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Safety Assessment of a Masonry Arch Bridge:Field Testing and SimulationsJ. M. Chandra Kishen, M.ASCE1; Ananth Ramaswamy, M.ASCE2; and C. S. Manohar3Abstract: The safety of an in-service brick arch railway bridge is assessed through field testing and finite-element analysis. Different loadingtest train configurations have been used in the field testing. The response of the bridge in terms of displacements, strains, and accelerations ismeasured under the ambient and design train traffic loading conditions. Nonlinear fracture mechanicsbased finite-element analyses areperformedtoassessthemarginofsafety.Aparametricstudyisdonetostudytheeffectsoftensilestrengthontheprogressofcrackinginthearch.Furthermore, a stability analysis to assess collapse of the arch caused by lateral movement at the springing of one of the abutments that iselastically supported is carried out.Themargin of safety with respect to crackingand stability failure is computed.Conclusions aredrawn withsome remarks on the state of the bridge within the framework of the information available and inferred information. DOI: 10.1061/(ASCE)BE.1943-5592.0000338. 2013 American Society of Civil Engineers.CE Database subject headings: Arch bridges; Bricks; Masonry; Cracking; Field tests; Nonlinear analysis; Fatigue; Simulation; Safety.Author keywords: Arch bridge; Brick masonry; Cracking; Field tests; Nonlinear analysis; Fracture; Fatigue.IntroductionThe Indian Railway system contains several masonry bridges thataremorethan100yearsold.Thesebridgeshavedeterioratedbothinterms of strength and stiffness for a variety of reasons. The bridgeshave been designed for live loads and service conditions that havechanged drastically with time. Increased axle loads and trafficdensity have necessitated bridge owners to have the bridge moni-tored and condition assessed to determine the residual structuralstrength and identify strengthening measures to be taken for safeperformance. Bridge monitoring has become a promising tool forbridge research, maintenance, assessment, and addressing real-timetraffic survey issues (Kiviluoma 2007).Fieldtestingprovidesdataandinformationthatwouldhelpintheestimation of residual capacity of damaged and old structures.Results from field andlaboratory testing of brickand stone masonryarches have been reported in the literature (Chatterjee and Datta1995; Melbourne and Gilbrt 1995; Laffranchi and Marti 1997;Fanning et al. 2001; Fanning andBoothby 2001; Thavalingam et al.2001). Very few data are available in the literature on full-scaletesting or actual field testing of existing masonry arch bridges.Boothby et al. (1998) have reported field testing of five masonryarch bridges. In their study, the behavior of filled masonry archbridges under truck loading was examined by service load testingand through a computational model. The bridges tested includea group of three structures having similar geometry, material, age,and geographic location. The testing program had demonstrated thesignificance of the linearity in the response to different loadinglevels and the importance of permanent deformations in evaluatingthe bridge structure. The field tests also showed evidence of thedevelopment of an incipient failure mechanism. Shigeishi et al.(2001) have done field testing on a masonry arch bridge with themain aim of evaluating the potential for using acoustic emissiontechnique for in situ long-term monitoring of the bridge condition.Their experimental study has shown that the acoustic emission isuseful in detecting crack growth and detecting the position of thecrack tips as and when they form. Marefat et al. (2004) have con-ducted load tests on a decommissioned plain concrete railway archbridge.Intheirwork,staticanddynamicloadtestshavebeencarriedout to evaluate the remaining strength of the arch bridge. The testresultsshowedthatallpartsofthearchbridge,suchasarch,spandrelwall, fill layer, pier, foundation, and ballast layer, contributed to thestructural resistance. The structural behavior and cracking patternfrom their study indicated that the masonry bridge acted like acontinuous multilayered structure rather than an arch form.The focus of the current study is on a brick masonry arch bridgein the South Western Railway zone of Indian Railways. The bridgewas constructed with brick masonry with possibly a compactedgranular soil infill and dates back to the 1870s, when it was part ofa meter gauge line. Over the years, the passenger and freight traffichave increased, and the section has been transformed through agauge conversion from meter gauge to broad gauge (1.67 m). Thepermitted axle load until a few years ago was classified as a 176-kN(18-t)axleloadandhassubsequentlyundergoneanupwardrevisionto a 215-kN (22-t) axle load based on an in-house assessment un-dertaken by Indian Railways. At present, there