VOLUME 70, NUMÉRO 4, 2016

VOLUME 70, NUMBER 4, 2016

GEOMATICATHE JOURNAL OF GEOSPATIAL INFORMATION SCIENCE, TECHNOLOGY AND PRACTICE

LA REVUE DES SCIENCES DE L’INFORMATION GÉOSPATIALE, DE LA TECHNOLOGIE ET DE LA PRATIQUE

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

DEPARTMENTS / CHRONIQUES

263 President’s Report / Rapport du président Rodolphe Devillers

265 From the Editor / Note du rédacteur en chef Izaak de Rijcke

319 Geomatics and the Law / The Interaction of Law and Geography in the Williams Lake Indian Band Specific Claim

Roger Townshend and Bert Groenenberg

325 Book Review.................................................................. Izaak de Rijcke

327 Fifty Years Ago............................................................... William R. (Bill) Brookes

330 CIG Executive and Councillors 2016–2017 / Membres exécutifs ßet conseillers de l’ACSG 2016–2017

337 Association of Canada Lands Surveyors / Association des arpenteurs des terres du Canada Jean-Claude Tétreault

339 CIG Sustaining Members / Membres de soutien de l’ACSG

342 Welcome New CIG Members / Bienvenue aux nouveaux membres de l’ACSG 2016

344 Membership List 2016 / Liste des membres 2016

348 5Index to/du Volume 70, 2016

350 Calendar of Events / Calendrier des événements

Vol. 70, No. 4, 2016 GEOMATICA 261

THE JOURNAL OF GEOSPATIAL INFORMATION SCIENCE, TECHNOLOGY AND PRACTICE /LA REVUE DES SCIENCES DE L’INFORMATION GÉOSPATIALE, DE LA TECHNOLOGIE ET DE LA PRATIQUE

GEOMATICA1

No. 42016Vol. 70

FEATURES / ARTICLES DE FOND 269 mR-V: Line Simplification through Mnemonic Rasterization Emmanuel Stefanakis 283 DEM Fusion of Elevation REST API Data in Support of Rapid Flood Modelling H. McGrath, E. Stefanakis, M. Nastev

ARTICLES / ARTICLES

298 Movements of the Quebec Bridge’s Suspended Span Measured by GNSS Technology ................................. Rock Santerre, Youssef Smadi, ....................... Stéphanie Bourgon

313 Initialization and Occupation Time for Kinematic Surveys using Online Precise Point Positioning C. Gil Mendoza, M. Berber

317 Harry D.G. Currie, OLS—an Appreciation David H. Gray

ANNOUNCEMENTS / ANNONCES

IFC/CAI Life Members Night / Soirée des membres à vie /

2017 CCA Conference / One Day Workshop

267 CIG Certification Program / Programme de certification pour les spécialistes en géomatique

268 Call for Papers: Geomatica 2017

318 GeoAlliance Canada 2017 Board of Directors

326 Geomatica Award / Prix Geomatica

336 Geomatica Volume 71, 2017, Online Subscription

340 New CIG Sustaining Member / Nouveau membre de soutien de l’ACSG : RME Geomatics

341 New CIG Sustaining Member / Nouveau membre de soutien de l’ACSG : GÉOLOCATION

343 FIG Working Week 2017 / ISPRS Geospatial Week 2017

City of Williams Lake, B.C. (see/voir page 322).

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

Published by / Publié par

Canadian Institute of Geomatics /L'Association canadienne des sciences géomatiques

Alex Giannelia President / Président

Editorial Staff / Équipe de rédaction

Izaak de Rijcke Editor / Rédacteur en chef

Laura Duke Production and Advertising / Production et publicité

Christine Parent French Copy Editor / Rédactrice-réviseure français

Amy Barker, William R. (Bill) Brookes, Jean MacGillivray, Alice Meilleur, Mike Pinch Assistant Editors / Réviseurs

William R. (Bill) Brookes / Jean-Noël LechasseurDepartments’ Editors / Rédacteurs des chroniques

Diane Cole Design Consultant / Consultante en conception

Associate Editors / Rédacteurs techniquesClaude Caron Business Geomatics / Géomatique d’affaires

Jean Gagnon Cadastral Surveys / Levés fonciers

Adam Chrzanowski Engineering and Mining Surveys / Levés miniers et d'ingénierie

Georgia Fotopoulos Geodesy and Control Surveys / Géodésie et levés de contrôle

Songnian Li Geographic Information Systems and Cartography /

Systèmes d'information géographique et cartographie

Izaak de Rijcke Geomatics and the Law / La géomatique et le droit

Robert van Wyngaarden Management of Geomatics / Gestion de la géomatique

Rodolphe Devillers Marine Geomatics / Géomatique marine

Suzana Dragićević Modelling and Decision Support / Modélisation et aide à la décision

Stéphane Roche Participatory GIS / SIG participatifs

Ayman Habib and / et Costas Armenakis Photogrammetry / Photogrammétrie

Ahmed El-Rabanny Satellite Positioning and Navigation / Positionnement et navigation par satellite

Gordon Plunkett Spatial Data Infrastructure / Infrastructure de données spatiales

Jonathan Li Remote Sensing and Digital Mapping / Télédétection et cartographie numérique

Saeid Homayouni Remote Sensing and GIS / Télédétection et SIG

Publication Committee / Comité des publicationsIzaak de Rijcke, Amy Barker, William (Bill) Brookes, Laura Duke,

Jean MacGillivray, Mike Pinch

Geomatica is published four times a year in the interest of professionals working in the geomatics sciences, by theCanadian Institute of Geomatics, 900 Dynes Road, Suite 100 D, Ottawa, Ontario K2C 3L6, Canada. Telephone: (613)224-9851, Fax: (613) 224-9577, E-mail: exdircig@magma.ca, Website: http://www.cig-acsg.ca. Subscription rate fornon-members is $290 Canadian per year + 13% HST in Canada (# R122381403). Membership dues include subscrip-tion to Geomatica. Subscription price of $25.00 is part of membership benefits and cannot be deducted from dues.Copyright of all text material from Geomatica belongs to the Institute. Abstracts and brief quotations may be madeif reference is credited to Geomatica. Large text abstracts may not be reproduced without permission. CIG cannotaccept responsibility for the accuracy of information supplied herein or for any opinion expressed.

La revue Geomatica est publiée quatre fois par année à l'intention des professionnels qui oeuvrent dans le domainedes sciences géomatiques par l'Association canadienne des sciences géomatiques, 900, rue Dynes, bureau 100 D,Ottawa, Ontario K2C 3L6, Canada. Téléphone : (613) 224-9851, télécopieur : (613) 224-9577, courrier électronique :exdircig@magma.ca, site Web : http://www.cig-acsg.ca. Le tarif d'abonnement pour les non membres est de 290 $canadiens par année plus la TVH de 13 % au Canada (No. R122381403). Les droits d'inscription comprennent l'abon-nement à Geomatica. Le tarif d'abonnement à la revue (25,00 $) fait partie des avantages aux membres et ne peutêtre déduit de la cotisation.Tous droits réservés à l'Association canadienne des sciences géomatiques en ce qui a trait aux articles publiés dansGeomatica. Les résumés et citations peuvent être utilisés en mentionnant la source. La reproduction des articles estinterdite sans autorisation. L'ACSG se désiste de toute responsabilité de l'exactitude des renseignements fournisdans cette publication et de toute opinion exprimée dans les présentes.

