Horizontally curved steel bridge seismic vulnerability assessment

Abstract

Most computational research related to steel bridge seismic vulnerability has focused on statistical extrapolation of analysis results for individual straight bridges. However, there has been a steady growth in the use of horizontally curved steel bridges in highways and interchanges in large urban regions. Given the large number of curved steel bridge structures in use in the US and abroad, with some of those structures being located in seismic zones, the feasibility of examining the effects of curvature on bridge vulnerability should be investigated. In this study, the seismic performance characteristics of an existing inventory of horizontally curved, steel, I-girder bridges located in Pennsylvania, New York, and Maryland were used to generate fragility curves. Representative fragility curves for horizontally curved, steel, I-girder bridges were estimated using Response Surface Metamodels (RSMs) in conjunction with Monte Carlo simulation. The methodology was used to construct fragility curves for select bridge components (bearings, columns and abutments). The curves were generated for four different, preexisting, performance states that represented slight, moderate, extensive, and complete damage under varying levels of earthquake intensity. The generated fragility curves provided information related to seismic response of the bridge inventory that was investigated, such as radial deformations at the bearings being the most susceptible component to seismic loads.

Introduction

Past research has demonstrated that the loss of one or multiple bridges in a transportation network can hamper recovery activities and can severely impact the economy of the region encompassing that network [1]. Bridges are known to be one of the most vital, and vulnerable, components of any transportation network. Therefore, in many instances during an extreme event, such as an earthquake, it is vital that bridges affected by the event remain operational. The generation of vulnerability functions in the form of fragility curves is a common approach for assessing bridge seismic vulnerability [1], [2], [3], [4], [5], [6]. A fragility curve provides a conditional probability that gives the likelihood that a structure, or one of its components, will meet or exceed a certain level of damage for a given ground motion intensity. Information provided from a fragility curve can be used for prioritizing bridge retrofits, for pre-earthquake planning and for post-earthquake response and evaluation. These curves usually account for a multitude of sources of uncertainty related to estimating seismic hazards, including bridge characteristics and bridge type and configuration.

Fragility curves have been generated using various approaches. Expert based fragility curves are typically generated using earthquake damage and loss estimates for industrial, commercial, residential, utility and transportation facilities and are based on expert opinions [7]. As a result, this methodology naturally involves subjectivity, resulting in a high level of uncertainty. Empirical fragility curves are generated from actual earthquake data and give a general idea about the relationship between structure damage levels and ground motion indices [2], [8]. Basoz and Kiremidjian [8] initially developed empirical fragility curves for bridges using Peak Ground Accelerations (PGAs) derived from damage data from the 1989 Loma Prieta and 1994 Northridge earthquakes. They used logistic regression analysis to generate the fragility curves based on a damage probability matrix for multiple span bridges. Analytical fragility curves are produced based on numerical simulations that consider different levels and types of ground motions [3], [4], [5], [6] and are generally developed using seismic response from nonlinear time history analyses [3], [4], [5], [6]. Shinozuka et al. [9] showed that analytical fragility curves are in reasonably good agreement with empirical curves. Due to the combination of the aforementioned subjectivity associated with defining earthquake damage states from expert opinions and the paucity of actual bridge damage data associated with seismic events, expert based and empirical fragility curves have rather limited application. Conversely, the creation of analytical fragility curves continues to increase in both academic and practical settings due to the improvement in analytical and statistical modeling tool accuracy and speed.

Although the generation of analytical fragility curves using nonlinear time history finite element analyses has been recognized as a relatively reliable technique, these types of models tend not to be included in probabilistic analysis frameworks. This is because an excessive amount of computational cost has historically been associated with generation and implementation of nonlinear analyses for a large population of complex bridges under a varying range of seismic hazards. Recently, analytical seismic fragility curves have been generated for a population of structures at low computational cost using Response Surface Metamodels (RSMs) approximations. RSMs, which can be described as mathematical polynomial regression functions [10], give the probability of failure of bridges as a function of the random variables that affect the seismic response [11]. RSMs have been efficiently used in connection with probabilistic approaches (e.g., the First Order Reliability Method, Monte Carlo simulation) to generate seismic fragility curves for concrete, steel, and masonry buildings and concrete bridges [11], [12], [13], [14], [15].

While most research that produced analytical fragility curves with RSMs has focused on building groups [12], [13], [14], [15], some work has been completed that has focused on straight, concrete bridges [11]. It has been reported that horizontally curved steel bridges make up a measureable portion of the approximately 597,500 bridges in United States road network [16] and that over one third of all constructed steel bridges are curved [17], numbers which continue to increase. Given the increasing number of curved steel bridge structures in use, with some of those structures being located in seismic zones, examination of the effects of curvature on bridge seismic performance, with a focus on bridge fragility, should occur. A number of analytical and experimental studies have been conducted related to the complicated static and dynamic behavior of horizontally curved steel girder bridges [18], [19], [20], [21], but studies that attempt to generate seismic fragility curves for these bridges have not been performed.

To adequately and efficiently assess the seismic vulnerability of an inventory of curved steel bridges, seismic fragility curves were generated using statistical examination of seismic response from RSMs developed from models that predicted the behavior of a group of actual curved steel bridges. Fragility curves were created using the RSMs in connection with Monte Carlo simulations with original bridge statistics supplied from an inventory of horizontally curved, steel, I-girder bridges in Pennsylvania, New York, and Maryland. This paper focuses on detailed description of the fragility curve generation and application process, with a focus on computational work involved to create the curves.