FATIGUE SAFETY MONITORING AND ASSESSMENT OF SHORT AND MEDIUM SPAN CONCRETE GIRDER BRIDGES

Transcription

1 FATIGUE SAFETY MONITORING AND ASSESSMENT OF SHORT AND MEDIUM SPAN CONCRETE GIRDER BRIDGES Chunsheng Wang 1,2,*,Musa Zha 1,2, Peje Zhang 1,2, Lan Duan 1,2 and Xn Chen 1,2 1 Insttute of Brdge Engneerng, College of Hghways, Chang an Unversty, X an, Chna, Engneerng Research Center for Large Hghway Structure Safety of Mnstry of Educaton, Chang an Unversty, X an Chna, ABSTRACT Concrete brdge s wdely used n hghway nfrastructure n Chna, especally n short and medum span brdges. Concrete brdges are prone to fatgue falure under the coupled actons of repeated vehcles loads, envronment and materal degradaton. In recent years, the traffc volume and vehcle weghts of hghway brdges have been contnuously ncreasng, so concrete brdge fatgue problem becomes more serous. Ths paper ntroduces advanced fatgue safety montorng technques and fatgue performance assessment methods for short and medum span concrete grder brdges. Wegh-n-moton (WIM) system was used to record the real traffc volume, and then the acqured load spectrum was appled on typcal concrete brdges through Matlab to analyze the fatgue performance of dfferent brdge types. From the analyss results, several typcal short and medum span concrete grder brdges are selected to conduct long-term servce montorng. The cross secton types nclude hollow slab grder, T-grder and short box grder, and the structure types contan smple supported brdge and contnuous grder brdge. WIM technque, dynamc stran montorng technque and acoustc emsson technque are used to montor the key detals. Fatgue performance s assessed and analyzed based on montorng data, consderng traffc ncrease, overload and corroson factors. KEYWORDS Concrete grder brdge, fatgue safety montorng, traffc load, corroson fatgue, fatgue assessment. INTRODUCTION In recent years, as the traffc volume and vehcle weghts of hghway brdges are contnuously ncreasng n Chna, concrete brdges are subject to serous fatgue problems (Wang et al. 2010, Wang et al. 2012, Wang et al. 2013a). Wth servce lfe ncreasng, concrete materal agng and mechancal behavor deteroraton wll appear gradually, as shown n Fgures 1. Affected by servce envronment and traffc effect, fatgue damage of renforced concrete (RC) brdges could become promnent after years n-servce. The ntaton and accumulaton of fatgue damage wll lead to rebar fatgue and fracture falure. Fgure 1 Corroson and damage n concrete grder brdges Fatgue and fracture study of concrete brdge was carred out n Amerca and Europe 60 years ago. Oh studed cumulatve damage theory of concrete structures under varable-ampltude fatgue loadng (Oh 1991). Tlly studed the reducton coeffcent of fatgue strength of rebar n dfferent corroson levels, whch was used to evaluate durablty and remanng lfe of concrete brdges (Tlly 1988). Based on fatgue falure mechansm of concrete brdges, fatgue lfe assessment approaches usng S-N curves and fracture mechancs were proposed by Schläfl and Brühwler to evaluate the fatgue safety of hghway and ralway brdges n Swss (Schläfl & Brühwler 1998). In Chna, researchers began to pay attenton to fatgue problems n concrete brdges n recent years when many concrete brdges are suffered from several dseases and the servce performance cannot be guaranteed. Technque fuson of Wegh-In-Moton (WIM), dynamc stran montorng and acoustc emsson 301

