ANALYSIS OF THE DISPLACEMENTS ROCK SANTERRE, LUC LAMOUREUX AND STÉPHANIE MICHAUD

Transcription

1 ANALYSIS OF THE DISPLACEMENTS OF THE PIERRE-LAPORTE SUSPENSION BRIDGE AS MEASURED BY PRECISE GPS SURVEYS ROCK SANTERRE, LUC LAMOUREUX AND STÉPHANIE MICHAUD DÉPARTEMENT DES SCIENCES GÉOMATIQUES UNIVERSITÉ LAVAL QUÉBEC, CANADA

2 ABSTRACT Algorithms for On-The-Fly ambiguity resolution have been modified for the deformation monitoring of a suspension bridge. Instantaneous relative positioning of a deformation network at a precision of about 5 mm horizontally and 10 mm vertically has been achieved using GPS L1 phase observations. Particular attention has been paid to the modelling of relative tropospheric delay and to the phase centre calibration between antennae of different makes. Moving averages on station coordinates have also been applied to reduce multipath effects. The Pierre-Laporte bridge is a 6 lane, 1040 m length suspension bridge which crosses the St. Lawrence river in Québec City. Three 48 hour GPS sessions have been conducted during the months of July and October 1996 and during February For each session, 5 GPS receivers were observing at a data rate of 2 seconds. Daily variation in the vertical position of the antenna located in the middle of the deck shows clear correlation with respect to temperature and vehicle loading. Transverse movement of the deck has been monitored and correlated with (transverse) wind speed. Seasonal variation in temperature caused a vertical displacement of the middle of the deck, a contraction of the towers as well as a displacement of the towers towards the river banks.

3 RÉSUMÉ Des algorithmes On-The-Fly pour la résolution des ambiguïtés de phase GPS ont été modifiés pour la mesure des déformations d un pont suspendu. Le positionnement relatif instantané d un réseau de déformation à une précision de 5 mm horizontalement et de 10 mm verticalement a été atteint en utilisant les mesures de phase GPS L1. Une attention particulière a été portée à la modélisation du délai troposphérique relatif et au calibrage des centres de phase entre antennes de différents manufacturiers. Des moyennes mobiles au niveau des coordonnées des stations GPS ont été calculées dans le but de réduire l effet des multitrajets. Le pont Pierre-Laporte est un pont suspendu d une longueur totale de 1040 m et compte 6 voies de circulation. Il traverse le fleuve St-Laurent en amont de la ville de Québec. Trois sessions d observations de 48 heures chacune ont été menées durant les mois de juillet et octobre 1996 et février Lors de ces 3 sessions, 5 récepteurs étaient en opération avec un taux d enregistrement de 2 secondes. La variation journalière de la position verticale de l antenne située au milieu du tablier montre une forte corrélation avec la variation de température et le flot de circulation automobile. Le mouvement transversal du tablier a été mesuré et corrélé avec la vitesse (transversale) du vent. La variation saisonnière de la température a causé un déplacement vertical du milieu du tablier, une contraction des tours et un déplacement des tours vers les rives.

4 OUTLINE OF THE PRESENTATION 1 Objectives of the research Modified OTF algorithms GPS error sources and modelling Deformation monitoring network Bridge deck movements, as functions of: - temperature -windspeed - traffic flow Distance between the 2 towers (comparisonwithedm) Seasonal displacements (towers and deck) - thermal dilatation of the 2 towers - sag effect at the middle of the deck Conclusions and further research

5 OBJECTIVES OF THE RESEARCH 2 To adapt GPS-OTF (On-The-Fly) algorithms for deformation monitoring of kinematic engineering structures such as a suspension bridge To develop software for the post-processing of GPS L1 phase observations with the modified OTF algorithms To deal with the most important errors, namely: relative tropospheric delay, antenna phase center variation and multipath To apply the methodology in real cases on the Pierre-Laporte suspension bridge and at different seasons To correlate the bridge displacements with temperature variation (thermal dilatation of the bridge structure), wind speed and traffic flow To compare GPS results with EDM measurements

6 MODIFIED OTF ALGORITHMS (1/2) 3 Y Start A: A priori coordinates B: A priori ambiguity Test 1: on ambiguity search range Next satellite? N Test 5: on cycle slips C: L.S.A. for each ambiguity set End N Y Next epoch? Y Next ambiguity set? N N N Test 2: on L.S.A. correction terms Y Test 3: on individual residuals E: Keep and display the L.S.A. solution Test 4: on ratio of variance factors Y D: Store L.S.A. solution(s)

7 MODIFIED OTF ALGORITHMS (2/2) 4 A: Initialisation from static processing of the first 30 minutes of data; and for the other epochs, coordinates from the previous epoch N B: L1 d tro p L 1 1: Check if the decimal part of eqn. (B) departs by more than 0.25 cycle from the closest interger value C: T 1 T X ( A A ) A W V AX W 1 2 = o ( A T A) X 2: Coordinate corrections < 10 cm? 3: Residuals < 10 cm? D: Store all solutions which pass tests 2 and 3 4: Ratio of the second smallest and the smallest variance factors > 2? 5: If phase variation between 2 epochs ~ prediction from Doppler frequency E: If one L.S.A. solution passes test 4 L.S.A.: Least Squares Adjustment

8 GPS ERROR SOURCES AND MODELLING 5 Type of error Troposphere Multipath Phase center variation Solution Meteorological values extrapolated in height from values recorded at the reference station (Rothacher et al., 1986) => Inputs for Hopfield model Antenna siting and moving average on adjusted coordinates Relative calibration between antennae on a known and short baseline (calibration beam) Ionosphere, Orbit and S/A Errors assumed negligible for short baselines (D < 1 km)