Authorized as publications mail by the Post Office Department, Ottawa, and for payment of postage in cash.Agreement #40007094. December 2016.

Autorisé comme envoi de publications par la Société canadienne des postes, Ottawa, et pour paiement des frais deposte en espèces. Numéro de la convention 40007094. Décembre 2016.

262 GEOMATICA Vol. 70, No. 4, 2016

COVER / COUVERTURE

The Quebec Bridge, stretching across theSt.  Lawrence River west of Quebec City, is theworld’s longest span cantilever bridge at 548.6metres between the main piers. Construction onthe Quebec Bridge was completed 100 years agoin 1917, following two tragic failures—in 1907and 1916—and the loss of 89 lives. Theimpres sive road, rail and pedestrian bridge waslargely designed and built by Canadian engineersusing an innovative K-truss design and was thefirst bridge in North America to use nickel steel asa structural material. Universally recognized as asymbol of engineering excellence, the Canadian(now the Engineering Institute of Canada) andAmerican Society of Civil Engineers declared theQuebec Bridge a historic mon ument in 1987, and, onJanuary 24, 1996, the bridge was declared a NationalHistoric Site of Canada.

The Quebec Bridge is the subject of a paper entitled:"Movements of the Quebec Bridge’s suspendedspan measured by GNSS technology," published inthis Geomatica issue (see p. 298).

Photographic credit : R. Santerre, CRG, LavalUniversity, Quebec City

Le pont de Québec, qui enjambe le fleuve Saint-Laurentà l’ouest de la ville de Québec, est le pontcan tilever ayant la plus longue portée libre aumonde, avec 548,6 mètres entre ses deux princi-paux piliers. La construction du pont de Québec aété complétée il y a 100 ans, en 1917, après deuxéchecs tragiques— en 1907 et en 1916—causant lamort de 89 personnes. Cet impressionnant pontroutier, ferroviaire et pié tonnier a été largementconçu et construit par des ingénieurs canadiensqui ont utilisé un concept inno vateur de systèmede poutres en K et il était le  premier pont enAmérique du Nord à utiliser l’aci er au nickelcomme matériau structural. Universellementreconnu comme symbole d’ex cel lence eningénierie, l’Institut canadien des ingénieurs etl’American Society of Civil Engineers ont classéle pont de Québec comme monument his toriqueen 1987 et, le 24 janvier 1996, le pont a étédésigné lieu historique national du Canada.

Le pont de Québec fait l’objet d’un article (enanglais) publié dans ce numéro de Geomaticapor tant sur les mouvements de la travée centraledu pont de Québec mesurés avec la technologieGNSS (voir p. 298).

Crédit photographique : R. Santerre, CRG,Université Laval, Québec

GEOMATICAISSN (print / imprimé): 1195-1036

ADVERTISING /

PUBLICITÉEsri Canada ................................outside back cover/ couverture arrière extérieure

GeoEd Canada ......................................................329

ISSN (electronic / électronique): 1925-4296

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

298 GEOMATICA dx.doi.org/10.5623/cig2016-405 Vol. 70, No. 4, 2016

IntroductionThe origin of this project was to

bet ter establish the actual clearance ofthe Quebec Bridge, which crosses theSt.  Lawrence River near Quebec City,and to potentially increase the numberof tall ships that can securely pass underthe bridge and reach the Port ofMontreal. For this purpose, the MontrealPort Authority installed a radar instru-ment under the structure of the QuebecBridge to monitor the St.  LawrenceRiver water level. This project was donein collaboration with the CanadianCoast Guard (CCG) and the CanadianHydrographic Service (CHS), with theagreement of the Canadian  National(CN) Railway Company, the  owner of

the Quebec Bridge. Furthermore, in orderto take into account the movement of theinstalled radar, a GNSS antenna (GlobalNavigation Satellite Systems includingthe American GPS and the RussianGLONASS systems) connected to aGNSS receiver, was installed on top ofthe central suspended span of the bridge34 m above the radar.

Although the original goal of theexperiment was not dedicated to moni-toring the 3D deformation of theQuebec Bridge, we asked to haveaccess to the GNSS data collected ontop of the Quebec Bridge’s suspendedspan for analysis. This was an opportu-ni ty to monitor one of the most famousengineering structures in Canada builta century ago.

This paper contains the analysis ofthe 3D deformation of the QuebecBridge’s suspended span as measuredby GNSS technology as functions oftrain and wind loads, along with theeffects of temperature, including solarradiation. The next sections present ashort description and the history of theQuebec Bridge and the equipment anddata used to perform this analysis.

The Quebec BridgeThe Quebec Bridge (46° 45’ N, 71°

17’ W) is the first bridge over theSt.  Lawrence River encountered byships travelling upstream from the Gulfof St. Lawrence and the Atlantic Ocean.

MOVEMENTS OF THE

QUEBEC BRIDGE’S SUSPENDED SPAN

MEASURED BY GNSS TECHNOLOGY

Rock Santerre, Youssef Smadi and Stéphanie BourgonUniversité Laval, Québec (Canada)

The Quebec Bridge was completed in 1917 and it is still the longest cantilever bridge in the world. Overall, the actualmovements of its suspended span, as detected by GNSS (between 2012 and 2013), are in fair agreement with the originaldesign calculations: for the train loading effect on the vertical movement (17 cm for one freight train); the transversal windload effect on the transversal movement (32 cm for a wind speed of 170 km/h); and the temperature loading effect on thever ti cal movement of the suspended span (3.2 cm for a 50°C temperature variation). Further movements have been detectedby GNSS technology, namely: the transversal and longitudinal movements of the suspended bridge span due to train passages(11 cm transversally, at the top of the suspended span, and 1 cm longitudinally); the transversal movement of the bridgecaused by solar radiation (differential) conditions on both sides of the bridge (5 cm for high solar radiation values); and thelongitudinal movement of the suspended span of the Quebec Bridge at temperatures lower than 6°C (7 cm to −25°C).

La construction du pont de Québec a été achevée en 1917 et il est toujours le plus long pont cantilever au monde. Dansl'ensemble, les mouvements actuels de sa travée suspendue détectés par GNSS (entre 2012 et 2013) correspondent bien avecles calculs d'origine : pour l'effet de charge des trains sur le mouvement vertical (17 cm pour un train de fret); l'effet decharge du vent transversal sur le mouvement transversal (32 cm pour une vitesse de vent de 170 km/h); et l'effet de chargede la tem pérature sur le mouvement vertical de la travée suspendue (3,2 cm pour une variation de température de 50°C).D'autres mouvements ont été détectés par la technologie GNSS, à savoir : les mouvements transversaux et longitudinaux dela travée suspendue du pont en raison du passage de trains (11 cm transversalement, au sommet de la travée suspendue et1 cm lon gi tudinalement); le déplacement transversal du pont provoqué par les conditions du rayonnement solaire(dif féren tiel) sur les deux côtés du pont (5 cm pour les valeurs élevées de rayonnement solaire); et le déplacement longitudinalde la travée suspendue à une température inférieure à 6°C (7 cm à −25°C).

