Millimeters in motion: dynamic response precisely measured

GPS World, Jan, 2005 by Ana Paula C. Larocca, Ricardo Ernesto Schaal

Brazilian researchers devised a way to detect dynamic millimetric displacements in large structures using single-frequency GPS receivers. They combine interferometry, satellite geometry, and a novel analysis of L1 double-difference phase residuals of regular static observations over a short baseline. The results from a set of trials on a footbridge affirm that the methodology can detect displacements of large structures such as bridges, tall buildings, and towers undergoing dynamic loads.

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Effective data analysis, rational data interpretation, and correct decision making pose challenges for engineers monitoring large structures. Accurate response data, at high levels of precision, form the foundation of this entire process, so that engineers can check performance against design criteria that allow for response, within limits, to loads.

To obtain millimeter-level data of structural response, we developed a method to detect dynamic behavior, based on interferometry applied to data collection and analysis of L1 double-difference phase residuals of regular static data processes. As our testing laboratory, we used a small, cable-stayed pedestrian footbridge, but the concepts and methodology should apply equally well to large suspension bridges and tall buildings.

A cable-stayed bridge operates on a simple concept, carrying mainly vertical loads acting on a horizontal girder. Stay cables provide intermediate supports for the girder so that it can span long distances. A highly redundant, statically indeterminate structure, a cable-stayed bridge can have an infinite number of possible combinations of permanent load conditions, with its response determined solely by equilibrium requirements.

Monitoring scope includes two major parameters: load effects and responses. Load effects can be due to wind, temperature, and live loads. Responses refer to displacements, accelerations, strains, and forces of the members of footbridge structures, and displacements and stresses of its main cables. Accurate response data enable engineers to check the as-built performance against design criteria, an increasingly useful exercise given the move toward "performance-based design" of structures. It can also provide the opportunity to identify anomalies that may signal unusual loading conditions or modified structural behavior, which can, in extreme cases, include damage or failure.

Timber Bridge. We carried out the trials described on a cable-stayed stress-laminated timber footbridge with curved modules and a 35-meter span, built in 2002 between two buildings at the Sao Carlos Engineering School, University of Sao Paulo, Brazil. The deck consists of seven wood modules each measuring 5.2 meters long, and a cylindrical tower also of wood, 13 meters high and 55 centimeters in diameter. Three 32-millimeter steel cables support the tower, and eight 15-millimeter steel cables support the decks.

Footbridges are predominantly affected by pedestrians. Therefore, vibrations induced by rhythmical body motions such as walking, marching and jumping, are of great importance. These vibrations may strongly affect the serviceability and, in rare cases, structural fatigue behavior and safety. Average pedestrian walking rate is 2 Hz with a standard deviation of 0.175 Hz. Pedestrian load effects have vertical, horizontal and torsional responses in relation to the axes of the footbridge. We focused on horizontal responses because of the deck curvature.

Bridge Trial

We conducted initial tests on the footbridge to get an idea of its dynamic behavior and to establish the necessary rate of GPS receiver and kind of displacement transducer necessary for further study. In this test some people walked over the deck, and with a total station we determined the number of oscillations of a fixed prism on deck during one minute. Subsequent trials in December 2002 and February 2003 used a pair of GPS receivers with choke-ring antennas with a 20 Hz data collection rate and a displacement transducer with 20 channels and a 10 Hz rate. Figures 1 and 2 show the bridge and equipment layout. The rover GPS receiver and the transducer were placed on module 02, where the previous load static trial found the highest vertical displacements. This module is supported by the longest stay cables and for that reason presents the greatest dynamic displacements.

We placed the reference station about 40 meters away from the rover station, aligning the rover GPS antenna with the center of module 02, and setting the displacement transducer at the same point, but beneath the module. Twelve students walking from module 07 to the beginning of module 02 and returning to module 07 induced bridge movements. This procedure lasted about four minutes for each trial.

Methodology

We applied the interferometry principle to data collection and analysis of L1 double-difference phase residuals of regular static data processes to detect dynamic structural behavior. Most displacement control scenarios include a reference point in the neighborhood of the structure, allowing the use of single-frequency receivers.