2 was adopted by Wang to montor concrete grder brdges. Fatgue safety assessment methods based on S-N curves and fracture mechancs were developed to assess the servce safety (Wang et al. 2013b). Zhu proposed a smplfed numercal smulaton method for the deteroraton process of n-servce renforced concrete (RC) brdges and the relablty and avalablty of ths method was verfed by a smple supported RC grder brdge (Zhu 2012). Based on current research achevements, relevant desgn codes and specfcatons should be developed to gude engneerng fatgue desgn and n-servce mantenance. Ths paper ntroduces advanced fatgue safety montorng technques and fatgue performance assessment methods for short and medum span concrete grder brdges. Wegh-n-moton (WIM) system was used to record real traffc volume, and then the acqured load spectrum was appled on typcal concrete brdges through Matlab to analyze the fatgue performance of dfferent brdge types. From the analyss results, several typcal short and medum span concrete grder brdges are selected to conduct long-term servce montorng. The cross secton types nclude hollow slab grder, T-grder and short box grder, and the structure types contan smple supported brdge and contnuous grder brdge. Fatgue performance s assessed and analyzed based on montorng data, consderng traffc ncrease, overload and corroson factors. FATIGUE MONITORING TECHNIQUES AND ASSESSMENT METHODS Fatgue Safety Montorng Technques WIM s an advanced weghng system whch ncludes two pezoelectrc sensors, one nducton col sensor and a data acquston unt. A temperature sensor s set n pavement, whch can acqure real temperature nformaton to provde proper temperature compensaton to the system. The controllng unt set besde the brdge s lnked to the pezoelectrc sensors and the nducton col. When vehcles pass the brdge, the nducton col pcks up dfferent responses, and the pezoelectrc sensors send the nformaton to the acquston unt. Then the controllng unt can calculator the specfc nformaton of the passed vehcle and record the nformaton. The system can record comprehensve nformaton about the vehcles movng through, such as weght, speed, drecton, axle number and so on. Fatgue damage of concrete grder brdge s caused by the coupled actons of envronment, cyclc vehcle loads and materal degradaton. Long tme contnuous montorng s a relable way to study the structural response n a certan perod, whch s also a popular method to assess the fatgue performance for exstng brdges. Fatgue stress montorng can record the stress hstory of fatgue senstve detals, and the stress spectrum can be calculated by ran-flow method to assess the fatgue performance. In stu montorng, stran gauges was attached on the concrete surface and the dynamc stran acquston s controlled by computer through network cables. Fatgue Lfe Assessment by S-N Curve The hypothess of the lnear damage accumulaton was derved by Mner, whch was often referred to as the Palmgren-Mner rule (Mner 1945). It defned that D 1 ndcated falure, where D was the damage degree n materal. Ths rule also assumed a lnearly accumulatve fatgue damage process. Namely n each stress range level,the damage fracton D was lnearly proportonal to n, where n was the number of cycles at and D was the rato of n / N. N means the total number of cycles that would cause falure under that stress range level. The followng lnear damage accumulaton rule s a sum of all the damage fractons for all stress range levels (Equaton 1). n D D (1) N Accordng to the above analyss, damage accumulatons of RC brdges were lnearly calculated wth the damage threshold value D c. Thus, the cumulatve fatgue damage of RC brdge under fatgue loads for one year can be estmated as Equaton 2. n DT (2) N Where D s the fatgue damage amount n the certan perod T, n T s the number of cycles at the stress range level n the certan perod T, N s the total number of cycles that would cause falure under the stress range level. Then the brdge fatgue lfe Y can be gven as Equaton