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

Vol. 70, No. 4, 2016 GEOMATICA 299

This bridge is located about 10 kmupstream from Quebec City and about250 km downstream from Montreal inQuebec, Canada.

As indicated on the actual chart ofCHS, the clearance of the Quebec Bridgewith respect to the High Water, LargeTide (HWLT) is 46 m. In Quebec City,the tide can reach up to 5–6 m dependingon the time of the year. In fact, there aresome ships that can pass under theQuebec Bridge only when the tide isfalling. This shows the importance ofestablishing the actual (and the predicted)bridge clearance along with the tidelevel measured by nearby tide gauges.

The technical specifications of thebridge are given in Table 1, as extractedfrom the original documentation givenin the Imperial (British) units [DRC1908a,b]. The metric equivalents arealso given in this table. Figure 1 dis-plays pictures of the Quebec cantileverbridge taken in summer and winter sea-sons. The GNSS antenna location, ontop of the suspended span, is indicatedby the red arrow.

To give a short history, it is worthmentioning that the central suspendedspan was successfully lifted and installedon September 20, 1917 (the first attemptfailed on September 11, 1916). It is also

interesting to note that the ends of thecantilever arms dropped by 19.4 cm(7 5/8 in) once the suspended span waslifted. The first transit of a train over thebridge occurred on October 17, 1917,and it was officially inaugurated onAugust 22, 1919. Let us also rememberthat the southern part of the first QuebecBridge, under construction, collapsedon August 1907 because of a structuraldesign problem.

The Quebec Bridge is still thelongest cantilever bridge in the worldand it was the longest bridge (of alltypes) between 1917 and 1929. It wasrecorded as a Canadian national historicsite in 1996 by the Government ofCanada and it was recognised as aninternational historic civil engineeringlandmark in 1987 by the AmericanSociety of Civil Engineers and theCanadian Society for Civil Engineering.

In 1917, the bridge had two railwaysand two sidewalks. A car lane wasadded between the two railways in1929. Later on in 1948, one of the rail-ways (to the downstream side) and oneof the sidewalks (to the upstream side)were removed, and the second railwaywas slightly shifted (to the upstreamside) in order to widen the car lane.

Currently, three traffic lanes forcars are present: two lanes in the northdirection and one lane in the southdirection in the morning, and vice versain the evening. The central car lane is

Length, Width, Height Feet Metres

Length of suspended span 640 195.1

Length of cantilever arms 580 176.8

Length of anchor arms 515 157.0

Total length of steel work 3 239 987.2

Distance between main piers* 1 800 548.6

Width (external) of the bridge 100 30.5

Height of main posts 310 94.5

Height of suspended span (at the center) 110 33.5

Weight imperial metrictons tons

Total weight of steel** superstructure 66 480 60 310

Weight of the suspended span 5 510 4 999

Table 1: Technical specifications of the Quebec Bridge.

* World record for a cantilever bridge; ** 75% carbon steel and 25% nickel steel

Figure 1: The Quebec Bridge, left—in summer from the south shore; right—in winter from the north shore.

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

300 GEOMATICA Vol. 70, No. 4, 2016

closed at noon and during nights andweekends. Every week day (but lessoften during the weekend), around35 000 cars (500 cars per 15 minutesduring rush hours), 4 freight trains(with about 30 wagons) and 8 passen-ger trains transit the bridge (there is nopassenger train service between 10p.m. and 5 a.m.). The maximum trainspeed is regulated to 64 km/h and themaximum car speed is limited to70 km/h. Since 1991, the transit oflarge trucks has been forbidden.Figure 2 (left) also depicts the view ofthe train track, the three car lanes andthe sidewalk as seen from the GNSSantenna location.

GNSS Equipment andthe Auxiliary Data

A chokering (Antcom) antenna(see Figure 2, left) connected to a multi-frequency geodetic Ashtech (Proflex500) GNSS (GPS-GLONASS) receiverwas installed on top of the central sus-pended span of the bridge on theupstream side (the side of the railway).The data set was available from thebeginning of July 2012 up to mid-July2013, with observations recorded at 1 s

intervals. Altogether, almost 18 mil lionobservation epochs were recorded andprocessed for a total of 140 GB of GNSSdata (including the GNSS reference sta-tion files) in the ASCII RINEX format.

The distance between the QuebecBridge and the nearest permanent GNSSreference station (QBC2) was about7 km with a height difference of about70 m. This might be a proper setup forthe original objective of the project,which was to measure (at an accuracy of0.1 m) the bridge clearance for safe shipnavigation, but this is not optimal forbridge deformation monitoring becauseof the long distance and large height dif-ference between these two GNSS anten-nas. Even though it would have beenpreferable to have a closer GNSS refer-ence station to mitigate GNSS errors(especially the tropospheric error whichmainly affects GNSS height determina-tion), one can expect that for a short periodof time (such as a train passage of a fewminutes) the tropospheric modellingerror will stay almost constant and willnot significantly deteriorate the detectionof the vertical displacement of the GNSSantenna located on the top of the bridge’ssuspended span. Let’s also recall thattropospheric delay mismodelling hasalmost no effect on the horizontal GNSScoordinates [Santerre 1991].

The reference station wasequipped with a multi-frequency GNSSTrimble NetR5 receiver and a geodeticTrimble Zephyr antenna. The GPS-GLONASS ambiguity fixed ionos-pher ic free (L1 and L2) solutions with a10° elevation mask angles werepro duced using the Trimble BusinessCenter (TBC) post-processing software[Trimble 2012].

Due to the large amount of GNSSdata, the TBC software was used forseveral features: efficient data screen-ing, reliable ambiguity-fixing algo-rithms, automated cycle-slip detec tionand correction engine, and its user-friendly interface. The observation filesin the RINEX format were processedin the kinematic mode. Therefore anew set of 3D coordinates was esti-mated at every epoch. Altogether, ittook 15 days to post-process this vol-ume of GNSS data (140 GB) on 10personal computers. All the results arereported in Smadi [2015].

The instantaneously estimatedprecision (epoch by epoch) of the hor-izontal components at 95% probabilitylevel was typically 1.5–2.5 cm for thehorizontal and vertical components,respectively [Smadi 2015]. Let us keepin mind that the precision of the dis-placement (the coordinate variation in

Figure 2: Left—Location of the GNSS antenna on the top of the Quebec Bridge (in the background, thePierre-Laporte suspension bridge with the anemometer location indicated with the circled arrow). Source ofthe pho to graph: Canadian Coast Guard. Right—The Miros radar installed under the suspended span of theQuebec Bridge. Source of the photograph: Canadian Hydrographic Service.

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

Vol. 70, No. 4, 2016 GEOMATICA 301

time) is much better, especially for ashort time duration where the GNSSerrors are highly correlated. From theanalysis of this large GNSS data set, arealistic precision of 5 and 8 mm for thehorizontal and vertical displacements,respectively, can be stated. Moreover,the moving average filtering helps tosignificantly reduce the noise associat edwith the GNSS observations, as will beshown in the next sections.

