Measuring Total Transverse Reference-Free Displacements of Railroad Bridges Using Two Degrees of Freedom: Experimental Validation

Knowing the extent of displacement experienced by railroad bridges when loaded is useful when evaluating the safety and serviceability of the bridge. However, measuring displacements under train crossing events is difficult. If simplified reference-free methods would be accurate and validated, owners would conduct objective performance assessment of their bridge inventories under trains. Researchers have developed new sensing technologies (reference-free) to overcome the limitations of reference point-based displacement sensors. Reference-free methods use accelerometers to estimate displacements, by decomposing the total displacement in two parts: a high-frequency dynamic displacement component, and a low-frequency pseudostatic displacement component. In the past, researchers have used the Euler-Bernoulli beam theory formula to estimate the pseudostatic displacement assuming railroad bridge piles and columns can be simplified as cantilever beams. However, according to railroad bridge managers, railroad bridges have a different degree of fixity for each pile of each bent. Displacements can be estimated assuming a similar degree of fixity for deep foundations, but inherent errors will affect the accuracy of displacement estimation. This paper solves this problem expanding the 1 degree of freedom (1DOF) solution to a new 2 degrees of freedom (2DOF), to collect displacements under trains and enable cost-effective condition-based information related to bridge safety. Researchers developed a simplified beam to demonstrate the total displacement estimation using 2DOF and further conducted experimental results in the laboratory. The authors assumed linearity on properties and connections and used real train crossing event data as input to evaluate the accuracy of the proposed 2DOF method. The estimated displacement of the 2DOF model is more accurate than that of the 1DOF model for ten train crossing events. With only one sensor added to the ground of the pile, this method provides owners with approximately 40% more accurate displacements. Future work includes the study of nonlinearities and parametric study of the effect of resonance in displacement estimation accuracy for practical field implementation.

The main application of this research is the optimization of the number of sensors and the simplification of sensor location, for lateral displacement estimation. Infrastructure managers can install a minimum number of sensors in tall piers or structures and determine the transverse displacement. The main practical aspect of this work is that engineers can collect the rotation at the base of the pier by locating sensors in the base. Using both the rotation both at the bottom and the top of the pier, the total displacement at the top can be obtained. In the practical domain, timber railroad piers could demonstrate additional lateral displacement under train crossing events not associated with the rotation above ground. Engineers could observe or collect that lateral displacement and add it to the total estimated displacement to obtain the total transverse displacement. Based on the field observations of the main author of this paper the lateral separation between the timber pile at the base of the pier is small, however it can be a practical next step in further development of the proposed method for practical applications.