Tens of thousands of drivers cross Costa Rica’s bridges every day, and most never give it a second thought. Public confidence in these structures stems from the government’s success in monitoring their safety and reliability. But how does the government make sound decisions about how to allocate limited bridge maintenance resources to ensure the public remains safe?
The professors and students involved in the Costa Rica Institute of Technology’s (TEC) eBridge Project have collected and analyzed data from numerous bridges to establish a bridge evaluation system. Their goal is to make it easier and faster for the government to make bridge repair decisions that are supported by rigorous data analysis.
For one key bridge, data analyzed with Minitab Statistical Software helped the government recognize the need for repairs before it became an emergency. Now the project team is refining their evaluation system by monitoring data from selected bridges, assessing their reliability, and providing the government with their findings.
The government initiated repairs on the bridge over the river Purires (above) based on data generated by students that indicated points of stress.
The bridge that spans the Purires River in Cartago, Costa Rica, bears the weight of 11,318 vehicles daily. Given limited annual resources for bridge maintenance throughout the country, the government needed to determine whether this bridge required immediate attention, or whether it could continue to be relied on for additional years.
Team members from the eBridge project placed sensors underneath the bridge to measure movement and vibrations in the steel-and-concrete structure as vehicles passed over it. They collected more than 90,000 data points, which they needed to analyze in order to predict the bridge’s reliability and identify the structure’s high stress points.
The task involved multiple steps, and many statistical methods. They needed to develop a mathematical model of the bridge’s performance based on their data, then create and analyze simulated data to forecast how the bridge might perform in the future under different scenarios.
How Minitab Helped
The team used Minitab to perform time series analysis on the sensor data, which revealed how well the bridge’s steel and concrete were standing up to the weight of traffic over time. “With Minitab we were able to look for outliers and identify stress points easily,” said Federico Picado, researcher for the eBridge Project.
In their effort to establish a bridge evaluation method, team members performed time series analysis in Minitab to identify patterns in data over time. In the chart above, we can see at what times the deformation, or movement, of the bridge occurred.
The team also used Monte Carlo simulation to facilitate their analysis of the bridge. This method creates large amounts of simulated data using known parameters and an equation that describes the relationship between variables, permitting researchers to predict outcomes in situations where gathering similar amounts of real data is costly or impossible.
Using the sensor data they collected, as well as known information about the mechanical and structural properties of the bridge, the eBridge team used Minitab to simulate load and resistance data that mimicked the strain of traffic from which they collected sensor data. From here, they performed a reliability analysis to predict the reliability of the bridge and to determine the probability of failure. Accurate reliability analysis depends on selecting the right statistical distribution for your data, and Minitab made it easy to confirm that the team’s data followed the normal distribution.
The probability plot above displays data used in the first data simulation.
The team used the results of its initial reliability analysis to generate normally distributed data for a second bridge traffic scenario, and performed another reliability analysis. They then compared the results of the two scenarios, looking at whether the simulated load and resistance stressors exceeded the bridge’s capacity to safely handle those stressors.
Histograms assess the shape of data and can be used in conjunction with an analysis to help confirm assumptions. Above, the load and resistance values in both scenarios are displayed.
If the bridge’s capacity was greater than the predicated stressors, the reliability index would be high enough that the bridge could be considered safe. If the reliability index was low, international safety codes could be used to make an immediate determination about the use and maintenance of the bridge.
The team’s analysis revealed that the reliability index of the bridge over the Purires was low—the capacity of the steel and concrete was not strong enough to consistently accommodate the predicted weight of the traffic, and the bridge was at risk of being compromised. When evaluated against international codes, the bridge did not satisfy safety requirements. The Costa Rican government referenced these findings while determining a repair plan for the bridge..
“Our analysis in Minitab helped us conclude that trucks crossing the bridge were causing high deformations,” said Picado. In fact, two months after the analysis, one of the bridge’s steel beams collapsed. “Thankfully, no one was hurt. We were happy to learn our predictions were accurate, and that the government could intervene once we realized the bridge was in trouble.”
As repairs to the bridge over the river Purires continue, the eBridge Project will apply its methodology to other bridges in Costa Rica and refine its bridge assessment process using Monte Carlo simulation and reliability analysis. Anticipating potential failures ensures the safety of Costa Rica’s citizens, and reduces the cost of repairs by predicting safety hazards before they occur.