Several auxiliary data sensorswere available, such as an ultrasonicanemometer (Young Model 81000), tocollect wind velocity in N-S, E-W andU-D directions, averaged every 10 minalong with the air temperature. Thisanemometer is located on top of a lightpole just south of the north tower on theupstream side of the Pierre-Laporte sus-pension bridge, which is located 200 mupstream of the Quebec Bridge (seeFigure 2, left). Unfortunately, noanemometer is installed over theQuebec Bridge. The solar radiation val-ues were recorded by the MeteoLavalstation located about 4 km from theQuebec Bridge. The traffic loops operat-ed by Quebec Department ofTransportation (MTQ) were used toprovide the total number of cars for the15 min intervals. The arrival and depar-ture times of passengers and freighttrains were provided by the CN RailwayCompany for the two nearby train sta-tions, namely Ste-Foy and Charny,respectively. These are located 1.5 kmnorth and 4 km south from the center of

the Quebec Bridge. Table 2 shows thesummary of the auxiliary sensor valuesduring the observation period.

A Miros microwave radar remotesensor for the ocean surface radar,model SM-094, was used to measure theclearance (instantaneous vertical distanceat 1 s intervals) between the bottom of thesuspended span of the Quebec Bridge andthe water level of the St. Lawrence River(Figure 2, right). According to the manu-facturer, the accuracy of an individualmeasurement is 1 cm. As one will seelater, the measurements not only containinformation about tides, but they are alsoaffected by waves. During the winter sea-son, the radar pulses bounce back from iceblocks that are floating on the river. Thusthe radar data obtained in this season werenot used for the analysis.

The variations in the coordinates ofthe antenna are with respect to the aver-age 3D coordinate values obtained froma 24 h static solution for the day March 3,2013. This day was selected because theaverage air temperature value was closeto zero (0.7°C) and the wind velocity wasas low as 4 km/h in the transversal direc-tion. The results presented in the nextsections are, in fact, the coordinate varia-tions (displacement) of the GNSSanten na (located on top center of the sus-pended span) expressed in the bridgelocal reference frame (L, T, V), where thelongitudinal (L) component has a positivevalue toward the river’s north shoredirection, the transversal (T) componenthas a positive value toward the river’s

downstream direction and the verticalcomponent has a positive value in the up(zenith) direction. This transformationwas done using the known bearing ofthe longitudinal axis of the QuebecBridge, which is 340°.

To analyse the Quebec Bridgedeformations, let us remember that theGPS system has been used for decadesfor deformation monitoring of largeengineering structures such as bridges[Hyzak et al. 1995; Xu et al. 2010].Dams [DeLoach 1989], towers andbuildings [Lovse et al. 1995; Yi et al.2012] are also monitored using GPS(GNSS) technique. Some of therecent ly constructed mega structuresare permanently equipped with GPS(GNSS) receivers along with othersensors such as accelerometers, tiltsensors and so on. GPS (GNSS) tech-nology is now part of structural healthmonitoring toolboxes [USACE 2002;Santerre 2011].

Movement AnalysisCaused by Train andCar Load

Vertical and TransversalDisplacements

Figure 3 (top) shows typicaleffects of freight train transits on thevertical (V, green lines) and transversal(T, blue lines) components as detectedby the GNSS receiver every second fora period of 6 min. Radar measure-ments (vertical distances at every s)are represented by dark lines and areintentionally shift ed by 5 cm to avoidmasking the two other lines. In fact,the radar values are the measurementresiduals after the main tidal con-stituents have been removed (by theCHS). Remember that the tide heightcan reach 5–6 m in Quebec City. Thesuperimposed lines are the results ofapplying a 10 s window moving aver-age filtering. This technique helps tosignificantly reduce the data noise,especially for the radar measurementsaffected by the roughness of the river

Table 2: Summary of the auxiliary sensor values from July 2012 to mid-July 2013.

Minimum Maximum Mean

North car traffic flow (/15 min.) 0 509 118

South car traffic flow (/15 min.) 0 503 103

Trains (/week) 45 71 61

Ambient air temperature (°C) –28 33 7.3

Solar radiation (W/m2) 5 1397 299

Longitudinal wind speed (km/h)(positive from South)

–41 30 –2.4

Transversal wind speed (km/h)(positive from West)

–71 98 3.4

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

302 GEOMATICA Vol. 70, No. 4, 2016

water surface. There is indeed a goodagreement between the radar measure-ments and the vertical variation of theGNSS antenna coordinates.

One can notice that the less noisyGNSS antenna coordinate variationsare related to the transversal compo-nents and the vertical coordinatevari a tions are noisier. This is becauseGNSS (GPS) is less precise in thever tical direction [Santerre 1991]and that the bridge movementsinduced by car and train transits aremainly in the vertical direction.Transversal values were not alwayscentered at zero because when thewind blows transversally, the sus-pend ed span moves in the transversaldirection. The effect of the wind loadis discussed later.

The shape and the size of thedetected movements certainly depend

on the weight and the length of the train.The duration of the transit probablydepends also on the speed of the train.Unfortunately, no such information wasavailable from the CN train file providedto us. For the freight train transits, thelargest subsidence value reached 17 cmand the maximum transit duration was3 min. The asymmetric shape of thegraphs is attributed to change in the trainspeed or different weights of wagons. Thisasymmetric shape happens more often forfreight trains going toward the north direc-tion probably because they have to reducetheir speed to enter the curve travellingwestward before approaching the near bySte-Foy train station.

The vertical variations of the GNSSantenna were in fair agreement with thecalculated values [DRC 1908a,b], whichstate that the deflection at middle ofchannel (suspended) span caused by a

live load consisting of 2 Cooper’sClass E60 locomotives (60 000pounds or 27 273 kg), followed by5000 pounds/linear foot (7456 kg/m)on each track, should be 33.7 cm(13.25 in). As mentioned before, thereis currently only one railway track andthe bridge was originally designed withtwo railway tracks.

The transversal displacement ofthe antenna can be explained by alever arm (tilt) effect. Remember thatthe train track and the GNSS antennawere located on the upstream side ofthe bridge (not in the middle point ofthe transversal section of the bridge,which is 31 m wide), and the GNSSantenna is about 34 m above the rail-way. The ratio of the peak valuesbetween the transversal and the verticaldisplacement (T/V) is 0.66 ±0.08 (forall types of freight or passenger train).

Figure 3: Vertical (V) and transversal (T) displacements during the transit of a freight train (top) and during the transit of apassenger train (bottom).

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

Vol. 70, No. 4, 2016 GEOMATICA 303

The maximum value of the transversaldisplacement was about 11 cm. Thismeans that the train load seems also toproduce a tilt effect on the suspendedspan along with a sub si dence effect. Thetransversal movement correlates perfectlywith the vertical displacement. In thiscon figuration, it is even easier to detecttrain transit with the transversal GNSScomponent because it has a greaterpre ci sion than the vertical component.

Figure 3 (bottom) shows typicaleffect of passenger train transits. Thepassenger trains, which are typicallysmaller and travel at higher speed thanfreight trains, produce smaller peaks.The maximum measured vertical sub-sidence value was about 2.5 cm, whilethe min i mum subsidence was as lowas 1.0 cm. The longest duration of theload effect of the passenger trains was

about 1 min. For comparison, the weightby unit of length of a passenger wagon isless than 2500 kg/m vs about 6000 kg/mfor a tank wagon.