3 Y D c T (3) Where D s the crtcal fatgue damage and t s defned as 1.0 when the fatgue falure wll occur. c D T Fatgue Lfe Assessment Based on Fracture Mechancs For steel renforcement, fracture mechancs descrbes crack growth as a functon of materal parameters, crack sze geometry and geometry of specmen. Fracture of rebar occurs, when the depth of crack reaches a a and the appled stress s equal to the resstance of the remanng cross secton. In a fatgue test wth a constant 0 stress range that stress corresponds to the superor stress level, thus 0 sup. The brttle fracture and fracture by yeldng are two exsted fracture modes (Herwg 2008). In order to calculate the crack propagaton, the ntal flaw on a cylndrcal steel bar s assumed as a semcrcular crack, whch has a depth of a a. The plane, n whch the sem-crcular crack les, s perpendcular to the steel axs. The stable crack growth from ntal crack s assumed as follows (Fgure 2). fr Intal flaw, a = a a = a fr r Crack tp Fgure 2 The cross secton of rebar wth ntal flaw and crack propagaton Then the Pars Law gven n Equaton 4 s obtaned by transformaton. da m C K dn (4) Where C and m are parameters based on the materal. FATIGUE PERFORMANCE ANALYSIS FOR TYPICAL CONCRETE GIRGER BRIDGES Concrete Hollow Slab Grder Brdge Concrete hollow slab grder brdge s approprate for the span length rangng from 4m to 25m. Four dfferent span lengths were chosen to calculate the fatgue stress spectrums n ths paper, the span length s 10m, 13m 16m and 20m, respectvely. In engneerng applcaton, several hollow slab grders are hnged together to form the brdge, the transverse dstrbuton coeffcent of outer slab grder s larger than other slab grders when a vehcle passes through the brdge. Therefore, to ensure structural safety, the transverse dstrbuton coeffcent of the outer slab grder under eccentrc loadng case was adopted to calculate the fatgue stress. Analyss result s shown n Table 1, t can be learned that hollow slab grder brdges wth larger span have lower fatgue stress range and tend to suffer less fatgue damage. As for the longtudnal steel bar n the md-span secton, the stress level s relatvely low snce the maxmum stress reaches just 12MPa. Concrete T-grder Brdge Consderng the most dsadvantage lve loadng case and dfferent span length, the fatgue stress range of the T- grder brdges wth fve T-grders n transverse drecton were obtaned. Smple supported and contnuous concrete T-grder brdges wth dfferent span length and dfferent span numbers are taken nto consdered. The span length for smple supported brdge s 20m, 25m, 30m, 35m and 40m, the span length for contnuous brdge s 20m, 30m and 40m wth 3 or 4 spans. For contnuous grder brdge, the fatgue stress range of sde span s hgher than that of md-spans, so fatgue stress range of steel bar n sde span s calculated, and the results are shown n Table 2. For smple supported concrete T-grder brdges, fatgue stress level of 20m-span and 25mspan grders are smlar, the maxmum fatgue stress s 23MPa. Wth the span length ncrease, the maxmum stress tend to decrease, whch ndcates the smple supported T-grder brdge wth larger span length tends to 303

4 suffer less fatgue damage under the same vehcle spectrum. As to contnuous concrete T-grder brdges, fatgue stress level s obvously lower than smple supported brdge (Table 2(b)). Smlar as smple supported brdges, contnuous T-grder wth larger span length tend to have lower fatgue stress and suffer less fatgue damage. However, the span numbers have lttle nfluence on the fatgue stress. Based on the calculaton results, t ndcates that shorter span T-grder brdges suffer more fatgue damage. Table 1 Fatgue stress spectrums of smple supported hollow slab grder brdges Stress range Stress cycles for dfferent spans (MPa) 10m 13m 16m 20m Table 2 Fatgue stress analyss of concrete T-grder brdges (a) Smple supported grder brdge (b) Contnuous grder brdge Stress Stress Stress cycles for dfferent spans Stress cycles for dfferent spans range range 20m 30m 40m (MPa) 20m 25m 30m 35m 40m (MPa) span span span span span span Concrete Box-grder Brdge Accordng to general usage status, concrete box-grder brdge wth four box-grders n transverse drecton s selected to analyze the fatgue stress. The span length for smple supported brdge s 10m, 13m, 16m and 20m, 304

