Bozidar Stojadinovic

Seismic performance comparison of two rocking isolation alternatives for an overpass bridge

Rocking isolation of structures is evolving as an alternative design concept in earthquake engineering. The present paper investigates the seismic performance of an actual overpass bridge of the Attiki Odos motorway (Athens, Greece), employing two different concepts of rocking isolation: (a) rocking of the piers on the foundation (rocking piers); and (b) rocking of the pier and foundation assembly (rocking footings) on the soil. The examined bridge is an asymmetric 5-span system having a continuous deck and founded on surface foundations on a deep clay layer. The seismic performance of the two rocking isolated bridges is compared to that of the existing bridge, which is conventionally designed according to current seismic design codes. To that end, 3D numerical models of the bridge–foundation–abutment–soil system are developed, and both static pushover and nonlinear dynamic time history analyses are performed. For the latter, an ensemble of 20 records (10 ground motions of 2 perpendicular components each) that exceed the design level are selected. The conventional system collapses in 5/10 of the (intentionally severe) examined seismic excitations. The rocking piers design alternative survives in 8/10 of the cases examined, with negligible residual deformations. The safety margins of the rocking footings design concept are even larger, as it survives in all examined cases. Both rocking isolation concepts are proven to offer increased levels of seismic resilience, reducing the probability of collapse and the degree of structural damage. Nevertheless, in the rocking piers design alternative high stress concentrations at the rotation pole (pier base) are developed, indicating the need for a special design of the pier ends. This is not the case for the rocking footings concept, which however is subject to increased residual settlements but no residual rotations.

A PROBABILISTIC APPROACH TOWARDS AN EVALUATION OF EXISTING CODE PROVISIONS FOR SEISMICALLY ISOLATED STRUCTURES

Following modern design codes, seismically isolated superstructures are designed to respond in the elastic response range or to exhibit limited inelastic behavior. However, the behavior of seismically isolated structures when the superstructure enters the inelastic response range has not been extensively investigated in the past. This paper aims at answering the following questions: What is the probability that a (code-compliant) seismically isolated structure will yield? Will it develop a ductility demand μ larger than that implied by its design strength reduction factor? The probabilistic investigation of such a behavior is important for two reasons: First, to estimate the conservativism implied by the existing code provisions for seismically isolated structures. Second, to account for the case in which the seismic forces acting on an existing seismically isolated structure could exceed the design forces due to a ground motion stronger than the design ground motion level. The investigation is conducted using a two-degree-offreedom model of a seismically isolated structure. The hysteretic behavior of the seismic isolation devices and the isolated superstructure is simulated in Matlab and OpenSees using a bilinear elastic-plastic model. The results are obtained by analyzing the responses of the isolated structure to a large number of recorded ground motions. Fragility curves to estimate the probability that the structure enters the inelastic range (μ>1), if it is designed according to the existing American and European code provisions for seismically isolated structures are determined through probabilistic seismic demand analysis (PSDA). The influence of the isolated structure overstrength and the isolation system hardening is discussed. Additional fragility curves are provided for other values of the engineering demand parameter (EDP) that are not allowed in the existing code provisions (e.g. superstructure displacement ductility μ>2). The effects of seismic isolation and superstructure design parameters on the fragility curves is quantified through parametric analysis.

Improved probability distribution models for seismic fragility assessment

The paper presents a new formulation for the probabilistic modeling of the variables to reduce the errors between the model and the available data sets and to facilitate seismic fragility assessment. Traditionally, one probability distribution, e.g., lognormal distribution, is adopted to describe one variable throughout the domain of values. However, there are potential errors in the probability content, especially in the high tail. The consequences of such tail sensitivity are particularly detrimental in fragility assessment when the limit states under consideration result in small probabilities of failure. To address the tail sensitivity problem, the data sets of the variables are divided into two parts, i.e., bulk and high tail. Each part is considered separately for the probabilistic modeling and integrated into one continuous distribution for fragility analysis. For illustration purposes, probabilistic seismic assessment of a typical reinforced concrete bridge column is compared using the proposed framework and compared to the results based only on lognormal random variable distributions. Results show that for complementary cumulative distribution function (CCDF), the difference may reach one or more magnitudes; for limit states that exercise the tails of the random variable distributions, the difference in the fragility estimates can increase with the hazard level.