(IMIM一篇非常经典的转角以及位移测试)Reference free method for re

Reference free method for real time monitoring of bridgedeflectionsKarim Helmi a ,Todd Taylor b ,Ali Zarafshan b ,Farhad Ansari b ,⇑a Construction and Building Engineering Department,Arab Academy for Science,Technology and Maritime Transport,Abu Qir,Alexandria,EgyptbCivil and Material Engineering Department,University of Illinois at Chicago,2095Engineering Research Facility,842W.Taylor Street,Chicago,IL 60607,USAa r t i c l e i n f o Article history:Received 9February 2014Revised 31August 2015Accepted 1September 2015Available online 15September 2015Keywords:Bridges Real time DeflectionFiber optic sensors Fiber Bragg gratings Tiltmeter TrucksStructural health monitoringa b s t r a c tMonitoring deflections provides a powerful diagnostic tool for structural health monitoring of bridges.Excessive deflections under service loads may be indicative of structural changes,damage and deteriora-tion.For the real time monitoring of deflections under operating traffic loads,it is often difficult to estab-lish a fixed reference point for displacement transducers either because the bridge crosses over a body of water or a roadway.Moreover,vandalism and environmental conditions disrupt and more than likely alter the fixity of the reference points.The work presented in this study pertains to the development of a method for real time remote monitoring of bridge deflections.From the practical point of view,the primary attribute of the proposed method is its capability for making reference free estimates of bridge deflections.The formulations employ the measured rotations and curvatures of the bridge for this purpose.The feasibility of the approach was tested on two different highway bridges.Both bridges were instrumented with a number of different fiber optic sensors that included tiltmeters and strain gauges.Conventional transducers and displacement measurement devices were also used in parallel in order to evaluate the performance of the proposed method.A series of load tests were conducted at both bridge sites that included use of trucks with known weights.In addition,finite element models were developed and employed for further verification of the proposed approach.Field test measurement results and their correlations with the conventional methods as well as comparison with the finite element models are described in this article.Ó2015Elsevier Ltd.All rights reserved.1.IntroductionBridges are designed to carry the intended design loads and per-form efficiently during their service lives.In-service performance is attributed to structural response in terms of deflections,cracking and inelastic deformations.In general,these performance charac-teristics pertain to serviceability.For example,American Associa-tion of State Highway and Transportation Officials (AASHTO)provides optional limitations on live load deflections as a fraction of the span length (e.g.span length/800).The deflection limitation controls at the design stage are mainly established to accommo-date motorists’comfort.Alternatively,monitoring of deflections provides a powerful diagnostic tool for structural health monitor-ing (SHM)of bridges.Gradual or sudden changes in-service load deflections are indicative of structural changes,damage or deteri-oration.For example crack growth in girders,corrosion of various reinforced concrete elements,support movements,inelastic deformations of steel girders,bearing failures,debonding of steel reinforcement and other phenomena all fall into this category.The measured deflection response can be used in a finite element model of the bridge to back calculate residual capacity,compare the in-service versus designed behavior,or to assess the extent of damage.Linear displacement transducers such as linear variable differ-ential transformers (LVDT)are employed for direct measurement of deflections.They are often used during load tests when the bridge is closed to traffic or when it is possible to use a fixed refer-ence point for the transducers [1,2].For real time monitoring of deflections under operating traffic loads it is often difficult to establish a fixed reference point for displacement transducers,either because the bridge crosses over a body of water or a road-way.Moreover,vandalism and environmental perturbations could dislocate or cause the movement of the reference points.Other methods that have proven to be effective for periodic measurements but not suitable for real time long term monitoring of bridges include laser Doppler vibrometery (LDV),use of total stations,photogrammetry,and microwave radar.Examples include Jauregi et al.’s [3]work on digital close-range terrestrial photogrammetry (DCRTP)in which their laboratory and field tests on steel and prestressed concrete girder bridges indicated close/10.1016/j.engstruct.2015.09.0020141-0296/Ó2015Elsevier Ltd.All rights reserved.