5 the span length for contnuous brdge s 20m, 30m and 40m wth 3 or 4 spans. Smlar to the hollow slab grder brdges and T-grder brdges, the transverse dstrbuton coeffcent of the outer box grder under eccentrc loadng case s adopted to calculate the fatgue stress. From the analyss result (Table 3), smple supported concrete box-grder brdge tends to suffer hgher stress, but the maxmum stress decreases wth the span length ncrease. For contnuous concrete box-grder brdge, the span numbers have lttle nfluence on the fatgue stress. Table 3 Fatgue stress analyss of s concrete box grder brdges (a) smple supported grder brdge (b) Contnuous grder brdge Stress Stress Stress cycles for dfferent spans Stress cycles for dfferent spans range range 20m 30m 40m (MPa) 10m 13m 16m 20m (MPa) span span span span span span CASE STUDIES: FATIGUE SAFETY MONITORING AND ASSESSMENT FOR EXISTING CONCRETE GIRDER BRIDGES Concrete Hollow Slab Grder Brdge Mazu Brdge (Fgure 3) s a typcal prestressed concrete (PC) hollow slab grder brdge, whch was open to traffc n The layout s 7 20m, the concrete deck s contnuous whle the slab grder s smple supported. The wdth of the brdge s 8.5m ncludng 2 lanes n two drectons, and the cross-secton contans 6 slab grders wth hnge jonts connectng each other. Based on the manual traffc montorng result, there are many heavy trucks passng across the brdge, so dynamc stran montorng s conducted contnuously for several days. Stran gauges are manly arranged on the bottom plate of the md-span cross secton # 2# 3# 4# 5# 6# 950 BS1 BS1' BS2 BS2' BS3 BS4 BS5 BS6 Fgure 3 Maozu Brdge (Unt: mm) In order to assess the fatgue performance of hollow slab grder brdge, fatgue stress of longtudnal steel bar and prestress strand (Fgure 4) are selected to analyze the fatgue stress under real traffc load. Accordng to plane stran assumpton, stran of longtudnal steel bar and most unfavorable wre s calculated. Snce the steel bars and prestress steel tendons or strands n the lower poston are subject to more fatgue damage, the lowest longtudnal steel bar and the lowest prestress steel wres or strands are selected to evaluate the fatgue lfe. S-N curve for longtudnal steel bar used n ths paper s from European Conventon for Constructonal Steelwork 305

6 (ECCS 1985), S-N curve for prestress steel wres s proposed by Song (Song 2006), and S-N curve for prestress steel strand s suggested by Ma (Ma 2000). The dameter of longtudnal steel bar s 16mm, the yeld strength s 335MPa. In fatgue performance assessment based on fracture mechancs, fracture toughness K s taken as 50MPa m, fracture constants C, m are taken as and 4, respectvely. Threshold value of fatgue crack propagaton Kth s 2.0MPa m, the ntal crack depth s assumed as 0.5mm snce no crack has been detected. IC Prestress strand Corrugated ppe Most unfavorable strand Φ Φ Most unfavorable wre (a) Longtudnal steel bar (b) Prestress strand layout Fgure 4 Longtudnal steel bar and prestress strand layout layout (Unt: mm) Consderng contrbutons of low stress ranges, fatgue lfe of the lowest steel bar n PC hollow slab grder brdge s years for grders under the heavy lane, and fatgue lfe of lowest prestress steel wre s years (Table 4). Based on LEFM, fatgue lfe of the lowest steel bar n PC hollow slab grder brdge s years for grders under the heavy lane, and fatgue lfe of lowest prestress steel wre s years. Snce Maozu Brdge was open to traffc only several months, the traffc volume s relatvely small, fatgue lfe of longtudnal steel bar and most unfavorable prestress wre s far longer than desgn servce lfe. But f fatgue crack occurs on concrete and corroson occurs on the steel bar or the prestress wre, the fatgue lfe wll decrease sharply. The fatgue lfe wll also decrease f the traffc volume ncreases n the future. Table 4 Fatgue lfe evaluaton of PC hollow slab grder brdges Object Fatgue lfe (Year) S-N Curve LEFM Steel bar Prestress steel wre Concrete T-grder Brdge Two typcal prestressed concrete (PC) T-grder brdges,.e., a