The vertical coordinate variationsof the GNSS antenna caused by the carload were not visually perceptible evenduring traffic rush hours. In fact, the carload is considerably smaller than thetrain load (for comparison, the weightby unit of length of a car is less than400 kg/m ver sus about 6000 kg/m for atank wagon). To confirm the visualinspection, FFT analysis was per formedduring the night (0:00–1:15 a.m., withan average of 300 passing cars), duringthe morning rush hour (6:45–8:00 a.m.,with up to 6000 passing cars) anddur ing the evening rush hour (4:00–5:15p.m. with up to 6000 passing cars). Infact, no significant difference in FFT

amplitude or period values betweenthe night period (with the low estnumber of car transits) and the tworush hours was noticed.

LongitudinalDisplacements

The train load effect on thelon gi tudinal coordinate variation ofthe antenna (located at the middle ofthe suspended span) was also investi-gated. Figure 4 presents graphs wherelongitudinal displacement of theGNSS antenna (maximum value of1 cm) due to freight trains has beennoted. The longitudinal coordinatevariations are in magenta and thetransversal variation is in blue. Thelat ter was superimposed to clear lyidentify the train transits. In fact, the

Figure 4: Longitudinal (L) and transversal (T) displacements during freight train transits.

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

304 GEOMATICA Vol. 70, No. 4, 2016

longitudinal coordinate variation wasdetected for 45% of the freight traintransits and for only 10% of thepas senger train transits.

The slope of the longitudinalvari ation at the time corresponding tothe transversal peak value is positive(displacement in northward direction)for the northbound trains and negative(displacement in southward direction)for the southbound trains. This rela-tively small coordinate variationdemonstrates the great capability ofGNSS results to monitor engineeringinfrastructures. This behaviour mightbe explained by the kinetic energytransferring from the train to the sus-pended span. In fact, the suspendedspan is hinged on by the cantileverarms and the suspended span move-ment is also attenuated by shockabsorbers (traction brakes) installedbetween the cantilever arms and thesuspended span.

Xia et al. [2000] reported trainload effects on a suspension bridge asmeasured by GPS receivers. They alsopre sented a suspension bridge dynamic

response model to explain thisphe nom e non. However, this modelwould have to be adapted for a structuresuch as the cantilever Quebec Bridge.

Movement AnalysisCaused by Wind Load

Transversal DisplacementsFigure 5 presents examples for six

windy days, showing the transversalcoordinate variations (blue line in cm) ofthe GNSS antenna atop the suspendedspan at 10 min intervals, filtered using a10 min moving average and the aver-aged transversal wind speed as recordedby the anemometer every 10 min (greenline in km/h). In order to distinguish andstudy just the effect of the wind loading,the days with high solar radiation (from500 up to 1400 W/m2) were discardedand the periods of train transits wereremoved. The impact of solar radiationwill be dis cussed in the next sec tion.Furthermore, to have a minimal number

of values for the cal culation of thedaily cross correlation value (alsoreported on the lower left of eachgraph in Figure 5), only the days thathad at least 25% of common epochsbetween GNSS and wind data valueswere retained. Altogether, 54 daysmeet these criteria and 12 days hadwind speed values larger than 60 km/h(the maximum value recorded was98 km/h). To better distinguish the twotime series, two different origins forthe vertical axes have been selected.

The cross-correlation coefficientsrange from 0.80 to 0.97, as indicatedin the lower left corner of the graphs.This indicates that the bridge reactsquite instantaneously to the transversalwind load. The high correlationbetween both time series is clearly vis-ible from the graphs, especially whenthe wind speed is high. The largestreported winds were 98 km/h from thewest (day: 13-01-31) with a displace-ment of 10 cm in the eastward direc tionand almost 60 km/h from the east (day:13-01-20) with a displacement of 6 cmin the westward direction. The largest

Figure 5: Transversal displacement of the central suspended span versus transversal wind speed for six different days.

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

Vol. 70, No. 4, 2016 GEOMATICA 305

diurnal wind speed variation alsooccurred in day 13-01-20; about130 km/h wind change for totaltrans versal displacement of 14 cmduring that day. It is worth mention-ing that the time of wind zero cross-ings (green line) coincides with thetransversal dis placement zero cross ings(blue line).

To see the complete behavior ofthe transversal wind effect on thetrans versal coordinate variation, all thedata sets have been displayed togetherin Figure 6. The total number of values

(sampled every 10 min) was 7161. In thisgraph, the transversal displacementsassociated with the east transversal wind(in green) have been changed of sign.The blue dots are associated with the westwinds. Altogether, there were 10 dayswhere the west wind blew above 60 km/h(up to 98 km/h) and two days with maxi-mum east wind at 60 km/h. The best fitparabola (in magenta) has been estimatedby least-square and their coefficients andtheir precisions are reported in Table 3.Using the parabola coefficient, the valuefor a 170 km/h wind speed was extrapo-

lated and a value of 34.6 cm wasobtained. The red parabo la was interpo-lated from the 1908 pre diction for atransversal wind speed of 170 km/h(see below). The third parabola (inbrown) was obtained from the best fitto the west wind speed only (for a totalof 2938 measurements). The R2 valueof 0.79, associat ed with the parabolafits, successfully passed the Fisher test.

It can be seen in Figure 6 that thetransversal effect of the wind fromthe east direction (green dots) seemsto be greater than the east wind (blue

Figure 6: Distributions of the transversal displacement of the central suspended span as a function of the transversal wind speed.

Table 3: Coefficients of the best-fit parabola and their precisions.

a ±σa (m h2/km2) b ±σb (m h/km) c ±σc (m) R2 y(@170 km/h) (m)

East and west winds(7161 values)

0.000 007 3 ±0.000 000 3

0.000 82±0.000 02

-0.005 4±0.000 3

0.79 0.346

West wind only (2938 values)

0.000 008 2±0.000 000 4

0.000 49±0.000 03

–0.000 9±0.000 4

0.79 0.320

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

306 GEOMATICA Vol. 70, No. 4, 2016

dots). This suggests that the westspeed measured by the anemometerlocated on the Pierre-Laporte bridgemight be attenuated by the QuebecBridge itself and the small hill locatedto the east of the bridge. In  fact, theaverage of the highest velocity eastwinds were blowing from a directionwith an azimuth of 65°. The windfrom this direction impacts directlythe sus pended span of the bridgewhere the GNSS antenna is locatedand must pass above the hill andacross the Quebec Bridge structurebefore reaching the anemometer. Theaverage azimuth of the strongest westwind was 255°. From this direction,the wind was directly measured(without obstruction) by theanemometer and the wind can reachthe Quebec Bridge suspend ed spanwith almost no obstruction, since thewind flow can pass over the hollowspace of the suspension cables of thePierre-Laporte bridge. Direct meas-urements of the wind at the top of theQuebec Bridge (especially the onefrom the east direction) could cer-tain ly improve the R2 value of thebest fit parabola reported in Table 3.