has been a growth infreight traffic in this section, in particular for iron ore and coalmovement, and Indian Railways is considering the possibility offurther enhancing the permitted axle load to 245 kN (25 t) imme-diately, with possible further upward revisions at a later date.In this paper, details of field measurements undertaken at thebridge under design train traffic and fracture mechanicsbasedfinite-element analysis are presented. Conclusions are drawn with1Professor, Dept. of Civil Engineering, Indian Institute of Science,Bangalore 560 012, India (corresponding author). E-mail: chandrakcivil.iisc.ernet.in2Professor, Dept. of Civil Engineering, Indian Institute of Science, Ban-galore 560 012, India.3Professor, Dept. of Civil Engineering, Indian Institute of Science, Ban-galore 560 012, India.Note. This manuscript was submitted on March 15, 2011; approved onNovember 15, 2011; published online on November 17, 2011. Discussionperiod open until July 1, 2013; separate discussions must be submitted forindividual papers. This paper is part of the Journal of Bridge Engineering,Vol. 18, No. 2, February 1, 2013. ASCE, ISSN 1084-0702/2013/2-162171/$25.00.162 / JOURNAL OF BRIDGE ENGINEERING ASCE / FEBRUARY 2013J. Bridge Eng. 2013.18:162-171.Downloaded from by CENTRAL SOUTH UNIVERSITY on 03/11/14. Copyright ASCE. For personal use only; all rights reserved.some remarks on the state of the bridge within the framework ofthe information available and inferred information.Description of the BridgeThe bridge considered in this study is a brick masonry arch bridgebuiltinthe1870sonametergaugesectionthatisnowamajorbroadgauge line. The bridge consists of two major arches across a water-fall with spans of 17.7 and 17.3 m at the springing level and a fewsmaller arches of approximately 7.7 m that are land arches and arepartially closed. The carriage width of the bridge is 8.8 m, and isslightlycurvedinplanhaving a steep rising gradient of 1 in 30. Therailway line alignment is eccentric with respect to the bridge cen-terline. The arch has a central rise of about 4.5 m. The rings of thearchareabout0.93minthicknessacrossthearchbarrel,withabrickmasonry facing on either side rising up to the top of the bridge witha parapet of a meter height on either side. The abutments and piersappeartoconsistofbrickmasonrythatwasencasedinRCduringanearlier intervention. The piers and abutments rest on bed rock. Thepier width is about 3.82 m at the base and varies over the height.Fig. 1 shows the schematic sketch of the bridge.InstrumentationA 64-channel data acquisition system (M/s Dewetron) was used foracquiring the data continuously from all the sensors. The sensorsused with this acquisition system consisted of a LVDT to measuredisplacements,namely,verticalcrowndisplacementsandhorizontalspringing displacements; electrical resistance strain gauges to mea-sure surface strains in a particular direction, either along the cir-cumferential direction of the arch or the arch barrel- at the crown,quarter,andthree-quarterpointandspringinglevelsandontherails;vibrating wire strain gauges mounted on the arch and parapet; anduniaxial and triaxial accelerometers to measure the accelerationlevels in terms of g levels at the track level (sleepers) and corre-sponding locations on the arch surface. A temperature sensor wasfixed on the bridge to measure variations in the temperature. A tiltsensorwasplacedontheverticalsurfaceofthepier.TheLVDTswerelocated to measure the movement in arch surface, and strain gaugeswerelocatedonthearchintrados,parapet,andrail.Tocheckwhetherany activity in the form of movement or cracking takes place on theoutside or inside of the arch, eight acoustic sensors were installedunderneath on the right half portion (Castle Rock-CR) of Span 1.Loading SchemesA series of four major loading tests (static load tests, quasi-staticmoving load tests, speed tests, and longitudinal load tests) wascarried out. The static load test was done with the aim of obtainingthe stiffness properties of the structure. The quasi-static movingload test was performed to obtain variations in deflections andstrains for different positions of the load and is a confirmation ofthestiffnessproperties.Suchvariationsaretypicallydeterminedincomputational models using the well-known method of influencelines. The dynamic amplification factor and the dynamic charac-teristics of the bridge structure such as the natural frequencies areobtained from the speed test. The main objective of the longitu-dinal tests is to determine the stability of the structure when sub-jected to extreme horizontal loads such as from braking on thebridge or accelerating from rest on the bridge. Furthermore, theload transfer onto the bridge structure and the approaches is de-termined from this test.Static Load TestTwo Bogie Flat Rail-carrying (BFR) wagons loaded with pre-stressed concrete sleepers of a fixed number were placed on thebridge structure at a fixed position (axle spacings are shown inFig. 