GPS data is used to understand bridge motion
Project: GPS monitoring demonstration system on the Sunshine Skyway Bridge spanning Tampa Bay in Florida
Team members: General Positioning LLC, Roeland Park, Kan.; Leica Geosystems, Inc., Norcross, Ga.; Florida Department of Transportation, Tallahassee,Fla.
Project application: Continuous and automatic monitoring of bridges is possible in near real time with centimeter-level accuracy using GPS.
Monitoring the health of bridges, dams, buildings, and other structures has evolved into an interesting mix of cutting-edge and tried-and-true technologies. Using automated sensors, which provide virtually real-time information, in conjunction with periodic inspections and maintenance, enable the response of a structure to almost all naturally occurring physical conditions to be studied over almost any time regime.
In 2003, the Florida Department of Transportation (FDOT) and Leica Geosystems, Inc., deployed a GPS monitoring demonstration system on the Sunshine Skyway Bridge, which is the part of U.S. Interstate 275 spanning Tampa Bay, connecting Manatee and Pinellas Counties in Florida. This bridge is one of the longest cable-stayed bridges in the world and has become an area attraction because of its size, history, and award-winning appearance.
For the monitoring demonstration project, FDOT placed three, Leica RS500 GPS receivers with LEIAT504 antennas on the bridge—one on each of the towers and one in the middle of the span. Additionally, a GPS reference site was deployed nearby. Data from all four sites was collected at a one-second rate.
In early 2005, General Positioning LLC (GPos) was invited to evaluate approximately six months of data that was collected from mid-August 2004 through January 2005. The firm's analysis led to a number of interesting conclusions.
Methodology GPS data was processed using PAGERS software, a version of PAGES software originally developed by the National Geodetic Survey but enhanced by GPos for this type of monitoring.
PAGERS uses double-differenced phase data as the observables, in this case, the ion-free combination. The coordinates of the reference site established for the project and those of the satellites were held rigidly fixed in this processing. Neutral atmosphere (tropo) corrections relative to the reference site were estimated from the GPS data for each location on the bridge. Phase ambiguities were set to their integer values, except where uncertainties put those integer values in question. In these cases, the phase ambiguities were estimated. All data processing was completely automated.
Fig. 1: The GPS determined changes in the position of the site on the center span (left), the north tower (center), and the south tower (right) Model predictions, shown in orange, were superimposed on graphs of the actual measurements for the up (U), longitudinal (L), and transverse (T) directions.
Defining a meaningful coordinate system aligned with the bridge helped clarify the GPS results and simplified the interpretation.
The Sunshine Skyway Bridge is oriented 32.9 degrees west of north. A bridge-based coordinate system was defined such that if one looked east-northeast across the bridge span, one would be looking in the direction of the positive transverse axis. The northnorthwest direction along the bridge was designated the positive longitudinal coordinate axis. Lastly, the ellipsoidal height remains the positive up axis, completing a right-handed coordinate system.
All discussion and results are expressed in this transverse-longitudinal- up (TLU) coordinate system.
For convenience and consistency, all times are expressed in GPS time (GPST), the time system created for the Global Positioning System and common in all GPS data processing. GPST differs from Coordinated Universal Time by only a few seconds and avoids any confusion that might be caused by U.S. daylight savings time.
Fig.2: A subset of the GPS results for the site on the center span (left), the north tower (center), and the south tower (right), with the model predictions superimposed in orange.
The six-month time series for the three sites on the bridge are shown in Figure 1. Each coordinate measurement is a 15-minute average and shown as a black dot connected by a light gray line to the previous and next points. If a gap occurred in the original data of sufficient duration to cause a 15-minute measurement to be missed, the points on either side of the gap are not connected by a line. The orange line is the predicted position from a numerical model for the bridge (see discussion below).
A cursory examination of these figures reveals that all three sites on the bridge appear to move, not a surprising revelation for this or any structure. In particular, both the north and south tower sites show apparently identical motions of several centimeters in the transverse direction but move in opposite directions in the longitudinal direction. The motion of the center span site is much smaller than, and bears little resemblance to, those on the towers. These motions are thought to be seasonal in nature.
