Point of Beginning

Whole Lotta Shakin` Goin` On

April 24, 2008


The December 2007 article “Monitoring the Mighty Mac” by Michael Olson, PE, discussed a pilot project on Michigan’s Mackinac Bridge that demonstrated the utility of GPS technology for deformation monitoring. In this follow-up article, the data analysis team discusses the findings in more detail.

Like airplanes, skyscrapers, dams and other large engineered structures, bridges constantly deform by design and by necessity. All modern bridges, for example, contain expansion joints to ensure that thermal expansion and contraction will not buckle the bridge or tear it apart. Following the wind-induced collapse of Washington’s Tacoma Narrows Bridge in November 1940, structural design engineers have taken considerable care to ensure that wind stresses will not trigger destructive mechanical resonances in suspension bridges. Despite these efforts, the mechanical behavior of a bridge is likely to change as it ages, particularly if it has not been adequately maintained. Underestimating the extent of these changes can lead to catastrophes such as the recent collapse of the Interstate 35W bridge in Minneapolis last August.

In recent years, bridge engineers, geodesists and surveyors have been working together to explore cost-effective ways to monitor bridge deformations over extended periods of time. When such monitoring systems become operational, their data is expected to enable other professionals to recognize when a bridge is changing due to corrosion, metal fatigue, foundation instability and other age-related problems and help to plan appropriate action.

Workers band a section of the 42,000 miles of steel cable used on the Mackinac Bridge during its construction in the mid- to late-1950s. These cables contribute to the bridge’s flexibility but expand and contract with temperature changes. Image courtesy of MDOT’s photography unit.

Monitoring Mac

In August 2005, a pilot project began in Michigan to demonstrate the use of GPS for continuous monitoring of the movements of the Mackinac Bridge, one of the longest suspension bridges in North America. The eight-day experiment was organized and implemented by the Michigan Department of Transportation, the Mackinac Bridge Authority, Leica Geosystems Inc. (www.leica-geosystems.us) and General Positioning LLC (www.generalpositioning.com), the provider of the GPS analysis software.

Six Leica GX1230 GPS receivers were used during the project, four of which were installed on the bridge (one each on the tops of the north and south bridge towers and two near the middle of the center span on either side of the bridge). Another two GPS stations were installed off the bridge on stable ground to provide the necessary reference points. Since the bridge has an azimuth of N 5.8o E, the north component of displacement at any GPS station located on the bridge is very nearly a longitudinal motion and the east component is very nearly transverse to the bridge.

Analysis of the data collected during this experiment reveals that the bridge continuously deforms in response to wind loading, temperature changes and the weight of crossing vehicles.

Figure 1. Vertical displacement of the east (E) and west (W) GPS stations located on either side of the middle of the center span of the bridge for a two and a half day period and the temperature (plotted with the positive direction downward) reported by the meteorological station CYAM located about 47 kilometers NNE of the Mackinac Bridge. The GPS solution interval is 15 minutes.

Software Selections

Two distinct proprietary software packages from General Positioning LLC, PAGERS and KPOS, were used to analyze the project data and exploit the temporal characteristics of the various modes of bridge deformation.

PAGERS
PAGERS involves temporal averaging of the GPS data, which suppresses multipath noise, thereby improving the accuracy of positioning at the cost of reduced temporal resolution. PAGERS is best suited for monitoring relatively slow-developing motions, such as thermoelastic deformation. Thermally induced deformation tends to be cyclical in nature and have characteristic times scales of one day and one year. Figure 1 shows the impact of diurnal temperature variations on the heights of the pair of midspan GPS stations just above the level of the roadway. As air temperature increases, the cables expand and, as a result, the center of the bridge droops downward. The direction of the temperature axis in this plot is the reverse of the normal convention so as to emphasize the coherence between the up component of displacement at each midspan station and ambient air temperature. (Temperature and the up component of displacement at midspan are actually anti-correlated.) This coherence would be even stronger if air temperature measurements were made at the bridge, but our temperature readings were supplied from a weather station located about 47 kilometers NNE of the bridge.

PAGERS software was also used to document wind-induced horizontal displacements of the midspan stations. The largest wind signals were observed in the east (or transverse) component of the midspan stations. Sustained lateral deflections as large as 3 feet were observed,1 but even larger displacements could be expected during severe weather events.