2). The response of all the sensors was taken for four differentloadinglevels.Inthefirstinstance,200prestressedconcretesleeperswerepresentoneachofthetwowagons.Afterthedisplacementsandstrainsweremeasuredatvariouslocationsonthebridge,16sleeperswere removed from each wagon, and responses were measured at184, 168, and 152 sleepers. Two hundred sleepers correspond to anaxle load of 187 kN (20.75 t). The two wagons could apply a staticload on both the spans of the bridge.Quasi-Static Moving Load TestA train formation (referred to as Formation 1), consisting of twolocomotive engines (WDG4), two BFR wagons with 152 sleepersin each, two goods wagon filled with iron ore corresponding toa 245-kN (25-t) axle load with four axles each (BOXNEL, whoseaxle spacing is shown in Fig. 2), and two locomotive engines(WDG3A), was positioned on the bridge at different predeterminedlocations, and measurements were taken. At the start of the test, thefirst wheel of the WDG4 wagon was placed on the left springingposition of Span 1. The test progressed with subsequent wheels oftheformationoccupyingthisreferencepointinsuccession.Sincetheformation had 40 wheels, 40 measurements were taken.Speed TestIn this test, the same formation as was used in the quasi-staticmoving load test is used and made to run at nominal speeds of 5,10, 20, 30, and 40 km/h in both directions across the bridge.The accelerations are measured as the train formation runs on thebridge and most importantly when the train exits the bridge. As theFig. 1. Schematic sketch of the brick masonry arch bridgeJOURNAL OF BRIDGE ENGINEERING ASCE / FEBRUARY 2013 / 163J. Bridge Eng. 2013.18:162-171.Downloaded from by CENTRAL SOUTH UNIVERSITY on 03/11/14. Copyright ASCE. For personal use only; all rights reserved.train exits the bridge, the magnitude of vibrations decrease becauseof damping, and the free vibrational characteristics can be used toextract the natural frequencies of the bridge.Longitudinal Load TestFor this test, a formation (referred to as Formation 2) consisting of54 goods wagons (BOXNEL), each loaded with a 223-kN/axle(22.78-t/axle) load and seven locomotive engines (WDG4), twoat one end andfive (two enginesin idling condition) at the other, areused. Measurements were taken for the following cases:1.Test rake running at 5 km/h Kulem (K) to Castle Rock (CR)end. This test is referred to as L1;2.Testrakerunningat5km/h(CRtoK).ThistestisreferredtoasL2;3.Test rake running at 36 km/h (maximum possible speedpermitted on this section from K to CR). This test is referredto as L3;4.Test rake running at 36 km/h (maximum possible speedpermitted on this section from CR to K). This test is referredto as L4;5.Test rake running at 20 km/h (from K to CR). This test isreferred to as L5;6.Test rake at 20 km/h (from CR to K) and applying dynamicbrake(allactiveWDG4sonly)whenfirstaxleoffirstWDG4isat midspan of Span 1. This test is referred to as L6;7.Coupler test: First wheel of third WDG4 at right springing ofSpan 1 and accelerates from K to CR with full tractive effortfrom rest. This test is referred to as L7;8.FirstwheelofthirdWDG4atleftspringingofSpan2andthenaccelerating with full tractive effort from K to CR. This test isreferred to as L8;9.First wheel of third WDG4 at midspan of Span 1 and accel-erating with full tractive effort from K to CR. This test isreferred to as L9;10.Rake approaches at 20 km/h from K to CR end. The servicebrakeswere applied onthe entire formation whenthe firstaxleof the leading WDG4 was at midspan of Span 1. This test isreferred to as L10; and11.Brake-bindingtest:FirstwheelofthirdWDG4wasatmidspanof Span 2. Brakes of the last four BOXNEL applied. The rakestartsfromrestacceleratingwithfulltractiveeffort.Thistestisreferred to as L11.The dynamic brake is applied only by the active locomotives toslow the train, whereas the service brakes are applied by the entiretrain formation to stop a train during normal operations.Results of Field TestsResults of Static TestsTheresponseofthebridgestructurewhensubjectedtostaticloadsoffouraxlesoneachspanisshowninTable1. In this table, the verticaldeflections at the center of crown in Spans 1 and 2, the tangentialstrains along the centerline of the rail track at three different posi-tions on Span 1 quarter span (CR side), crown, and quarter span(Kside)andthetransversestrainsatthecrownofSpan1areshown.It is seen that the bridge behaves linearly for the three load levelsapplied over it. No visual cracking was seen during this test, andthe structure unloaded elastically on load removal. The minor dif-ferences in the displacements of the two spans are indicative of themild asymmetric nature that exists in the arch geometry. The trans-verse strains along the crown are seen to be tensile in nature.Results of Quasi-Static