A probabilistic strategy for seismic assessment and FRP retrofitting of existing bridges

Abstract

This study proposes a holistic probabilistic framework to evaluate existing road and railway bridges after an earthquake by means of analytical fragility curves and visual inspections. Although visual inspections are affected by uncertainties, they are usually considered in a deterministic way, while in this work they are taken into account in a probabilistic point manner. Moreover, extra focus is given on retrofitting interventions by means of Fiber Reinforced Polymer materials and their costs. A probabilistic methodology is formed to evaluate possible standardized interventions on existing bridges after a seismic event. The proposed framework, consists of six basic steps and it is applied on a reinforced concrete bridge case study, which is a common structural typology in Italian roadway infrastructural networks. The main aim is to provide useful information to public authorities in order to decide whether or not they should allow traffic over the bridge and whether to repair immediately earthquake-damaged bridges. The outcomes of this framework can be used to improve procedures used for the seismic assessment of the whole road and railway networks to better plan emergency, post-emergency actions and define a general priority for an optimal budget allocation.

Appendix

In the following, the main steps for the construction of the fragility curves for a bridge, according to the above-mentioned procedure, are presented.

• 1. Assemblage of a group of accelerograms compatible with the elastic spectrum of the site of interest. In this study, according to the Italian Code for Constructions (Italian Ministry of Infrastructures 2008), seven artificial accelerograms were considered for the analysis of the structure in longitudinal and transverse direction. Each artificial accelerogram is scaled by a numerical factor to obtain various values of peak ground acceleration (PGA) to perform the fragility analysis.

• 2. Generation of statistical samples of the bridge considering significant modelling parameters. Accordingly, two main variables have been considered for the pier: steel yielding strength $f_{y}$ and unconfined concrete strength $f_{c}$. A probability density function is associated to each variable. These functions are subdivided into finite intervals to match the intervals and make nominally identical bridge samples, but statistically different.

• 3. Non-linear time history analyses are developed for each ground motion-bridge sample. In this study, displacement on pier top was monitored throughout the analyses.

• 4. For each run, peak responses in longitudinal and transversal directions were recorded in order to calculate the damage as shown in Eq. (5). These results were plotted versus the value of the intensity measure for that ground motion in a bi-logarithmic plane (see Eq. 2). A linear regression of these data is then used to estimate $A$ and $B$ coefficients, medium value and dispersion.

• 5. The fragility curve for a significant bridge component (e.g., the pier), at a certain Performance Level and direction (longitudinal or transversal) can be calculated numerically solving the integral:

  $$\begin{aligned} \int _{D\left( a \right) > dPL } f_D (d/a)\partial d \end{aligned}$$

  (9)

  by means of Eq. (3) and the procedure described in Sect. 2.2.

• 6. Finally, the fragility curve of the entire bridge for each Performance Level can be calculated via Eq. (4).