The original plan of the QuebecBridge [DRC 1908a,b] provided thefollowing interpretative remark: themaximum lateral deflection at middleof the channel (suspended) span from30 lb/ft2 of the wind load normal to thebridge plus the wind load on a passingtrain on the channel (suspended) span.This value was 13.5 in (34.3 cm).According to Unsworth [2011], a windlateral force of 30 lb/ft2 is applying awind pressure corresponding to themaximum wind speed for safe opera-tion of trains. This value correspondsto a wind speed of about 170 km/h

(equal to 47 m/s) using the fol lowingequation and the appropriate unitcon ver sion: P = ½ ρair V2, where P is thepressure in Pa or N/m2, V is the windspeed in m/s, and ρair is the air den sity atsea level, approximately 1.255 kg/m3.

For numerical comparison, Table 4presents the values of the predicted andthe measured transversal displacements(from the best-fit parabola). The lastvalues were calculated with the best fitparabola given above and the firstval ues (in metres) were calculatedwith  this approximate estimation:1.19 x 105 VT

2, where the coefficient isderived from the ratio of the maximalpredicted transversal displacement andthe corre sponding wind speed squared(0.343 m / (170 km/h)2).

Overall, the differences between thesecond best fit parabola (west windsonly) and the 1908 prediction weresmaller, as seen in Figure 6. This fact isfurther evidence that the speed of theeastern wind, recorded by theanemometer on the Pierre-Laportesus pension bridge, was attenuated ascompared with the eastern wind thatblew at the location of the QuebecBridge’s suspended span.

For comparison, let us note that forthe nearby Pierre-Laporte suspensionbridge (1040 m in length), Santerre andLamoureux [1997] reported an 8 cmtransversal displacement at the center ofthe suspension span provoked by a windspeed of 25 km/h (7 m/s). Wong [2004]had measured a lateral displacement of46 cm for the wind speed of 26 m/s(95 km/h) for the Tsing Ma bridge (overthe 1377 m suspended span). Wong alsoreported that the wind tunnel test confirmsthe proportionality with the wind speedsquared. Nakamura [2000] report ed, for a720 m main span suspension bridge, a

transversal displacement of 20 cm fora wind speed of up to 20 m/s(72 km/h). The relationship betweenthe lateral displacement and the windspeed squared was also reported in thelatter study.

Vertical Displacements The original design plan of the

Quebec Bridge [DRC 1908a,b]shows the predicted vertical displace-ment of the cantilever arm and thesuspended span for the same loadcondition as described in the previ-ous sub-section. At the middle of thesuspended span, the predicted valuewas 2.2 in (5.6 cm) for a transversalwind speed of 170 km/h. That is apositive value (upward direction) forthe bridge windward side and a nega-tive value (downward direction) forthe leeward side of the bridge. Thiscan be approximately modelled bythe following relation: 1.94 x 10-6

VT2, where the coefficient comes

from the ratio of the maximal verticalpredicted displacement and the corre-sponding wind speed squared(0.056 m / (170 km/h)2). For a100 km/h and a 50 km/h wind speed,the vertical displacements would be1.9 cm and 0.5 cm, respectively.

The transversal wind speed mustbe strong enough to be detected bythe measured GNSS vertical coordi-nate variations, since GNSS is lesspre cise in the vertical componentcompared with the horizontal direc-tion [Santerre 1991]. In fact, for theday with the highest wind speedrecorded (100 km/h), a vertical dis-placement of 2.8 cm was measured byGNSS, a value larger than thepre dict ed one of 1.9 cm.

Table 4: Comparison of transversal displacements for different transversal wind speed values.

Speed (km/h)

Speed (m/s)

170

47.2

150

41.7

100

27.8

60

16.7

30

8.3

10

2.8

1908 Prediction (cm)

Best fit (all) (cm)

Best fit (west wind) (cm)

34.3

34.6 ±0.9

32.0 ±1.2

26.8

28.2 ±0.7

25.7 ±1.0

11.9

15.0 ±0.4

13.0 ±0.5

4.3

7.0 ±0.2

5.8 ±0.2

1.1

2.6 ±0.07

2.1 ±0.09

0.1

0.4 ±0.04

0.5 ±0.04

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

Vol. 70, No. 4, 2016 GEOMATICA 307

Movement AnalysisCaused byTemperature andSolar Radiation

Table 5 (last line) shows thelength and height of the bridge steelvariations (in inches) due to a temper-ature variation of -30°F to 120°F (for atotal variation of 150°F, or 83.3°C) asreported in DRC [1908a,b]. The valueof the steel thermal coefficient was

assumed to be 0.000 006 1/°F. Thiscor responds to 11.0 ppm/°C. With thisvalue, the displacements in mm for a10°C temperature variation have beencalculated; see Table 5 (line 3). Thedimensions given in line 2 of Table 5 arealso shown in Figure 1.

Vertical Displacements

The first effect of temperatureinves tigated was the vertical variation ofthe GNSS antenna with respect to the air

temperature (Figure 7). Unfortunately,no steel bridge temperature was avail-able. In the time series, the train transiteffect, which can be as large as 15 cm(see first section above), was removedin order to only keep the effect oftem perature on the vertical coordinatevariations. In Figure 7, the pale bluedots represent the 10-min moving aver-age vertical coordinate variations of theGNSS antenna; the dark blue dots arethe mean values for a complete dayassociated with their correspondingdaily mean air temperature. In this time

Table 5: Length (height and width) of the bridge variations (in mm) caused by a 10°C temperature variation using the theoreticalsteel thermal coefficient.

L. arm cantilever

½ L. centralspan

H. main tower

H. total central span

H. central span

½ bridge width

177.0 mm19.5 mm

97.5 mm10.7 mm

94.5 mm10.4 mm

69.5 mm7.6 mm

33.5 mm3.7 mm

15.3 mm1.7 mm

* 6.34 in 3.50 in 3.40 in 2.52 in N/A N/A

* Equivalent values in inches for a 150°F temperature variation (from DRC [1908a,b]).

Figure 7: Vertical coordinate variation as a function of the (ambient) air temperature.

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

308 GEOMATICA Vol. 70, No. 4, 2016

series, the daily mean temperatureranged from –23.6°C to 25.9°C,49.5°C temperature variation.

In general and as expected, whenthe temperature is above 0°C, thever tical variation is positive and viceversa. A linear regression was estimat-ed (the purple line in Figure 7) using thedaily values. This provided a corre-sponding thermal coefficient of9.3 ±1.5 ppm/°C (instead of the theoret-ical value of 11.0 ppm/°C) with a R2

value of 0.50 (although a small value,the Fisher test was passed). The red linein Figure 7 represents the predictedval ues calculated with the 11.0 ppm/°Cthermal coefficient using the totalheight of the suspended span (69.5 m).For the 49.5°C total daily temperaturevariation during the year, the measuredvertical variation was then 3.2 cmver sus 3.8 cm for the predicted value(for a discrepancy of 6 mm).

To explain this discrepancy(6 mm), one might suspect remaining

errors in the relative wet troposphericdelay model, especially during summerwhere the relative humidity (partialwater vapor pressure) is high (in com-parison with the winter season), and thiseffect is not totally cancelled in relative(differential) positioning, especiallybecause the (closest) GNSS referencestation was located 7 km away with aheight difference of 70 m with respectto the Quebec Bridge GNSS receiver.Residual tropospheric errors mainlyaffect the GNSS height determination[Santerre 1991]. Moreover, no steeltemperature data were available, aspre viously noted.

