ABSTRACT
The efficiency of different probabilistic methodologies for the safety assessment of short span railway bridges is compared in the current paper. The Monte Carlo and the Latin Hypercube simulation methods are combined with two different procedures to enhance the efficiency of the assessment: one based on the extreme value theory and another that uses an approximation procedure based on the estimates of the failure probabilities at moderate levels for the prediction of the far tail failure probabilities by extrapolation.
Generally, structural reliability problems are determined by the tail of the obtained statistical distributions. Therefore, the computational cost can be significantly reduced if an extrapolation of the Cumulative Distribution Function (CDF) is made using tail modelling techniques. The classical tail modelling is based on the extreme value theory and consists on approximating the tail portion of the CDF above a certain threshold by the Generalized Pareto Distribution.
The other selected method exploits the regularity of the tail probabilities to set up an approximation procedure based on the estimates of the failure probabilities at more moderate levels for the prediction of the far tail failure probabilities. An approximation function is fitted to the estimates allows estimating the target probability of failure by extrapolation. The optimum values for the approximation function parameters is obtained through a least square optimization method. The extrapolation of the fitted curves to the level of interest will determine the estimated probability of failure.
As a case study the Canelas railway bridge was selected. The bridge has six simply supported spans of 12 m each leading to a total length of 72 m. The bridge deck is a composite structure and has two half concrete slab decks with nine embedded rolled steel profiles HEB 500, each supporting one rail track.
To assess the efficiency of the methodologies proposed the train running safety is analysed through the assessment of the wheel unloading coefficients. Examples of the fit of the GPD function to the data obtained from the simulations and of the application of the ES procedure is shown in Figures 1 and 2, respectively, for a train speed of 425 km/h. GPD fit to the upper tail of the wheel unloading coefficient distribution. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315207681/cd556cd4-4dcf-4efe-8e29-56fc67b8bfbd/content/fig246_1.tif"/> Assessment of the probability of loss of contact between the wheel and the rail by the ES procedure. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315207681/cd556cd4-4dcf-4efe-8e29-56fc67b8bfbd/content/fig246_2.tif"/>
In order to guarantee the train running safety the speed over the bridge should be limited to 415 km/h. Furthermore, it is observed that 12,000 simulations are sufficient accurately assess the train running safety. The obtained results are extremely promising and indicate the feasibility of the application of this type of methodology due to the very reasonable computational costs that are required.