Moving Load TestThe results of this test indicates that the maximum vertical dis-placement on the crown is about 0.88 mm and the maximum hor-izontal springing deflection is 0.1 mm at the abutment and 0.17 mmat the central pier in Span 1. In Span 2, the maximum vertical de-flectionatthecrownis0.75mm,whereasthespringingdeflectioninthe abutment is 0.01 and 21.4/11.2 mm in the central pier becauseof a 245-kN (25-t) axle load. The negative value implies horizontalmovement of the central pier to the left (K side; Fig. 1), and thepositive value represents horizontal movement toward the CR side.The LVDT was mounted on the repaired (encased) concrete at thespringinglevel.Thelargevaluesofhorizontaldeflectionsuggestthatdelamination (separation) of the repaired concrete from the parentmasonrypiercouldhaveoccurred.Furthermore,theacousticsensorsindicated an increase in the threshold energy level, implying thatFig. 2. Spacing of axles (mm) in BFR wagon, BOXNEL, and WDG4locomotive164 / JOURNAL OF BRIDGE ENGINEERING ASCE / FEBRUARY 2013J. Bridge Eng. 2013.18:162-171.Downloaded from by CENTRAL SOUTH UNIVERSITY on 03/11/14. Copyright ASCE. For personal use only; all rights reserved.some kind of activity has taken place inside the structure, such asa small movement of the filler material.Results of the Speed TestTable2 shows the highest response of the displacements and strainsobtainedfromafewsensorsduringthespeedtest.Table3showsthedynamic magnification factors computed for displacements andstrains for different sensors and for different speeds. This factor iscomputed as the ratio of maximum dynamic displacement/strain tothe corresponding component under a quasi-static moving load. ItisseenfromTable3thatthemaximumamplificationfactoris1.0487for displacement, and this occurs at the crown of Span 2 for For-mation1movingfromCRtoKataspeedof30km/h.Forstrains,themaximum amplification is 1.68 for the tangential component at thecrownofSpan1fortheFormation1movingfromKtoCRataspeedof 20 and 40 km/h. This indicates that the crown experiences thehighest amplification of strains, and this is further augmented be-cause of the steep gradient in elevation and curvature in the plan ofthe arch. Further, the amplification factors do not appear to changesignificantly with a change in speed. This suggests that the bridgemass is substantially higher than the train masses, reducing theirinteractive effects.Speed tests were also conducted using Formation 2 as detailedpreviously under the longitudinal load test. Table 4 shows thehighest response of the displacements and strains obtained froma few sensors during the speed test using Formation 2. It is seen thatthe highestdownward displacement underthe loading from runningFormation 2 occurs for a speed of 5 km/h, with the amplitudesreducing for higher speeds. Conversely, for constant speed move-ment from K to CR (upward gradient), an amplification of 1.22 wascomputed as speed was varied from 5 to 30 km/h.Table 1. Vertical Deflection and Tangential Strains in Static TestLoad (sleepers)Crown displacement (mm)Tangential strain in Span 1 (m)Transverse strainat crown ofSpan 1 (m)Span 1Span 2Quarter spanCR sideCrownQuarter spanK side1680.490.47210.320.429.216.61840.530.54212.920.7210.913.42000.570.60215.020.8212.517.1Table 2. Highest Response Measured in Speed Test Using Train Formation 1NumberSpeed (km/h)and directionMaximum orminimumCrown displacementTangential strain in Span 1Span 1 (mm)Span 2 (mm)Quarter spanCR sideCrown (m)Quarter spanK side1Quasi-staticMaximum20.19720.17723.3535.657Minimum20.88220.745224.76326.848215.0325 CR to KMaximum20.17420.10321.7975.75620.145Minimum20.83520.756222.95829.936219.312310 CR to KMaximum20.16620.10322.5807.21720.666Minimum20.83520.736223.59629.082218.530430 CR to KMaximum20.16620.10322.5365.38020.145Minimum20.87920.781224.683210.456219.949540 CR to KMaximum20.17420.11023.0155.46720.203Minimum20.87920.781224.625210.558219.485620 K to CRMaximum20.16620.11623.5946.29121.650Minimum20.84320.755224.886211.512221.541740 K to CRMaximum20.14620.08423.7686.8700.405Minimum20.86720.743224.973211.469218.704Table 3. Dynamic Magnification Factors Using Train Formation 1NumberSpeed (km/h)and directionPositive ornegativeCrown displacementTangential strain in Span 1Span 1Span 2Quarter spanCR sideCrownQuarter spanK side15 CR to KPositive0.8820.5840.5361.018Negative0.9461.0140.9271.4511.284230 CR to KPositive0.8420.5840.7560.951Negative0.9961.0490.9971.5271.326340 CR to KPositive0.8820.6210.8990.966Negative0.9961.0490.9941.5421.295420 K to CRPositive0.8420.6571.0721.112Negative0.9551.0141.0051.6811.432540 K to CRPositive0.7420.4751.1241.214Negative0.9820.9971.0091.6751.243JOURNAL OF BRIDGE ENGINEERING ASCE / FEBRUARY 2013 / 165J. Bridge Eng. 2013.18:162-171.Downloaded from by CENTRAL SOUTH UNIVERSITY on 03/11/14. Copyright ASCE. For personal use only; all rights reserved.The