LongitudinalDisplacements

Since the GNSS receiver was locatedat the middle of the suspended span, onemight not expect any variation in thelon gitudinal coordinate. But some depar-tures were noticed, as illustrated in

Figure 8, representing two separateweeks during the sum mer season(bot tom) and the win ter season (top).During the summer, the longitudinalvariations remained very close to 0,regardless of the positive temperaturevalue, but as soon as the temperaturedropped below 0°C (roughly) duringwinter, the variations became negative(displacements toward the southshore). This is an indication that thesuspended span was blocked andpulled by the south cantilever arm oncethe (air) temperature was below about0°C. The cross-cor re la t ion values atzero time lag, indicated in the lowerleft corner of the graphs, were indeedvery large (0.93) for the weeks withnegative tem per a ture and smaller forpositive temperature (as low as 0.36during the week in summer).

For studying this phenomenonfur ther, a graph of the longitudinalcoordinate variation as a function ofthe air temperature is presented in

Figure 8: Longitudinal variation and air temperature for one week in winter (top) and one week in summer (bottom).

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

Vol. 70, No. 4, 2016 GEOMATICA 309

Figure 9. The large dots represent thedaily mean values and the smalle dotsrepresent the 10-min moving averagelongitudinal variation of the GNSSantenna. This figure shows that thelongitudinal displacement occurred at6°C instead of around 0°C. Then thedata time series were divided into twoparts: below (green dots) and above(blue dots) 6°C. The linear regressionsfor both parts are also plotted in Figure9 (solid lines).

By dividing the slope of the linearregressions by the length of the can-tilever arm plus half the length of thesuspended span (275 m), a thermaldilatation value of 0.2 ± 0.2 ppm/°Cwas obtained with R2 value of only0.01 when the temperature was above6°C. In this case, there was no signifi-cant correlation with temperature (asindicated by the Fisher test). However,when the air temperature was below6°C, the corresponding thermal dilata-tion was 8.3 ± 0.3 ppm/°C with R2

value of 0.92 (in this case, the Fisher testwas passed successfully). With respectto the theoretical thermal coefficient of11.0 ppm/°C and for a temperatureof –30°C (from 6ºC to –24ºC), oneshould obtain a transversal variationof –9.0 cm instead of –7.2 cm (seeFigure 9). It seems some part of the lon-gitudinal displacement was absorbed bythe damping mechanisms (shockabsorbers) and the supports between thesuspended span and the anchor arms. Itis worth recalling that the troposphericerror (mentioned in the previous section)does not affect GNSS horizontal (longi-tudinal and transversal) components.

Interesting to note that L’Hébreux[2001] reported that eight pins used forlinking the suspended span and the can-tilever arms were replaced in 1985because the bridge expansion did notbehave adequately. According to theCanadian National’s engineers (personalcommunication), the dampers (shockabsorbers) between the suspended span

and the cantilever arms were alsoreplaced more than 10 years ago(around 2005). From Figure 8 and 9, itseems that an unusual displacement inthe longitudinal direction of the sus-pended span of the bridge still exists.

TransversalDisplacements

Particularly during sunny summerdays, an important transversal varia-tion in the GNSS antenna coordinateswas noticed. Some examples are givenin Figure 10. In this figure, to avoidsuperposition of the different plots, therange of the solar radiations (right sidescale) was set between 0 and 4 kW/m2

even when the maximum recordedvalue was 1.4 kW/m2, and the temper-ature values (brown line), to be readwith the left scale, have to be multi-plied by 3 to obtain the real air temper-ature in °C. The time is indicated inhours in local time (LT), that is,

Figure 9: Longitudinal coordinate variation as a function of the air temperature.

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

310 GEOMATICA Vol. 70, No. 4, 2016

Eastern Time zone. In order to isolatethe effect of solar radiation, only thedays with low transversal wind (lessthan 30 km/h) were selected, whichalso affects transversal coordinatevariations (see previous section).

The transversal displacementscould easily reach up to –5 cm beforenoon and a bit less (about 3 cm) in theafternoon during summer sunny days,in which solar radiation values were ashigh as 1 kW/m2, as in the examplespresented in Figure 10. The rapid vari-ation in the solar radiation during theday indicates the presence of clouds.In fact, during cloudy days the trans-versal displacements were signifi-cant ly reduced (and of course at nightthere is no solar radiation). During thewinter season, the sun’s elevationangle is always low (maximum 21°during the winter solstice), and there-fore the transversal displacement wasalways close to 0. Indeed, the transver-sal displacement due to solar radiation

is also related to the sun orientation withrespect to the bridge structure (whichcreates a temperature difference betweenboth sides of the bridge) and the thermalinertia of steel.

Let us mention that solar radiationeffects have been reported for bridgetowers and telecommunication towers.For example, Schenewerk et al. [2006]have shown a tower lateral variation of9 cm due to differential temperature forthe Sunshine Skyway bridge (with tow-ers 132 m in height), located in Tampa(Florida). Breuer et al. [2008] studiedthe daily and seasonal drift of theStuttgart TV Tower caused by the dailysolar radiation and air temperature vari-ation. During a sunny day, the surfaceof the tower concrete shaft that wasexposed to sunlight was subjected tothe thermal expansion provoked bynon-symmetrical warming. The sideexposed to the sun would extend, andthe tower and its top would inclineaway from the sun.

Summary,Conclusions andRecommendations

Table 6 compiles the movementsof the suspended span of the QuebecBridge measured by GNSS, as reportedin the previous sections, along with thecalculations (larger expected deforma-tions) made by the Quebec Bridgeengineers who designed it more than acentury ago.

The freight train load causes thecentre of the suspended span to sub-side by up to 17 cm. This measuredvalue is in fair agreement with thevalue assumed by engineers during thedesign and the construction of theQuebec Bridge. The subsidence valueis smaller for passenger trains (rangingbetween 1.0 and 2.5 cm). The traintransits also provoke a tilt to the sus-pended span since the railway is locatedon the upstream side of the bridge. The

Figure 10: Variations in the transversal coordinate and solar radiation for six different days.

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

Vol. 70, No. 4, 2016 GEOMATICA 311

maximal transversal displacement ofthe GNSS receiver, located 34 mabove the railway, was 11 cm. The lon-gitudinal displacement (of about 1 cm)of the suspended span was also detect edfor freight train transits, but not forpassenger trains. Car loading effectwas not detected by the GNSS antennathat was located on top of thesus pend ed span of the Quebec Bridge.

It was also shown that the centerof the suspended span reacts instanta-neous ly to transversal wind load andthe transversal displacement is propor-tional to wind speed squared. Themeasured values can reach 13 cm forwind speed of 100 km/h. The extrapo-lated value fits very well with the pre-dicted value made during the stage ofthe bridge design.

The relationship between verticaldisplacements of the suspended spanand the transversal wind speed has notbeen demonstrated. To detect thiseffect using the GNSS technique, theauthors recommend the installation ofa reference GNSS station closer to thebridge and another GNSS antenna onthe other side of the suspended spanof the Quebec Bridge. In this lastconfiguration, for such a short base-line of 31 m (equal to the bridgewidth), GNSS will be able to meas-ure the inclination of the suspendedspan even if GNSS height accuracy isless than the horizontal accuracy.Another possibility is to install digi-tal inclinometers (tilt sensors) on thesuspended span at the top and at the

deck level. Longitudinal wind load doesnot affect the suspended span of theQuebec Bridge.