smple-supported PC grder brdge and a contnuous PC grder brdge are chosen to evaluate the fatgue lfe usng dfferent methods. The smplesupported PC grder brdge shown n Fgure 5(a) s a freeway brdge, whch contans two separate parts composed of 12 T-grders wth the total wdth of 26.2m. The contnuous one was open to traffc n 2013, whch s parallel to the old smple-supported PC grder brdge. As shown n Fgure 5(b), the cross-secton contans 8 T- grders wth the total wdth of 19.75m. The every span length of both brdges s all 30m. These two brdges are n the same dstrct, the traffc volume and vehcle knds are smlar. To evaluate the fatgue lfe of the PC T-grder brdges, n-stu dynamc stran montorng was conducted contnuously over one month, and traffc volume was recorded manually. Fgure 6(a) s the cross secton of smple supported PC T-grder brdge, whch s bult n Carbon steel wres are used n prestress steel tendons, and every tendon contans 24 wres wth 5mm n dameter. Longtudnal steel bar n the bottom part of T-grder s 20mm n dameter. Fgure 6(b) s the cross secton of contnuous PC T-grder brdge, prestressng steel strands (9-7Ф5) and 20-dameter steel bars are used n T-grders. 306

7 (a) Smple supported PC T-grder brdge (b) Contnuous PC T-grder brdge Fgure 5 The two PC T-grder brdges In order to consderng contrbutons of corroson and low stress ranges, fatgue categores of steel bars and prestress steel wres or strands are lowered to the 65% (Walker 1975). Consderng contrbutons of low stress ranges, fatgue lfe of the lowest steel bar n smple supported PC grder brdge s 4421 and 9380 years for grders under the heavy lane and lght lane, respectvely; and fatgue lfe of lowest prestress steel wre s 1390 and 1616 years. Fatgue lfe of lowest steel bar n contnuous PC grder brdge s and years for grders under the heavy lane and lght lane, respectvely; and fatgue lfe of lowest prestress steel wre s and years. Based on LEFM and the depth of ntal cracks are assumed as 1.0mm consderng the corroson pt flaws, fatgue lfe of the lowest steel bar n smple supported PC grder brdge s 1094 and 1287 years for grders under the heavy lane and lght lane, respectvely; and fatgue lfe of lowest prestress steel wre s 1734 and 2326 years. Fatgue lfe of lowest steel bar n contnuous PC grder brdge s and years for grders under the heavy lane and lght lane, respectvely; and fatgue lfe of lowest prestress steel wre s and years, as ndcated n Table 5. Prestressng steel strand Prestressng steel tendon Steel bar (Ф10) Steel bar (Ф20) Carbon steel wre 24-Ф5 The lowest steel wre 9-7Ф5 The lowest steel strand 7Ф5 The lowest steel wre (a) Smple supported PC Grder (b) Contnuous PC Grder Fgure 6 Crtcal Steel Bar and Steel Wre n PC Grder Brdges Table 5 Fatgue Lfe Evaluaton Results of PC Brdges Fatgue lfe (Year) Brdge Poston Object S-N Curve LEFM Smple supported PC brdge Contnuous PC brdge Heavy Lane Lght Lane Heavy Lane Lght Lane Prestress steel wre Steel bar Prestress steel wre Steel bar Prestress steel wre Steel bar Prestress steel wre Steel bar

8 From the two PC brdges evaluaton results, t can be concluded that under the smlar traffc load, the fatgue lfe of contnuous PC grder brdge s longer than smple supported PC grder brdge. For PC grder brdges, fatgue lfe of steel bar and wre calculated by LEFM method or S-N Curve method s more large than the brdge desgn servce lfe (100 years), but the fatgue lfe should be shortened sharply consderng the overloadng, concrete crack, corroson fatgue and durablty damage. Concrete Box-grder Brdge A separated nterchange brdge (Fgure 7(a))wth box grder s selected to assess the fatgue performance, whch was open to traffc n The span layout s 7 20m contnuous PC box grder, the wdth of the brdge s 12.5m wth four box grders n transverse drecton. Snce there are many heavy trucks passng across ths brdge, dseases lke fatgue crackng, corroson and deck damage occurred on the brdge. In order to