Figure 2. Loading event A. These displacement time series were obtained by kinematic analysis of the GPS stations at the top of the south tower, the east side midspan location and the top of the north tower for approximately six-minute periods during the early hours of the morning. The GPS solution interval is 1 second. The north component of displacement is shown for the two tower stations, and the up component of displacement is shown for the midspan station. These time series record the bridge’s response to the passage of a single heavy vehicle crossing the bridge from south to north. The green dashed lines indicate the beginning and ending times of the displacement transients when they can be clearly discerned, and the red dashed line indicates the midtime of the event. Note the symmetry of the vertical displacement history at midspan and the anti-symmetric nature of the north and south tower responses. The labels 1, 2 and 3 indicate the times depicted in the figure below.

KPOS
The main focus discussed in this article is the high-frequency or impulsive deformation caused by the weight of the vehicles crossing the bridge. We used the kinematic GPS analysis package KPOS to position each of the four GPS stations on the bridge at the data-sampling rate of once per second. This allowed us to follow rapid oscillations and short-lived transient displacements of the bridge at the cost of abandoning temporal averaging and, therefore, accepting a somewhat lower signal-to-noise ratio.

During the day, there are so many vehicles on the bridge at any given time that the pattern of loading is both complicated and constantly shifting, and the bridge is deforming on a continuous basis in response to these loads. One can obtain greater initial insight into the loading process by examining the displacement time series roughly halfway between midnight and dawn when heavy vehicles frequently cross the bridge only one or two at a time.2

One vehicle-loading event, referred to as event A in Figure 2, took place on Aug. 17 between 8:45 and 8:50 Coordinated Universal Time (UTC). This event began with the southward deflection of the top of the south tower by about 1 inch and an upward deflection of 2-3 inches of both midspan stations (only the east midspan time series is shown because the two time series appear almost identical). During the middle of the event, the midspan stations deflected downward more than 8 inches and both tower stations deflected horizontally toward the center of the bridge with maximum horizontal deflections in excess of 1 inch. Finally, the top of the north tower moved northward by a little more than an inch, while the midspan stations lifted upward by 2 to 3 inches. This entire event lasted about four minutes.

Figure 3. An illustration expressing the direction and magnitude of the peak displacements (red arrows) recorded at three stages of loading event A. These stages, labeled 1, 2 and 3, correspond to the times that were similarly labeled in the previous figure. The blue object represents the position of the load.

This pattern of longitudinal deflection at the tower tops and vertical deflection at the midspan stations is what one would expect from a heavy vehicle crossing the bridge from the south to the north (see Figure 3). By examining the duration of these signals and the geometry of the bridge, we deduced that this vehicle was traveling close to the truck speed limit of 25 mph. Loading signals of this kind are ubiquitous, but during the day, they overlap to the extent that their character or signature is obscured. Traffic loading produces no significant signal in the east (or transverse) component of displacement.

Figure 4. The horizontal displacement time series recorded during event A at the north and south towers, plotted in such a way as to demonstrate the fundamental similarity of each tower’s response.

The remarkable symmetry of the horizontal displacement time series obtained at the two towers is illustrated in Figure 4 on page 37. When the south tower time series has its sign reversed in order to depict the south (not north) component of deflection, and when the time series obtained for the north tower is “reflected” around the center time of the event, the resulting curves look almost identical. This is the expected result when the vehicle travels at nearly constant speed.

Figure 5. Loading event B in which the vehicle traveled in the opposite direction (from north to south) from case A. The time of maximum vertical displacement at the midspan is more than halfway between the start time of the transient at the north tower and the end time of the transient at the south tower indicating that the vehicle was traveling faster during the second half of its crossing.

Many similarly discrete (non-overlapping) loading signals can be seen in our time series during the early morning hours of each day. A second example, designated Event B, reverses the sequence of horizontal displacements at the north and south towers in comparison to Event A ( see Figure 5 on page 38). This is because during event B, the vehicle crossed the bridge in the opposite direction, traveling from north to south. The peak vertical deflection at midspan was larger for event B indicating that it was caused by a heavier vehicle. It is also quite clear that the vehicle was traveling faster after it passed the midspan than it was during the first half of its crossing. This is not unusual in that a vehicle travels uphill on the first half of its crossing and downhill on the second half.

Human-induced Loads

These loading signatures could be studied in more detail to provide greater insight into the mechanical behavior of the bridge. First, rather than observing one isolated vehicle traveling across the bridge in one of the two lanes, the Mackinac Bridge Authority could perform controlled experiments by closing the bridge to traffic for an hour or so several times a year and sending two large trucks across the bridge traveling side by side in the same direction, one in the northbound lane and one in the southbound lane. By increasing the total weight of the moving load, the amplitude of the bridge’s response would be increased making it even easier to measure. The trucks could be weighed prior to the experiment to better quantify the relationship between load and deflection. The loads could be increased even further if four trucks were used rather than two, again splitting the weight evenly between the two lanes and traveling in a tight group. All trucks could carry GPS receivers so their positions could be determined (after the fact) throughout the course of the experiment.

