  Railroad bridge engineers are interested in the displacement of railroad
bridges when the train is crossing the bridge for engineering decision making
of their assets. 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
pseudo-static displacement component. In the past, researchers have used the
Euler-Bernoulli beam theory formula to estimate the pseudo-static 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 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.