natural frequency of the bridge system is estimated byconsidering the Fourier transform of the accelerometer data thatcaptured the free vibration of the bridge following the exit of thetrain formation from the bridge. Fig. 3 shows typical accelerationdata obtained from an accelerometer when the train formationmoves on the bridge at a speed of 20 km/h from K to CR. Thecomplete acceleration history for a total time of about 52 s is shownalongwiththeenlargedviewofthedataobtainedforthelast6swhenthe train formation left the bridge. Fig. 4 shows the amplitude of theFourier spectrum of the free vibration acceleration response fol-lowing the exit of the train from the bridge. It is observed that thedominant frequencies of the bridge system are in the range of 510Hz, which is relatively low because of its heavy mass.Results of the Longitudinal Load TestThe main objective of this test is to determine the stability of thestructure when subjected to extreme horizontal loads such as thosecaused by braking on the bridge or accelerating from rest on thebridge. As mentioned in the testing program, a series of tests wasconducted to determine the load transfer on to the bridge structureand the approaches. One of the two rails was instrumented withstrain gauges at three different sections of the bridge: one each onthe approach, the abutment level, and within the bridge. By mea-suring the strain response, the horizontal load transfer from thelocomotives to these three different sections could be estimated.Table 5 summarizes the results of the longitudinal test. In thistable, the tractive force applied by the locomotives and the horizon-tal force transferred to the rails above the approach and above thebridge underdifferent loadingconfigurationsareshown.Thevaluesreported in this table are the maximum values at different timeinstants and hence they should not be added algebraically. The dif-ferences between tractive effort measured in the engine and on therails may be attributed to other engines being active at the end ofthe formation (pushing), frictional force dissipation along the rails,slip of the wheels, and other rail dynamic effects. Table 6 sum-marizes the highest responses based on the measurements usingFormation 2 under various loading scenarios.Other Field MeasurementsA tiltmeter was placed on the central pier for measuring the amountof tilt on the vertical surface. The maximum measured value of tiltwasoftheorderof0.3?duringthelongitudinaltest.Thistiltiselasticin nature and is observed to have recovered completely on removalof the load.Nondestructive evaluation of the pier was undertaken using ul-trasonicpulseequipment.Thedirectmethodofmeasurementacrossthe central pier was adopted in this test, and the pulse had a velocityof 6.43 km/s, giving an estimate of the concrete strength to be 46MPa and the dynamic modulus to be 86,000 MPa. A similar valueof the strength was also obtained from the rebound hammer tests.These strength values have been used in the numerical model forthe pier and abutment.Coefficient of Dynamic AugmentAccording to the Indian railway code (IRS 2006), the coefficientofdynamicaugment(CDA)applicableuptoaspeedof160km/honbroad gauge and single tracks is obtained using the relationCDA 0:15 86 L1where L 5 loaded length of span in meters for the position of thetraingivingthemaximumstressinthememberunderconsideration.Forthepresentarchbridge,withthespanLbeing17.3m,theCDAis0.493. From field measurements, the CDA obtained for displace-ment is 0.22 and for strains it is 0.68, indicating a code violation.Numerical SimulationsIn this section, details of finite-element simulations of the arch bridgeunder various loading conditions are presented. The analysis isdone using the finite-element programs ATENA (ATENA) and NISA(NISA). The ATENA software has been used to study the bridgeunder monotonically increasing loads positioned as in rail load con-figurations to understand cracking in masonry and its propagation.Furthermore, parametric studies have been undertaken by consid-ering the tensile strength of brick masonry and filler and theboundary conditions as variable parameters. The speed tests aresimulated using the finite-element program NISA, wherein thenaturalfrequenciesandmodeshapesarecomputedtogetherwiththeprincipal stresses.The masonry arch bridge with a soil infill has been idealized ascomposed of two isotropic homogeneous materials: masonry andfiller. A two-dimensional (2D) plane stress model of the bridge wasused in this study. The finite-element package ATENA (ATENA)encompasses many material model formulations for quasi-brittleconcrete-likematerials,suchasabiaxialfailuresurfacewithdifferenttension and compression thresholds, postcrack strain softening basedTable 4. Highest Response Measured in Speed Test Using Train Formation 2NumberSpeed (km/h)and directionMaximum orminimumCrown displacementTangential