⇑Corresponding author.Tel.:+13129963428.E-mail addresses:kareem.helmy@ (K.Helmi),ttaylo20@ (T.Taylor),ali.zarafshan@ (A.Zarafshan),fansari@ (F.Ansari).agreements with total station readings and elastic analysis.While this technique is applicable only to measurements under static loading conditions,more advanced3D studies,including long exposure imagery are being developed for dynamic measurements [4].LDVs have been employed in remote monitoring of transverse dynamic displacements in stay cables[5].Also,LDVs can be used while the bridge is subjected to traffic loads and the scanning ver-sion of LDV(SLDV)is capable of multi-point measurements[6]. Deflection measurements by LDVs however,depend on measuring the speed of vibrations,and they are ineffective when bridges vibrate at low frequencies,i.e.slow speeds during rush hours.In a manner similar to LDV,radar interferometry has been employed for periodic remote monitoring of bridge deflections.Gentile and Bernardini[7]demonstrated the applicability of the microwave based interferometric technique for static as well as dynamic measurements in laboratory experiments andfield applications in bridges.Global Positioning Systems(GPS)have been used for real time monitoring of displacements in a number of applications,including tall buildings[8],towers[9],and bridge decks and pylons[10–12]. The reported activities are promising since over the years the res-olution and error in the measured responses have improved from several centimeters to a few millimeters,and sampling frequencies of up to100Hz[12,13].The disadvantages of GPS systems include errors due to multipath and loss of lock.These errors occur because it is not always possible to maintain a robust geometric configura-tion of satellites in view at all times[10,14].Sanli et al.[15]proposed an indirect method to measure the bridge deflections by a combination of tiltmeters and LVDTs.A con-crete slab on steel girder bridge was employed for testing the method.They used electrolytic tiltmeters with capability for oper-ating under adverse thermal and high humidity environments on the bridge.Their method involved the use of a cubic spline function for computation of deflections from acquired data.Their results on the live load tests of the Drweca River Bridge compared well with the results from LVDT measurements.The drawback with their method was the fact that the computations required direct mea-surement of deflections from LVDTs at the locations of tiltmeters in order to establish reference.A number of methods have been developed based onfiber optic Bragg grating(FBG)sensors[16,17].The use of FBG sensors resulted in higher resolution and lower noise measurements due to the sensitivity and immunity of the optical sensors to electrical and electromagnetic interference.The results have been promising due to the fact that FBG measured strains provided better esti-mates of deflections than the measurements with conventional optic sensors were used for high resolution monitoring of rotations and strains.The elastic curve formulations were programmed into the interrogation units of the sensors at two bridge sites for auto-mated real time remote monitoring operations.The approach described herein does not require ground-reference or the use of displacement sensors for monitoring the deflections.The method is described next,followed by implementation at the bridge sites and comparison of the results with deflections measured by con-ventional methods and those obtained from thefinite element analysis of the bridge.2.Method2.1.Description and formulationFig.1corresponds to a simple beam subjected to an arbitrary load and its response in terms of rotations,u and deflection,d.Assuming that the rotation along the beam at any given point in time could be represented with an n th order polynomial,the rela-tionship can be expressed as:u¼a1x nþa2x nÀ1þÁÁÁþa i x nÀiþ1þÁÁÁþa n xþa nþ1ð1Þwhere u is the rotation,x is the distance along the beam and a i is the polynomial coefficient.The curvature of the beam at any point is calculated by:j¼M=EI¼e=yð2Þwhere j is the curvature,M is the bending moment,E is the mod-ulus of elasticity,I is the moment of inertia,e is the strain and y is the distance of the section from the neutral axis for which the strain is computed.The relation between the rotation and the curvature is given by the following relation[18]:j¼d u=dxð3ÞThe curvature,therefore is calculated by differentiating Eq.(1) with respect to x,resulting in the following relationship:j¼na1x nÀ1þðnÀ1Þa2x nÀ2þÁÁÁþðnÀiþ1Þa i x nÀiþÁÁÁþa nÀ1xþa nð4ÞThe relationship between the rotation and deflection is[18];d¼Zu dxð5Þwhere d is the deflection at any point along the beam.Deflection isFig.1.Schematic view of the deflected shape of a beam.K.Helmi et al./Engineering Structures103(2015)116–124117d¼a1ðnþ1Þxnþ1þa2nx nþÁÁÁþa inþ2Àix nþ2ÀiþÁÁÁþa n2x2þa nþ1xð7ÞDeflection at a given point in time is computed by using Eq.(7) provided that the polynomial coefficients are known.These coeffi-cients are obtained by solving a system of equations,where the curvatures,rotations,deflections or any combination thereof are known or measured at locations along the beam length.Curvatures are obtained from measured strains using Eq.