- This proposed method utilizes micro-tremor data to mechanically estimate a viaduct’s elastic natural period which is then converted to yield an equivalent natural period.
- Accurate estimation of the equivalent natural period can be used to evaluate, inter alia, the seismic capacity of track sections.

The vibrational characteristics of a structure’s elastic natural period and equivalent natural period, inter alia, are key indicators to determine that structure’s performance.

The elastic natural period is utilized as an evaluation criterion to assess among other things, a structure’s overall state of health. On the other hand, the equivalent natural period as a factor is used to evaluate its behaviour during relatively major seismic movement and its seismic capacity (Fig 1).

The present research has produced a simple method to estimate the elastic natural period of a viaduct from micro-tremor data with the development of a method to determine the elastic natural period through combined evaluation of the vibration frequency, attenuation, mode form and oscillation stability, etc. (Fig 2). The resulting method yields a mechanical and accurate estimation of the elastic natural period.

In addition, a method was proposed aimed at older existing structures built with former technical standards for which the equivalent natural period was not clear, which employs the measured elastic natural period of these structures to convert it into an equivalent natural period. Given that the measured elastic natural period encompasses structural rigidity, type of foundation, ground conditions and other factors which influence equivalent natural periods, estimations obtained with this method are very accurate.

For example in the case of a rigid frame viaduct constructed on a pile foundation, when the equivalent natural period is multiplied with the conversion modulus 1.8 obtained statistically in the course of this research, an estimation to within 5% error can be found, in comparison with the equivalent natural period yielded by detailed non-linear analysis. The present method may be applied to determine the seismic capacity of railway sections and to identify vulnerable points in terms of running safety (Fig 3).