ensure the structure safety, brdge owners adopted prestress carbon fber renforced plate (CFRP) and steel plate to strengthen the brdge. Contnuous dynamc stran montorng s carred out to assess the strengthenng effectveness and fatgue performance of brdge structure after strengthenng. The dameter of longtudnal steel bar n the bottom plate s 20mm, the yeld strength s 335MPa. Carbon steel wres are used n prestress steel tendons, and every tendon contans 28 wres wth 5mm n dameter. Longtudnal steel bar and prestress strands layout are shown n Fgure 7(b) # 2# 3# 4# (a) Cross-secton layout Prestress wres(28-ф5) 12-Φ Most unfavaorable wre (b) Longtudnal steel bar and prestress strands layout Fgure 7 Separated nterchange brdge Consderng contrbutons of low stress ranges, fatgue lfe of longtudnal steel bar n box grder s 1940 and years for sde grder and md-grder, respectvely (Table 6). Fatgue lfe of most unfavorable prestress steel wre s and years. Based on LEFM and the depth of ntal cracks are assumed as 0.5mm consderng the corroson pt flaws, fatgue lfe of longtudnal steel bar n box grder s 5888 and years for sde grder and md-grder, respectvely. Fatgue lfe of most unfavorable prestress steel wre s 4700 and years. From the fatgue performance assessment results, t can be concluded that fatgue lfe of steel bar and wre calculated by LEFM method or S-N Curve method s more large than the brdge desgn servce lfe (100 years) after strengthenng. Yaoxan Brdge s a contnuous PC box grder brdge open to traffc n 2006 (Fgure 8(a)), whch s an mportant brdge of provncal road 305 n Shaanx Provnce. The span layout s 4 30m+4 30m, and the cross-secton contans four grders n transverse drecton. Snce the brdge s near a coal mne, the vehcle load of the brdge s dverse, rangng from full-load trucks to small cars, whch makes ths brdge suffer great stress level. The dameter of longtudnal steel bar n the bottom plate s 16mm, the yeld strength s 335MPa. The prestress strand used n the brdge s 4 j15.2, the yeld strength s 1860MPa. Longtudnal steel bar and prestress strands layout are shown n Fgure 8(b). In order to assess the fatgue performance of concrete box grder brdge, stu dynamc stran montorng was conducted contnuously for 21days. 308

9 Table 6 Fatgue lfe assessment of separated nterchange brdge Grder number Poston Object Fatgue lfe (Year) S-N Curve LEFM 1 Sde grder 2 Md-grder Steel bar Prestress steel wre Steel bar Prestress steel wre AST1 1# AST2 AST3 2# AST4 AST5 3# AST6 AST7 4# AST8 ASB ASB ASB3 ASB4 ASB ASB ASB7 ASB (a) Cross-secton layout Prestressed strand Corrugated ppe Most unfavorable strand 7-Φ Φ16 (b) Longtudnal steel bar and prestress strands layout Fgure 8 Yaoxan Brdge 900 Most unfavorable wre Longtudnal steel bar and most unfavorable prestress wre are selected to evaluate the fatgue performance, fatgue stress spectra can be calculated by plane stran assumpton. Based on S-N curve method, low stress ranges are consdered the contrbuton to fatgue damage. Fatgue lfe of longtudnal steel bar n PC box grder brdge s 1428 years, and fatgue lfe of most unfavorable wre s years (Table 7). Based on LEFM, fatgue lfe of longtudnal steel bar n PC box grder brdge s 578 years, and fatgue lfe of most unfavorable wre s years. Fatgue lfe of longtudnal steel bar and most unfavorable prestress wre s longer than desgn servce lfe. But accordng to exstng experence, f fatgue crack occurs on concrete and corroson occurs on the steel bar or the prestress wre, the fatgue lfe wll decrease sharply. Table 7 Fatgue lfe evaluaton of Yaoxan Brdge Object Fatgue lfe (Year) S-N curve LEFM Steel bar Prestress steel wre CONCLUSIONS Concrete brdges are prone to fatgue falure under the coupled actons of repeated vehcles loads, envronment and materal degradaton. In recent years, the traffc volume and vehcle weghts of hghway brdges have been contnuously ncreasng, so concrete brdge fatgue problem becomes more serous. Fatgue performance of typcal concrete grder brdges wth dfferent cross-secton and structure types are assessed, and several typcal short and medum span concrete grder brdges are selected to conduct long-term servce montorng. Fatgue stress of concrete grder brdges wll decrease wth the span length ncrease, and the span number shows lttle 309

