theblock, from which the fatigue damage generated by therepresentative block of the cycles can be derived.

Considering firstly the mean stress sm=0 for simplicityof the calculation, and neglecting the variation of(12D)a in the integration over one block of cycles, inte-grating Eq. (8) over one block yields:

ED1

dDdNbl

D

dD5Omrbi51

EsMri

0

sb+2

B(1 - D)ads for s50 (9)


where mrb is the number of cycles with the maximumstress over the stress limit to fatigue in the representativeblock, Nbl the number of blocks, and sMri the maximumstress at the ith cycle and its value is greater than thestress limit to fatigue.

Noticing the stress amplitude sar when sm=0 is equalto the maximum stress sMr, the fatigue damage rate gen-erated in one block of cycles is obtained from Eq. (9)

dDdNbl

5Omrbi51

sb+3ariB(1 - D)a(b+3) (10)

Now, consider the effect of mean stresses by usingthe equation similar to that of Morrow, or that of Smith,Watson and Topper [30]:sar5(sMsa)1/2 (11)where sa represents stress amplitude when mean stresssm0.

Substituting the above equation into Eq. (10), andsince sM=sa+sm, it gives:

dDdNbl

5Omrbi51

[(sai+smi)sai](b+3)/2B(1 - D)a(b+3) for sMi$sf (12)

The above equation gives the fatigue damage rate gen-erated by the representative block of cycles of stress. Itdepends on the stress spectrum in the representativeblock of cycles of the local stress history, the state ofdamage and the material properties in elasticity, micro-plasticity and damage.

3.4. Updating of the stress spectrum in therepresentative block of cycles

The stress spectrum in the above analysis is based onthe online strain generated by the live load on the bridgethat is mainly due to the current volume of traffic load-ing. It has to be updated from time to time since thetraffic volume on the bridge varies with the economicdevelopment in Hong Kong. The updating method isas follows:

(a) Record the online straintime history on theupdated time, for the period at least over one week.For considering the effect of temperature in differentseasons, it is better to record online data for fourweeks in four seasons, respectively.(b) Determine the representative block of cycles ofthe local stress history by statistical analysis of thedaily samples of the local stress history at the samelocation of interest.(c) Determine the updated stress spectrum (sai,smi)by use of the rain-flow counting program.

Then the updated fatigue damage rate generated by therepresentative block of cycles of stress can be obtainedby replacing the updated stress spectrum into Eq. (12)as follows:

dDdNbl

5Omrbi51

[(sai+smi)sai](b+3)/2B(1 - D)a(b+3) for sMi$sf (13)

4. Fatigue damage evaluation and service lifeprediction

With the fatigue damage rate given by Eqs. (12) and(13), the fatigue damage can be evaluated by the integralof these equations over time for a blocked cycle. Inte-grating Eq. (12) at the initiation condition: Nbl =0, D=0,it gives

D512H12(a+1)NblB(b+3) Omrb

i51

[(sai1smi)sai](b+3)/2J1/(a+1) (14)If there are N0bl blocks with the stress spectrum sai,

smi (i=1, 2, . . ., mrb) and then more blocks with updatedstress spectrum (sai,smi) (i=1, 2, . . ., mrb), the integralof Eq. (13) at the initiation condition: Nbl=N0bl, D=D0gives:

D512H(12D0)a+12(a+1)(Nbl - N0bl)B(b+3) Omrb

i51

[(sai (15)

1smi)sai](b+3)/2J1/(a+1)in which D0 is obtained by Eq. (14) when Nbl=N0bl.

For multiple updates made on the service period ofthe bridge, the evaluation of the fatigue damage is aniterative process. The iterative equation after the (k+1)thupdating of the stress spectrum is expressed as:

D(k11)512H(12D(k11)0 )a112

(a11)(N(k11)bl - N(k11)bl(0) )B(b13) O

m(k11)rb

i51

[(s(k11)ai (16)

1s(k11)mi )s(k11)ai ](b13)/2J1/(a11)D(k11)0 5Dk; N(k11)bl(0) 5Nkbl

in which, Nkbl, the number of blocks before the (k+1)thupdating, equals the sum of all increments of the blockin the updating period DN jbl (j=0, 1, . . ., k):Nkbl= S

k

j50DNjbl.