strain in Span 1Span 1 (mm)Span 2 (mm)Quarter spanCR sideCrown (m)Quarter spanK side15 CR to KMaximum20.14620.03920.4355.510Minimum20.94220.943231.554217.124320 CR to KMaximum20.09520.0780.7685.8864.051Minimum20.86720.710227.597212.785217.214430 CR to KMaximum20.12720.0652.0735.8284.340Minimum20.89820.697221.88210.760216.05755 K to CRMaximum20.1580.12921.5656.20423.182Minimum20.87920.549229.568214.173225.604630 K to CRMaximum20.14320.03220.6095.2352.296Minimum20.87120.672226.525211.107216.491166 / JOURNAL OF BRIDGE ENGINEERING ASCE / FEBRUARY 2013J. Bridge Eng. 2013.18:162-171.Downloaded from by CENTRAL SOUTH UNIVERSITY on 03/11/14. Copyright ASCE. For personal use only; all rights reserved.on exponential and multilinear softening, specific fracture energy ofthe material, compression softening in cracked concrete, and otherfracture-based parameters, such as crack interface shear transfer.A 2D plane stress finite-element model for the masonry archbridge is shown in Fig. 5. The brick masonry was assumed to havea modulus of 1,800 MPa, Poissons ratio of 0.2, and a specificfracture energy of 5.8 N-m/m2. The soil infill was idealized to havea modulus of 800 MPa, with a Poissons ratio of 0.18. A relativelysmall tensile strength of 0.3 MPa was assumed for the masonry, witha similar value of 0.3 MPa for the infill. These values are obtainedthrough an iterative process of model calibration using the fieldmeasurements of the static load deflection and quasi-static movingload studies. The boundary condition on the vertical face of theabutment (left end of Span 2) is restrained in the longitudinal trafficdirection, and the base of the abutments and central pier isconstrainedinthehorizontalandverticaldirections.Theboundaryatthe right abutment of Span 1 is elastically constrained for longi-tudinal movement using linear springs (the value of this springconstant is reported later).The following studies were undertaken:1.Simulationofstaticload-deflectiontest(BFRwagonscarryingprestressed concrete (PSC) sleepers positioned as in the fieldstudies);2.Simulation of quasi-static moving load test (245-kN axle loadBOXNEL wagons arranged at critical position as in the fieldstudies); and3.Parametric studies varying tensile strength of brick masonryand filler and the boundary condition of the abutment of Span1 on the CR end. A few smaller land arches of approximately7.7-mspanarepresentontheCRendofSpan1thatarepartiallyFig. 3. Acceleration data under moving load: (a) full record; (b) segment of data after the train has left the bridgeJOURNAL OF BRIDGE ENGINEERING ASCE / FEBRUARY 2013 / 167J. Bridge Eng. 2013.18:162-171.Downloaded from by CENTRAL SOUTH UNIVERSITY on 03/11/14. Copyright ASCE. For personal use only; all rights reserved.closed. Hence, this boundary is simulated by providing springsand also by restraining it completely.Simulation of Static Load TestIn this study, the two BFR wagons with PSC sleepers (as previouslydetailed)areplacedonthebridgewithloadscoincidingwiththeaxlepositionasinthefieldtest.Theseloadsaredirectlyappliedatthetopof the bridge,which thengets transferred to the arch throughthe fill.The vertical deflection obtained at the crown of Span 1 is 0.55 mm(versus a measured value of 0.57 mm for BFR with 200 sleepers).The corresponding values of computed and measured vertical de-flection at the crown of Span 2 are 0.54 and 0.6 mm, respectively.This indicates that the material properties of modulus of elasticityandPoissonsratiousedforthemasonryandtheinfillintheanalysisarereasonable,leadingtocomputeddeformationbeinginagreementwith the deformations observed at field and thereby calibrating thematerial model.Simulation of Quasi-Static Moving Load TestIn this study, the entire rake (formation) used for this test as de-scribed previously is used for applying the load on the bridge ina sequential way. One particular position of the rake on the bridgethat causes maximum effects was simulated. Table 7 shows theresults of this simulation at various points, together with the fieldresults for one of the loading configuration that corresponds to thehighest crown vertical displacement.For this loading configuration, a parametric study was under-taken, by varying the tensile strength of the brick masonry and thefillerandtheboundaryconditionsattheabutmentofSpan1tostudytheir influence on the crack widths and the failure mode.No Cracking AnalysisThe finite-element analyses are done by assuming higher values oftensile strength of the brick masonry and the filler material in sucha way that no cracks are developed from increasing axle loads. Theanalysis is carried by increasing the axle loads on the BOXNELwagons in steps of 48 kN (5 t) from an initial value of 245 kN (25 t).Thecorrespondingloadsofthe168sleepersloadedonBRNwagonsare scaled up proportionately. The lateral boundary of the abutmentof Span 1 on the CR end (Fig. 1) is assumed to be on springssimulating the partially filled up land arches. The spring constant(1,300N/mm)iscalibratedsuchthatforanaxleloadof245kN(25t)onthe BOXNELwagons,the deflectionatthe crownof Spans1and2 match the field measurements. Fig. 6 shows the plot of maximumprincipalstressatthecrownofSpan1withrespecttotheappliedaxleload. From this figure, it is seen that the rise in the maximumprincipal stress is only about 0.1 MPa for an increase of a 980-kN(100-t) axle load, which is quite small. Furthermore, at a 245-kN(25-t) axle load and without the self-weight, the maximum principalFig. 