(2).Rotations are either measured using tiltmeters,or known from support condi-tions,e.g.zero rotation atfixed ends.Provided that curvatures, rotations and deflections are known at n+1or more points,a sys-tem of equations can be constructed and solved for the polynomial coefficients as shown below:x n u1x nÀ1u1ÁÁÁx u11...............x n ui x nÀ1u iÁÁÁx u i1nx nÀ1j1ðnÀ1Þx nÀ2j1ÁÁÁ10...............nx nÀ1j j ðnÀ1Þx nÀ2jjÁÁÁ10x nþ1 d1x nd1ÁÁÁx2d1x d1...............x nþ1 d k x nd kx2d k2 6666 66 66 66 66 66 66 66 66 66 4377777777777777777777775a1a2......a na nþ1266666666664377777777775¼u1...u ij1...j jd1...d k266666666666666666664377777777777777777775ð8Þinstrumented withfiber optic FBG tiltmeters and strain gauges.Acubic spline curve was used to represent the deflected shape,requiring at least four points of data to derive its equation.Thebridge in California was instrumented with four tiltmeters andtherefore computation of deflections did not require any additionaldata to derive the equation for the deflected shape.The bridge inIllinois was instrumented with three tiltmeters and therefore,anadditional point of data was required to derive the equation ofthe deflected shape.The additional point was obtained by calculat-ing the curvature from the strain readings of a strain gauge locatedat the midspan using Eq.(2).Field implementation of the proposedmethodology and real time remote monitoring of deflections aredescribed in the following section of this article.3.Test program3.1.Description of the bridgesField tests involved instrumentation of two typical highwaybridges,a prestressed concrete box girder bridge in Elk Grove Cal-ifornia and a concrete slab on steel girder bridge in Elmhurst Illi-nois.The bridges are shown in Figs.2and3.The bridge in California is located30miles south of Sacramento.The bridge consists of two separate sections carrying the north andsouthbound traffic of Interstate5over Lambert Road in the city ofElk Grove.The southbound section of the bridge was instrumentedin this study.The superstructure of the bridge is comprised of acontinuous concrete box girder span with a reinforced concrete Fig.2.Two span concrete box girder bridge in California.Fig.3.Three span concrete deck on steel girder bridge in Illinois.118K.Helmi et al./Engineering Structures103(2015)116–124during the sensor installation activities and load tests in order evaluate the precision of the deflections based on the methodology introduced in this study.Elevation and section views of the I-5Bridge with the locations the four tiltmeters as well as point A where the deflections were measured by LDV are shown in Fig.9.Fig.10shows an elevationFig.4.Strain gauge mounted to lower flange of surface of steel girder.Fig.5.Tiltmeter mounted on the girder web inside the concrete box girder.Fig.6.Site Interrogation unit and processor within NEMA rated enclosure.Fig.7.LDV employed for measurement of California bridge deflections.view of the Salt Creek Bridge with the locations of the three tilt-meters and strain gauge used.3.3.Field test program3.3.1.Concrete box girder bridgeA dump truck with a trailer was employed for the tests.The truck and trailer had a combined weight of 36.08metric ton (79.5kips).Fig.11shows the axle configurations of the truck and the attached trailer.Axle weights are given in Table 1.To minimize the effects of traffic on the controlled tests,live load tests were per-formed at night.Moreover,traffic was stopped prior to the bridge for a period of seven to ten minutes during each truck load test.Live load tests consisted of ten passes at two different truck speeds and at distances away from the western edge of the bridge.Details of the load test runs are given in Table 2.A total of eight passes were conducted at very slow pseudo-static speed over the bridge.The two high speed tests were conducted at normalcomputed through integration.Therefore,the LDV was not suitable for use in monitoring the deflections for lower speed truck tests.Tiltmeters however were able to collect the data corresponding to the slow speed truck loadings.Since it was not possible to use the LDV for the evaluation of the tiltmeter data at slow speeds the finite element model was employed for the evaluation of the sensors’data.In the finite element model,the axle configuration of the truck that was used for the load tests was employed as the simulated moving load at the speed of about 8km/h (5mph).Under the moving load condition,rotations of points on the model corresponding to the exact locations of the installed tiltmeters were recorded.Test run numbers nine and ten were performed at highway speed of 89km/h (55mph).A sampling frequency of 500Hz was selected for both the LDV and the fiber optic sensors.Fig.8.LVDT installed on one of the girders at the Salt Creek Bridge.Fig.9.(a)Elevation view.(b)Cross-section view of I-5Bridge.Fig.10.Elevation view of the Salt Creek Bridge.Fig.11.Truck and trailer axle load configurations.Table 1Test truck axle weight.System Axle 1Axle 2Axle 3Axle 4Axle 5Metric (kg)81887666691773255987fps (lb)18,05016,90015,25016,15013,200Table 2Details of load test runs.3.3.2.Concrete slab on steel girder bridgeA number of live load tests were conducted on the Slab on gir-der bridge at Salt Creek.Tests involved a random selection of weighed trucks from the nearby weigh station and acquisition of data during their passage over the bridge.The Salt Creek Bridge crossed the river and made it difficult to use the LDV as an inde-pendent measure of deflections.Instead,an LVDT was installed at the center of the middle span for this purpose.Also,since there were fewer tiltmeters installed,a strain gauge at the mid span location was used for calculating curvature of the beam.Therefore, in addition to the rotations,the radius of curvature was also employed as a known parameter in the solution of Eqs.