The prediction of the service life can be obtained fromEq. (15) when the fatigue damage reaches its value atfailure Df:

Nfbl5B(b+3)[(1 - D0)a+1 - (1 - Df)a+1]

(a+1)Omrbi51

([(sai+smi)sai](b+3)/2)1N0bl (17)

where, if the KUth update is made on the service periodof the bridge before failure, N0bl is the number of blocksbefore the last updating, and D0=DKU0 =D(KU - 1) is calcu-lated by using the iterative Eq. (16).

For reasons of comparison, the service life predictionis calculated using a modified PalmgrenMiner rule. ThePalmgrenMiner rule simply states that fatigue failure isexpected when life fractions sum to unity. It is a rulemost commonly used because of its simplicity. However,the summations of cycle ratios at fatigue failure wereobserved not to be unity in many situations, especiallyfor structures under variable-amplitude loading [5]. Inmany cases, the summation was found to be less thanunity and with the value in the region of 0.6|0.9. Fromthe point of view of continuum damage mechanics,fatigue failure occurs when fatigue damage in thematerial reaches a limit value of damage. The limit valueof damage, Df is an intrinsic material property to bedependent on the durability of the material. It can bedetermined from experiment for a given material and itsvalue ranges between 0.15 and 0.85, depending on thematerial [22]. The parameter Df has been used in theabove CDM model, so it is necessary to use the sameparameter as a threshold value for fatigue failure in thecompared calculation by Miners rule.

The summation of cycle ratios in the left of the equ-ation of the PalmgrenMiner rule is actually a kind ofexpression of cumulative fatigue damage, and Minersrule therefore implies that fatigue failure is expectedwhen the value of cumulative fatigue damage, expressedas a life fractions sum, equals unity. A modifiedPalmgrenMiner rule is proposed here, which states thatfatigue failure is expected when the value of cumulativefatigue damage, expressed as a life fractions sum,reaches the threshold value of the fatigue limit, i.e., thevalue of fatigue damage at failure, Df. For the blockedcycles of local stress history discussed here, the rule isexpressed as follows:

NfblFOi

NiNfiGone block5Df (18)

where Nfbl is the number of blocks to failure, and Ni, Nfiare the number of cycles at the stress amplitude sai andrelevant number of cycles to failure from the SN curvefor sai, respectively, in the representative block of cyclesof local stress history. Again if the KUth update is madebefore the fatigue failure, the Eq. (18) should be revisedas follows:

OKUk51

HNkblFOi

NkiNfkiGfor the kth updated blockJ5Df (19)

where Nkbl is the increment in the number of blocks withkth updated representative block, and S

KU

k51Nkbl=Nfbl the

number of blocks to failure.According to the standard [3], the number of cycles

to fatigue failure at the stress range Dsi used in the aboveequation can be obtained from the following equation:

Nfi5K2Ds - mi (20)where K2 and m have values given in the standard [3]for different class of details.

5. Concluding remarks

This paper studies how to evaluate fatigue damage andto predict the service life of bridge-deck sections for alarge suspension bridge with a permanent structuralhealth monitoring system installed such as that for theTsing Ma Bridge. The systematic study has developedthe methodology and strategy for the fatigue analysis.The fatigue damage models presented in the paper allowcalculation of the cumulative damage of high-cyclefatigue in a bridge which is considered at a continuumscale as a deteriorating process with its physical mech-anism such as fatigue crack initiation and growth.

The developed methodology and strategy allowsfatigue assessment to be carried out by taking full advan-tage of the online structural health monitoring data.Therefore, for bridges with the structural health monitor-ing system, accumulative fatigue damage can beassessed by the use of the proposed approach for bridge-deck sections under actual traffic loading.

The stress spectrum of the representative block ofcycles under normal traffic loading can be obtained byrain-flow cycles counting and statistical analyzing ofdaily samples of the stress spectrum. The location ofpossible fatigue failure will be detected by comparingvalues of fatigue damage at the toe of the welds nearthe critical members, and therefore the service life of thebridge is the predicted life of the detected critical mem-ber. As an important part of the computation, the updat-ing of the stress spectrum of a representative block ofcycles at the hot-spot by the real-time monitoring datais included in the proposed approach to cope with thechange of the traffic volume in the future.

The method and strategy developed in this paper havebeen applied to evaluate the fatigue life of the TsingMa Bridge, and the calculated results have verified thevalidity of the proposed approach, which will bepresented in the companion paperPart II [31].


Acknowledgements

Funding support to the project (Project Code: G-YY15) by the Hong Kong Polytechnic University isgratefully acknowledged. The writers wish to thank theHighways Department of the Hong Kong SAR Govern-ment for their support throughout the project.

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