Figure 2 shows one week of measurements in early November 2004. In this regime, both towers appear dominated by similar diurnal, transverse motions. The up motions are also very similar but smaller. The longitudinal motions of the towers are the most dissimilar, with the south tower exhibiting a small, diurnal cycle of motion while the north tower displays virtually none. The center span site is dominated by diurnal, vertical motion with only slight horizontal motion in this regime.
The sample standard deviations of these 15-minute measurements are approximately 0.5 cm in the transverse and longitudinal coordinates, and 1.7 cm in the up, indicating that all these motions are statistically significant.
In an effort to conceptually understand these motions, a simple, numerical model for some structural components of the bridge was developed, and displacements at the GPS sites were computed. In this simplified bridge model, no attempt was made to compute in detail the heat flux through or forces upon any portion of the bridge. Rather, the functional forms of those equations were used to propagate a few basic parameters through these bridge components.
The result of this simplification was a model that could be run quickly and was dependent upon only four adjustable parameters that define how efficiently the bridge interacted with its environment: heating by solar radiation, transferring heat to and from the air, and two scaling factors for wind loading. These parameters were set by finding the optimal fit of the model to four days of GPS measurements from early November 2004.
Unfortunately, no observations of local environmental conditions at the bridge were available, but a continuously operating Automated Surface Observing System/Automated Weather Observing System at the nearby Albert Whitted Municipal Airport (about 16 km from the bridge) provided a variety of surface meteorological data and weather observations hourly, and more frequently during severe weather.
Most aspects of the diurnal motions ultimately were caused by the towers bending slightly because of temperature differentials between their sunward and shaded sides. The sunward sides of the towers are significantly warmer than the shaded sides because of solar heating. This causes the towers to bend away from the sun as it moves across the sky. This occurs in the negative transverse (-T) direction in the morning, in the positive longitudinal (+L) direction around local noon, in the +T direction in the afternoon, and, finally, slowly relaxing back to its nominal position as the stored heat is redistributed more uniformly through the tower and lost to the air at night.
The longitudinal motion is limited by heat diffusing through the tower, which reduces the temperature differential between the sunward and shaded sides, and by the cable-stays. In fact, the longitudinal motion of the north tower effectively is eliminated by countering forces transmitted through the cables. As the towers are heated by the sun and bend in the +L direction, the motion of the south tower (transmitted through the cable stays to the center span), plus the thermal expansion of the cables themselves, allow the center span to sag. In turn, the sagging, again transmitted through the cable stays, pulls on the north tower, limiting its motion in the +L direction.
A second periodic mode is driven by longitudinal thermal expansion of the bridge spans. As the center span heats, its expansion forces the towers apart: the north tower in +L direction, the south in the -L direction. This motion is limited by expansions of the approaches. Although the data and model are incomplete, it may be surmised that a similar effect, this time caused by expansion of the other sections of the bridge and transmitted through the approaches to the center span and towers, is believed to cause the transverse seasonal motions of the towers.
Some significant transient motions appear to be driven by wind loading. The model indicates that this bridge has about 4.5 times the response to transverse winds as to longitudinal winds, which is intuitively reasonable when one considers the larger cross section and limited self-support of the bridge in the transverse relative to the longitudinal direction. The bridge, as a whole, appears largely unresponsive to wind gusts at this measurement interval, therefore a wind steady in strength and direction is necessary to cause loading motions on these time scales.
From this demonstration, one concludes that GPS observations could be used to refine and evaluate a more sophisticated model.
Additionally, the GPS measurements and model predictions could be used in the structural health monitoring of this bridge, or any structure, by continuously and automatically searching for deviations from the expected behavior. This type of monitoring would be a powerful complement to conventional, periodic inspections and maintenance as it can reveal subtle or unseen changes in a structure from daily wear and tear; aging; or extraordinary events such as hurricanes, floods, or earthquakes.
Mark Schenewerk, Ph.D., is an owner-member of General Positioning LLC. He can be reached at firstname.lastname@example.org. R. Scott Harris is a surveyor-in-training with the Florida Department of Transportation's Surveying and Mapping Office. He can be reached at email@example.com. James Stowell is the director for Reference Station Systems and Engineering Solutions for Leica Geosystems. He can be reached at firstname.lastname@example.org.