9 DEFORMATION MONITORING NETWORK 6 RIN1 e d a RIN2 f UL2005 D (km) h (m) a b c d e f b TON TACE TOS c N 100 m GPS Station Identification UL2005: Laval University Campus RIN1 : Primary Reference Station RIN2 : Secondary Reference Station TON : North Tower (Tour nord) TOS : South Tower (Tour sud) TACE : Deck Center (Centre du tablier)

10 PIERRE-LAPORTE SUSPENSION BRIDGE: CHARACTERISTICS AND LOCATION OF GPS STATIONS 7 RIN1 110 m TON TOS 70 m TACE 670 m 1040 m TON TOS TON Anemometer TOS TACE T A C E TOS TACE

11 0.5 Vertical displacement as a function of Temperature Station TACE (07/96) Eastern Daylight Time 16:00 22:00 4:00 10:00 16:00 22:00 4: Vertical displacement (m) Temperature ( o C) Elapsed Time (hours)

12 0.5 Vertical displacement due to a car accident Station TACE (07/96) Eastern Daylight Time 13:15 13:30 13:45 14:00 14:15 9 Vertical displacement (m) min. 40 cm :00 3:15 3:30 3:45 4:00 4:15 4:30 Elapsed Time (hours)

13 Transverse displacement (m) Transverse displacement as a function of wind speed Station TACE (10/96) Eastern Daylight Time 17:00 23:00 5:00 11:00 17:00 23:00 5:00 East West Transverse wind speed (km/h) Elapsed Time (hours)

14 Vertical displacement (m) Vertical displacement and Traffic flow (1/2) Station TACE (02/97) Eastern Daylight Time 1:00 7:00 13:00 19:00 1:00 7:00 13: Number of vehicles /15 min Elapsed Time (hours)

15 Vertical displacement and Traffic flow (2/2) Station TACE (02/97) 12 Vertical displacement (m) Amplitude (m) Low traffic flow: 257 vehicles 3:30 3:40 3:50 4:00 Eastern Daylight Time FFT High traffic flow: 3514 vehicles 8:00 8:10 8:20 8:30 Eastern Daylight Time FFT Period (minutes) Period (minutes)

16 DISTANCE BETWEEN THE TWO TOWERS 13 Distance pillar to pillar DI2000 : m ±3 mm at a temperature of -4.5 o C Comparison with GPS (for a mean temperature of -4 o C) mean: m ±10 mm Distance (m) :00 7:00 13:00 19:00 1:00 7:00 13: DI2000 : m T(DI2000): -4.5 o C Elapsed Time (hours) (EDT) Temperature ( o C)

17 14 DEFORMATION OF THE PIERRE-LAPORTE BRIDGE (BETWEEN SUMMER AND WINTER SEASONS) TOS TACE West TON East displacements in cm mean temperature variation: -25 o C mean difference of transverse wind speed: 21 km/h

18 THERMAL DILATATION OF THE TOWERS 15 TON Vertical displacement between summer and winter seasons 3.8 cm TOS 110 m TOS using the Differential Essen&Froome tropo. model (Rothacher at al., 1986) TON: 3.4 cm TOS: 3.8 cm for a temperature variation of 25.3 o C Height of the towers : 110 m Dilatation coeff. (TON): m / 110 m / 25.3 o C = 12.2 ppm / o C Dilatation coeff. (TOS): m / 110 m / 25.3 o C = 13.7 ppm / o C Thermal dilatation coefficient of steel: 11.7 ppm / o C vertical displacement of 3.3 cm

19 SAG EFFECT AT THE MIDDLE OF THE DECK m TON TOS 67 m TACE 664 m Vertical variation of station TACE (between summer and winter seasons) 1) With the average coordinates of stations TON, TOS and TACE, for the summer session, obtain the constants of the sag equation. cable length between the 2 towers (L): m. 2) Calculate the theoretical cable length, for the winter session, with the thermal dilatation coefficient of steel (11.7 ppm/ o C) for a change of temperature of -25 o C. L: m. 3) With this theoretical cable length, the coordinates of stations TON and TOS (for the winter session) and the sag equation, calculate the vertical displacement of the middle of the deck: 51 cm. 4) The vertical displacement of station TACE (from GPS) is 46 cm.

20 CONCLUSIONS 17 A methodology, algorithms and software have been developed for bridge deformation monitoring The precision of instantaneous relative positioning is about ±5 mm horizontally and ±10 mm vertically (PDOP < 6) The analysis of the displacements shows: i) a transverse movement of the deck center due to transverse wind speed of about: 2 mm / 1 km/h ii) a vertical displacement of the deck center with respect to temperature variation of about: -2 cm / 1 O C (explainable with sag theory and thermal dilatation of the cables) iii) a vertical variation of the deck correlated with traffic flow iv) an elongation of the tower with respect to temperature variation of about 1.5 mm / 1 O C (compatible with the thermal dilatation coefficient of the towers) v) a displacement of the towers towards the river banks of about 1.5 mm/1 O C vi) an agreement of a few mm in the comparison of distance between the 2 towers from GPS and EDM measurements

21 FURTHER RESEARCH 18 Detailed study of the high frequency movements of the bridge (sessions with a higher GPS data rate) Addition of more GPS receivers with chokering antennae Real-time implementation of deformation monitoring Application to other engineering structures: towers, skyscrapers, dams, etc. ACKNOWLEDGEMENTS Ministère des Transports du Québec Natural Sciences and Engineering Research Council of Canada (NSERC) Fonds d enseignement et de recherche - Laval University, Faculty of Forestry and Geomatics