The response of the bridge to vehicle loading could be examined in even greater detail by adding additional GPS receivers to the structure or by supplementing a monitoring system with other sensor types such as tiltmeters and cable strain devices. If the loading response suddenly changed or changed slowly over extended periods of time, then it could be deduced that some important change must have occurred in the structure or rigidity of the bridge.

The Mother (Nature) Load

While traffic loading is just one important driving force, bridges deform in response to any force imposed on them. Wind loading, for example, often produces the largest signals of all, but they are highly irregular as they are tied to synoptic weather systems and storms. Thermoelastic loading is more cyclical in character but is far from being strictly periodic and is considerably more complicated than just simple cycles of expansion and contraction.

These distinct external forcings of a bridge tend to deform it in different ways. For example, only wind loading produces large transverse deflections of the midspans of suspension bridges. On cloud-free days, tall bridge towers tend to bend during the course of the day tracking the position of the sun due to differential thermal expansion driven by the selective radiative heating of the tower.3 These diverse forcings tend to manifest or illuminate distinct structural properties of the bridge. While we can stage controlled experiments in traffic loading, we cannot take a similar approach to wind or thermal forcing, which are controlled only by Mother Nature. It is highly desirable to monitor a bridge continuously--ideally throughout its lifetime--not only during controlled tests. Continuous monitoring would require the installation of meteorological sensor packages on various parts of the structure to provide the ancillary data necessary to decompose the mechanical response of the bridge to different classes of forcing. This would be less difficult than it sounds because, although different modes of deformation may be superimposed in time, these modes tend to have distinct spectral characteristics or time scales and different dominant orientations. For example, transverse wind loading is dominantly expressed in the east component of displacement at midspan, whereas vehicle loading is dominantly expressed in the vertical component of displacement at this same location.

Continuous Monitoring Potential

It’s hard to appreciate the enormous challenges bridge designers faced half a century ago when structures like the Mackinac Bridge were designed without the use of computers and modern structural analysis software. Modern designers can perform much more realistic simulations of how a bridge will deform in response to traffic loads and weather. But in most cases, these simulations are not systematically compared with the actual behavior of the bridge after it has been constructed. The advent of continuous monitoring of bridge deformation opens up the possibility of further advances in structural modeling. While the primary application of bridge monitoring is to assess overall health, the structural engineers who design our bridges also have something to gain. These theoretical advances would inform the engineers charged with long-term monitoring of bridge deformation by helping them to better interpret the time series they collect.

The Mackinac Bridge pilot project and other similar projects illustrate a remarkable complexity in the way that large bridges respond to weather and traffic loading, which should be taken into account when designing a bridge monitoring program. The software packages used to track bridge displacements must adapt analysis strategies to the characteristics of the various deformation modes of particular bridges. Retrofitting existing bridges with GPS monitoring systems and, whenever possible, incorporating these systems into the design of new structures, will ensure the longevity, health and safety of these structures.

Ultimately, a properly implemented monitoring program on bridges and other structures will lead to more cost-effective targeted maintenance schedules and provide earlier insight into potential failures. Such far-sighted efforts could minimize catastrophic events, such as the recent bridge collapse in Minnesota.

References

1. Olsen, PE, Michael, “Monitoring the Mighty Mac,” POB, December 2007.

2. A similar study that used differential GPS was presented by Roberts et al in 2006. Roberts, Gethin Wyn, Chris Brown and Xiaolin Meng, “Bridge Deflection Monitoring: Tracking Millimeters across the Firth of Forth,” GPS World, February 2006, pgs. 26-31.

Schenewerk, Mark S., R. Scott Harris and James Stowell, “Structural Health Monitoring Using GPS Observing the Sunshine Skyway Bridge,” GoBridges.com, March 13, 2006, www.gobridges.com/article.asp?id=319.


We would like to thank Dr. Richard R. Sauve II, Michigan technical sales representative for Leica Geosystems Inc., for helping to obtain the GPS data used in this pilot project. We would also like to acknowledge Dr. Gerald L. Mader for sharing with us his extensive experiences with kinematic GPS positioning. Lastly, we thank the Mackinac Bridge Authority and Michigan DOT for access to the bridge and for making this project possible.