10 nfluence on the fatgue stress. Among three typcal sectons, fatgue stress of T-grder brdge s hgher than hollow slab and box grder brdge. Structure type effect the fatgue performance very much, whle contnuous concrete brdge shows better fatgue performance than smple supported brdge. Based on the stu montorng result, fatgue lfe of longtudnal steel bar and most unfavorable prestress steel wre s assessed by S-N curve and LEFM method. Fatgue lves of selected montorng brdge are all longer than the desgn servce lfe (100 years). The assessment results are based on the present traffc volume and structure condtons, the fatgue lfe wll decrease sharply f fatgue cracks or corroson occurs. Snce concrete grder brdges are easy to suffer materal or structure dseases, fatgue safety problems need to be pad more attenton n the future. ACKNOWLEDGMENTS The authors gratefully acknowledge the fnancal support provded by the Major State Basc Research Development program of Chna (973 Program) Sub-program (2015CB057703), the Specal Fund for Basc Scentfc Research of Central Colleges of the P.R. Chna, Chang an Unversty ( , , ), the Transportaton Scence and Technology Project of Transport Mnstry of P. R. Chna ( ), and the Doctor Postgraduate Techncal Project of Chang an Unversty (2014G ). REFERENCES ECCS, (1985). Recommendatons for the Fatgue Desgn of Steel Structures, European Conventon for Constructonal Steelwork, Brussels, Belgum. Herwg, A., (2008) Renforced Concrete Brdges under Increased Ralway Traffc Loads, Ph.D. Thess, École Polytechnque Fédérale de Lausanne, Lausanne. Mner, M.A. (1945). Cumulatve fatgue damage, Journal of the Appled Mechancs, 1945, 67(12): Ma, L. (2000). Fatgue Performance Study of 1860 MPa Low Relaxaton Prestressng Steel Wres, Ralway Standard Desgn, 20(5): (n Chnese) Oh, B.H. (1991). Cumulatve damage theory of concrete under varable-ampltude fatgue loadng. ACI Materals Journal, 88(1): Schläfl, M. and Brühwler, E. (1998). Fatgue of exstng renforced concrete brdge deck slabs. Engneerng Structures, 20(11): Song, Y.P. (2006). Fatgue Behavor and Desgn Prncple of Concrete Structures, Chna Machne Press, Bejng, Chna. (n Chnese) Tlly, G.P. (1988). Durablty of concrete brdges. Journal of Insttute of Hghways and Transportaton, 35(2): Walker, E.F., Harrson, I.M. and Morley, J. (1975) Fatgue and Corroson Fatgue of Renforcement Bars, Proc. Conf. Underwater Constructon Technology, Department of Cvl and Structural Engneerng Report, Unversty College, Cardff. Wang, C.S., L, G., Dong, X.H., Hao, L. and Wang, J.H. (2010). Fatgue lfe evaluaton of exstng hghway renforced concrete brdges, The 5th Internatonal Conference on Brdge Mantenance, Safety and Management, Phladelpha, USA. Wang, C.S., Zhou, J., Wu, Q.Y., Wang, Y.J. and Dong X.H. (2012). Fatgue lfe and servce safety assessment for exstng concrete brdges, Chna Journal of hghway and transport, 25(6): (n Chnese) Wang, C.S., Zha, M.S. and Wang, Y.J. (2013a). Fatgue safety montorng and fatgue lfe evaluaton for exstng concrete brdges. The 13th Internatonal Conference on Fracture. Bejng, Chna. Wang, C.S., Wu, Q.Y. and Mao W.H. (2013b). Fatgue lfe estmaton of renforced concrete brdge deck. Journal of Chang an Unversty (Natural Scence Edton), 33(2): (n Chnese) Wang, C.S., Zha, M.S., Duan, L. and Wang, Q. (2015). Fatgue servce lfe evaluaton of exstng steel and concrete brdges, Internatonal Journal of Advanced Steel Constructon, 11(3): Zhu, J.S., Yan G.P. (2012). Method of numercal smulaton for renforced concrete brdge slabs under fatgue load, Chna Journal of Hghway and Transport, 25(1):