4. Amplitude of Fourier spectrum of free vibration accelerationresponse following the exit of moving trainTable 5. Maximum Horizontal Force Transfer in the Longitudinal LoadTestTestTractive force fromlocomotive (kN)Force on rails (kN)On twoapproachesOn bridge(two rails)L31,5961,093.6469.9L67681233440.6L71,560941.2355.6L81,5721,384.41,347.6L91,578950.8323.5L101,608957.9400.9L111,596456.1303Table 6. Highest Response Using Train Formation 2 in the Longitudinal Load TestTestMaximum orminimumCrown displacementTangential strain in Span 1Span 1 (mm)Span 2 (mm)Quarter spanCR sideCrown (m)Quarter spanK sideL6Maximum0.0040.0711.3636.2770.579Minimum20.89020.794228.510211.920219.240L7Maximum0.5460.54221.9883.81820.975Minimum20.02820.04522.71029.76221.881L8Maximum0.2220.2585.66710.9634.629Minimum20.58220.458218.96023.037213.598L9Maximum0.6290.60119.1765.90113.453Minimum20.11520.11626.56629.12624.340L10Maximum0.0360.0130.5075.4523.182Minimum20.72420.762222.40829.039215.623L11Maximum0.1780.17811.32011.0781.158Minimum20.02020.02020.49322.60326.365168 / JOURNAL OF BRIDGE ENGINEERING ASCE / FEBRUARY 2013J. Bridge Eng. 2013.18:162-171.Downloaded from by CENTRAL SOUTH UNIVERSITY on 03/11/14. Copyright ASCE. For personal use only; all rights reserved.stress near the crown is 0.0245 MPa (0.16 MPa with self-weight).Because no cracks were visually observed at this load in the fieldstudies, it is expected that the minimum tensile strength of themasonry arch is more than 0.16 MPa.Fig.7showstheverticaldeflectionatthecrownofSpan1withtheself-weight and increasing live load. The live load corresponding toarelativedisplacementof1.2mmonthecrown(permissiblevalueasper IRS 2006) caused by the live load alone is 441 kN (45 t). Thiscorresponds to amargin of safety at245 kN (25t;proposed increaseof axle load) equal to 1.8. This margin of safety is more than themargin provided by the code. Similarly, the horizontal deflection atthe springing of abutment and piers of Spans 1 and 2 are computedwith increasing axle load. The results indicate that for a relativedisplacement (for live load alone) of 0.2 mm (permissible horizon-tal deflection as per IRS 2006) at the springing of Span 1, thecorresponding live load is 637 kN (65 t). This offers a margin ofsafety at a 245-kN (25-t) axle load of 2.6, which is more thanthe margin provided by the code.Cracking AnalysisAcrackinganalysisiscarriedouttodeterminewhetherthefailureofthe arch bridge takes place because of excessive cracking near thecrownoranyothermode.Atensilestrengthofbrickmasonryof0.20MPa with a specific fracture energy of 5.8 N-m/m2is used, and theanalysisiscarriedoutbyapplyingtheself-weightandincrementallyincreasing the axle loads on the BOXNEL wagons in steps of 49kN (5 t). The corresponding loads of the 168 sleepers loaded on theBRN wagons are scaled up proportionately. It was found that theintrados ofarchatthecrownstartstocrackatanaxleloadof147kN(15t).Thecrackingprocesscontinues,andatanaxleloadof392kN(40 t), the crack propagates through the entire thickness of the brickarch. The crack widths from this incremental analysis are plottedagainst the axle load in Fig. 8. From this figure, the crack widthcorrespondingtoanaxleloadof147kN(15t)isslightlylessthan0.2mm, which is too small to be observed visually in the field tests.Further, the crack widths increase at a faster rate after the 392-kN(40-t) axle load, which is when the crack propagated through theentire thickness of the brick arch. Thereafter, on increasing the axleload, the crack width increases without the crack propagating fur-ther.Thearchsoftensconsiderablebecauseoftheincreasedopeningof the crack. The final failure takes place because of cracking at thecrown of the arch.Simulations with Tractive Forces Caused by BrakingA longitudinal tractive force analysis is carried out by includinghorizontal forces of magnitude 343 kN (35 t) based on an averagefield-measured value at the rail level and at wheel positions. For thisanalysis, a tensile strength of 0.2 MPa is assumed for both the brickmasonry and the filler material. From this analysis, it was observedthatcrackinginitiatedatthecrownofSpan1ataliveloadof637kN(65 t), offering a margin of safety of 2.6 with respect to a 245-kN(25-t) axle load. Furthermore, no cracks were observed at thespringing of the pier and abutments, suggesting that the hingingmode of failure is unlikely. The failure of the arch through theFig. 