(7)and (8)for the computation of the deflections.A sampling frequency of50Hz was selected for data acquisition by thefiber optic sensors and the LVDT.In order to reduce the higher frequency noise com-ponents,data was processed with a low-pass Butterworthfilter of the deflections measured by the method presented in this study. The FE model of the I-5Bridge was developed using the commercial structural analysis program SAP2000[22].Four node shell ele-ments were used to represent the top and bottomflanges,the webs and diaphragms.Eight node solid elements were used to model the beam over the middle pier.Fig.12shows the FE model of the bridge. Material properties and geometry of the structure were modeled using the original design drawings of the bridge.Verification of the FE model was accomplished by comparing the measured tiltmeter rotations to the FE model calculated rotations during slow speed load tests numbers2and7which were conducted on the bridge.The test runs were chosen randomly as representatives of the two extreme load paths that were conducted during the test.The recorded tiltmeter and FEM rotations were in good agreement as demonstrated by the sample comparison curves shown in Figs.13and14.The average differ-Fig.12.FEM model of I-5Bridge.Fig.13.Measured rotations vs FEM calculated rotations for tiltmeter2(test run2).Fig.14.Measured rotations vs FEM calculated rotations for tiltmeter3(test run7).K.Helmi et al./Engineering Structures103(2015)116–124121parison of mid span deflection calculated from tiltmeter data andmodel at pseudo-static truck speed(run2).parison of mid span deflection calculated from tiltmeter data andmodel at pseudo-static truck speed(run4).parison of mid span deflection calculated from tiltmeter data andmodel at pseudo-static truck speed(run7).LDV uses the Doppler Shift of the laser which is only applicableapplications involving dynamics and sufficient change in frequencydue to displacements.Therefore,for the slower speed truck runs,evaluation of the proposed method was achieved by comparingFig.18.Deflection at point A calculated from tiltmeter data compared to LDV readings for runs#9and#10.slight phase shifts between the responses recorded by the two methods.One reason,for this behavior is an insufficient number of sensors for constructing higher order polynomials.The other reason is presence of dynamic effects due to the interaction between the bridge and the truck which is more pronounced in this bridge because of its larger stiffness in comparison to the box girder bridge at I-5.5.Summary and conclusionsThe work presented in this study pertained to the development of a method for real time remote monitoring of bridge deflections. The primary attribute of the proposed method is its capability for making reference free estimates of bridge deflections.The formula-tions employ the measured rotations and curvatures of the bridge for the computation of deflections.In general,installation of either four tiltmeters,or a combination of tiltmeters,strain gauges,and displacement sensors providing information about four points along the span length is sufficient when the deflection shape is rep-resented by cubic splines.The tiltmeters,and the strain gauges employed herein,where based on a common FBG sensing platform with the same precisions and employed the same interrogation unit.Depending on the number of sensors,a polynomial can be for-mulated to estimate the elastic shape of the bridge.Installation of more sensors results in the formulation of higher order polynomi-als and more precise definition of the elastic curve.Field tests involved evaluating the method at two different bridges;a pre-stressed concrete box girder bridge in California and a concrete slab on steel girder bridge in Illinois.The box girder bridge was instrumented with four tilt meters along one of the spans,and the slab on girder bridge was instrumented with three tiltmeters and a strain gauge.In general,field test deflections monitored by the method described herein were in reasonable agreement with the independent measurements acquired by the conventional approaches.However,some of the deflections corresponding to the higher speed truck tests did not correlate with the independent tests.Because of limited number of tests,it is not clear whether the errors associated with the higher speed truck tests for the box gir-der bridge were systematic or random.More research is necessary in order to further evaluate the method in terms of truck speeds, bridge stiffness and types.Moreover,future work needs to also study the minimum quantity and proper spatial distribution of sensors along the span lengths for accurate estimation of deflec-tions.It is further noted that the method presented herein was tested on two bridges with span lengths of14and39m in length. The applicability of the method to longer span bridges has not been verified,and therefore,the application is limited to short to med-ium span bridges.AcknowledgementThis research is based on work supported by the National Science Foundation(PIRE program)grant number0730259. 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