The impact of the temperaturevari a tion on the vertical movement of theGNSS antenna located at the centre ofthe suspended span of the Quebec Bridgewas measured at a slightly smaller value(3.2 cm versus 3.8 cm, a 6-mm discrep-ancy) compared with the predicted one.One can suspect the GNSS height deter-mination to be affected by errors in thewet delay modelling during the summertime because the nearest GNSS referencestation is located 7 km away with a 70 mheight difference. A blockage of the sus-pended span with the south cantileverarm was measured when the temperaturedrops below 6°C. The magnitude of thislongitudinal displacement reached 7 cmfor a temperature variation of 31°C.Transversal displacement of the GNSSantenna easily reached up to 5 cm becauseof the high solar radiation values (up to1 kW/m2) during summer days. This phe-nomenon can be explained by the differ-ential temperature values between the twosides of the Quebec Bridge.

For a complete geodetic deformationmonitoring of the Quebec Bridge, theaddition of GNSS receivers on each sideof the suspended span and on top of themain towers is recommend ed, along withthe installation of inclinometers. In orderto improve the GNSS determination,especially in the vertical component, theauthors suggest installing closer refer-ence GNSS stations. To study the naturalfrequencies of the bridge, the authors

suggest recording GNSS data with ahigher data rate (some receiver modelscan measure at a rate of 100 Hz). SinceGNSS signals are blocked by metallicstructures, the authors also recom-mend complementing GNSS measure-ments with other sensors, such asaccelerometers and total station reflec-tive prisms, installed at the deck level.Finally, an anemometer should beinstalled directly on the QuebecBridge to measure the real parametersof wind (speed and direction) actingon the bridge as well as the installationof steel temperature sensors at strategicpoints of the bridge.

Acknowledgements

Firstly, we want to gratefullythank the Port of Montreal for givingus the access to the GNSS receiverdata as well as their partners in thisproject, the Canadian Coast Guard, theCanadian Hydrographic Service andCN (Canadian National RailwayCompany). The authors were alsooffered free access to the complemen-tary data described in this paper by theQuebec Department of Transportation,MeteoLaval and Cansel. We are verythankful for their collaboration.Finally, NSERC (Natural Science andEngineering Research Council ofCanada) is acknowledged for itsresearch grant that was used topar tial ly fund this research.

Load Direction 1908 design calculation GNSS measurements

Train

Vertical

Transversal

Longitudinal

34 cm (two trains)

N/A

N/A

17 cm (one freight train)

11 cm (at the top of the span)

1 cm

Car Vertical N/A Not significant (not detected)

Wind Vertical

Transversal

2 cm (at 100 km/h)

34 cm (at 170 km/h)

3 cm (at 100 km/h)

32 cm (extrapolated at 170 km/h)

Temperature and solar

radiation

Vertical

Transversal

Longitudinal

3.8 cm (for 50°C variation)

N/A

N/A

3.2 cm (for 50°C variation)

5 cm (for high solar radiation)

7 cm (at –25°C)

Table 6: Comparison of the GNSS measurements and the 1908 original design calculations.

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.

312 GEOMATICA Vol. 70, No. 4, 2016

References

Breuer, P., T. Chmielewski, P. Górski,E.  Konopka and L. Tarczynski. 2008.The Stuttgart TV Tower displacementof the top caused by the effects of sunand wind. Engineering Structures.30(10): 2271–2781.

DeLoach, S.R. 1989. Continuous deforma-tion monitoring with GPS. Journal ofSurveying Engineering. 115(1): 93–110.

DRC, Department of Railways and Canals.1908a. The Quebec Bridge. Report ofthe Government Board of EngineersVolume I, 259 Available fromhttp://www.historicbridges.org

DRC, Department of Railways and Canals.1908b. The Quebec Bridge. VolumeII. Plates to accompany Volume I ofthe Report of the Government Boardof Engineers. Available from:http://www.historicbridges.org

Hyzak, M. and M. Leach. 1995. Bridgemonitoring by GPS. Surveying World.3(3): 8–11.

L’Hébreux, M. 2001. Le pont de Québec.Ed. Septentrion. 255.

Lovse, J.W., W.F. Teskey, G. Lachapelle andM.E. Cannon. 1995. Dynamic defor-mation monitoring of tall structureusing GPS technology. Journal of

Surveying Engineering. 121(1): 35–40.Nakamura, S. 2000. GPS measurement of

wind-induced suspension bridge girderdisplacements. Journal of StructuralEngineering. 126(12): 1413–1419.

Santerre, R. 1991. Impact of GPS satellitesky distribution. ManuscriptaGeodaetica. 16(1): 28–53.

Santerre, R., L. Lamoureux. 1997. ModifiedGPS-OTF algorithms for bridge moni-toring: application to the Pierre-Laporte suspension bridge in QuebecCity. Proceedings of the InternationalAssociation of Geodesy ScientificAssembly, IAG Symposium 118:381–386.

Santerre, R. 2011. Use of GPS for bridgedeformation monitoring. GPS Chapter.in Monitoring Technologies for BridgeManagement, Eds. B. Bakht, A. Muftiand L.D. Wagner. 173–205.

Schenewerk, M.S., R.S. Harris andJ.  Stowell. 2006. Structural healthmonitoring using GPS—observing theSunshine Skyway Bridge. March-April. 18–25. Available from:http://bridgesmagazine online.com

Smadi, Y. 2015. Étude sur l’utilisation dusystème GNSS pour l’auscultationtopographique du pont de Québec.MSc Thesis, Department of GeomaticsSciences, Laval University.

Trimble. 2012. Trimble HD-GNSS processing.Trimble Survey Division White Paper.

Unsworth, J.F. 2011. Railroad bridgedesign criteria. Chapter 11 inStructural Steel Designer’s Handbook(5th Edition). R.L.  Brockenbroughand F.S. Merritt, Eds.

USACE. 2002. Structural deformationsurveying. Chapter 8: Monitoringstructural deformation using GPS.Engineering Manual—US ArmyCorps of Engineers EM 1110-2-1009.

Wong, K.-Y. 2004. Instrumentation andhealth monitoring of cable-supportedbridges. Structural Control andHealth Monitoring. 11: 91–124.

Xia, H., Y.L. Xu and T.H.T. Chan. 2000.Dynamic interaction of long suspen-sion bridges with running trains.Journal of Sound and Vibration.237(2): 263–280.

Xu, Y.L., B. Chen, C.L. Ng, K.Y. Wongand W.Y. Chan. 2010. Monitoringtemperature effect on a long suspen-sion bridge. Structural Control andHealth Monitoring. 17(6): 632–653.

Yi, T.-H., H.-N. Li and M. Gu. 2012.Recent research and applications ofGPS-based monitoring technologyfor high-rise structures. StructuralControl and Health Monitoring.20(5): 649–670. q

Geo

mat

ica

Dow

nloa

ded

from

pub

s.ci

g-ac

sg.c

a by

Uni

vers

ité L

aval

Bib

lioth

eque

on

05/0

5/17

For

pers

onal

use

onl

y.