5. Finite-element model of the arch bridge showing the boundaryconditionsTable 7. Comparison between Simulated and Measured Results of CrownDisplacements and Strains in Quasi-Static TestDescriptionSpan 1Span 2Crown displacementComputed (mm)0.640.3Measured (mm)0.680.2Crown strainsComputed (m)10.71.26Measured (m)8.35Not measuredFig. 6. Maximum principal stress (without self-weight) at crown ofSpan 1Fig. 7. Vertical deflection at crown of Span 1JOURNAL OF BRIDGE ENGINEERING ASCE / FEBRUARY 2013 / 169J. Bridge Eng. 2013.18:162-171.Downloaded from by CENTRAL SOUTH UNIVERSITY on 03/11/14. Copyright ASCE. For personal use only; all rights reserved.formation of hinge near the crown can take place only if there isexcessive horizontal movement at the springing of the abutment.Simulation of Speed TestsThe speed tests are simulated within the framework of the finite-element method using the program NISA (NISA). A mass densityof2,300kg/m3andamaterialdampingvalueof0.03areusedinthemodel. An undamped free vibration analysis revealed that the first25 system natural frequencies were in the range of 7.2439.50 Hz,with the first five frequencies being 7.24, 7.64, 10.40, 10.50, and15.60 Hz, respectively. This is quite close to the values extractedfrom the field measurements. The first five mode shapes corre-sponding to these frequencies were bending modes in Spans 1 and2. The damping model considered in the analysis assumes thatdamping in pier, abutment, arch vault, and filler materials could bedifferent. An equivalent damping for each mode is evaluated byusing the relationhpPi54i1hiEinPi54i1Ein2where hp5 viscous damping coefficient in the nth mode, hi5damping coefficient for the the ith material, and Ein5 strain energystored in parts of the structure made up of the ith material in the nthmode.Analysis of SubstructureThe stresses at the bottom of the pier were computed for the casewith self-weight, live load with 25-t axle load, and the longitudinalforce applied with the train moving in the direction of CR to K. Thetotal vertical and horizontal forces at the bottom of the pier werecomputed to be 33,780 and 2,203 kN, respectively. These valuestranslated to a vertical stress of 0.520 MPa and a horizontal stress of0.034 MPa at the base of the pier. These low values indicate that thepier is safe against bearing and sliding. The bearing capacity of rocktypically lies above 200 MPa, whereas the shear strength is above1.0 MPa.Estimation of the Fatigue Life of Arch BridgeThe bridge structure is subjected to repeated fluctuating loads be-cause of the passage of trains. As a result of repeated loading overaperiodoftime(about120years),stiffnessdegradationanddamageaccumulationcouldhavetakenplace,andhence,themajorprincipalstress near the crown region is inferred to be tensile. Models basedon the concepts of fracture mechanics have been developed to studythe fatigue behavior of materials. In the theory of fracture mechan-ics, a crack is assumed to exist at the position where maximumtensile stress occurs. The rate of propagation of this crack with re-spect to the number of cycles of fatigue load is computed, and thisdefines the fatigue life of the component/structure.The simplest crack propagation law is the Paris law, which isdefined as (Kumar 1999)dadN CDKm3where a 5 crack length, N 5 number of cycles of fatigue load(constant amplitude), DK 5 stress intensity factor range, and C andm 5 material constants. The fatigue life estimation for the archbridge is computed using the Paris law. Although this law considersthe fatigue crack growth to occur at constant amplitude loading andin reality variable amplitude loading was encountered, it could beused to obtain an estimate of the crack growth rate in a simplemanner. The material parameters for mortar used in the present casefor masonry are assumed as C51:70E203 m/cycle and m52:1(Slowik et al. 1996; Bazant and Xu 1991; Sain and ChandraKishen 2008).The stress intensity factor range is computed using (Prashant1999)DK fbDsffiffiffiffiffiffipap4where Ds 5 stress amplitude range equal to (smax2smin). This isconsidered to be equal to 0.06 MPa, which is the difference of themaximum and minimum principal stresses as obtained in the analysisusing the 245-kN (25-t) axle load. The factor fb is the geometryfactorthat is equalto 1.3foracirculararch (Prashant1999).Aninitialcrack size of 0.1 mm is assumed at the crown of the arch.Numerical integration is performed on the Paris law, and thenumberofcyclesrequiredforaninitialcrackof0.1mmtopropagateuntil the crack grows to 10 mm is 242.6E103 cycles. Assumingeach cycle of loading to be a passage of train (54 wagons 1 7WDG4) loaded to 245 kN (25 t) per axle and assuming 10 trainsrunni
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