Bridge support elastic reactions under vertical earthquake ground motion

Abstract

In North America, bridges are not typically designed for vertical earthquake ground motion. Design codes, AASHTO in the USA and S6-06 in Canada, do not explicitly consider the effect of vertical earthquake ground motion in the design of highway bridges. However, analytical and field evidences have often drawn engineers’ attention to the damage potential of vertical earthquake ground motion to engineered bridges. This paper proposes a simplified method to calculate elastic support reactions under vertical earthquake ground motion. Support reactions are first calculated by exact dynamic method. By applying a few assumptions, a simplified method has been developed. The developed method can be readily used in the design of typical bridges with regular span distribution. This simplified method has been demonstrated with several examples.

Introduction

Vertical earthquake ground motion is not explicitly considered in American and Canadian design codes for bridges [1], [2]. Canadian Highway Bridge Design Code [2] takes into account the vertical earthquake ground motion in a simplified way by increasing and decreasing the dead load action in load combinations, irrespective of earthquake magnitude, fault distance, and site soil condition. In the Caltrans seismic design criteria [3], vertical ground motion is only considered as an equivalent static vertical load when the site peak rock acceleration is 0.6$g$ or greater. The recent edition of Eurocode [4] has proposed to take into account the effect of vertical earthquake ground motion when the bridge is located within 5 km of an active seismotectonic fault or in high seismic zones.

When the effects of vertical earthquake ground motion are explicitly considered in the design process, the vertical response spectrum is taken typically as the two-thirds of the horizontal response spectrum for the entire period range of engineering interest. This approach was originally proposed by Newmark et al. [5] and has since been widely used. However, analyses of strong motion data indicate that in the vicinity of moderate to strong motion earthquakes, vertical to horizontal ($V/H$) peak ground acceleration ratio often exceeds unity; hence, the 2/3 rule is not reasonable [6], [7], [8], [9], [10]. In addition, a recent research investigation has also shown that $V/H$ spectral ratio can approach 1.8 at large magnitude earthquake events for short site source distances and short periods [10]. Some recent studies have focused on the shape of the vertical response spectrum and proposed design vertical acceleration response spectrum consisting of a flat portion at short periods (0.05–0.15 s) and a decaying spectral acceleration at longer periods [8], [10], [11]. Typically, the vertical ground motion has lower energy content than the horizontal ground motion over the frequency range of interest. However, all its energy is concentrated in a narrow frequency band and can be destructive to the engineered structures having vertical frequencies within that range (5–20 Hz).

A literature survey indicates that only a few studies have been conducted to quantify the effect of vertical ground motion on bridges [12], [13], [14], [15]. Analytical studies, in line with field observations, found that certain failure modes are directly related to high vertical ground acceleration [15]. In addition to the possibility of compressive over-stressing or failure due to direct compression, vertical motion may induce failure in shear and flexure and can cause bearing and expansion joint failures. All the analytical studies carried out to date are based on finite element modelling of the bridges and emphasize the importance of incorporating the vertical ground motion in the design process [12], [13], [14], [15]. However, these studies have not clearly defined the way to incorporate the effects of vertical ground motion into the design process. One of the studies emphasized the need to develop a simplified method for the inclusion of the vertical earthquake ground motion in the design process [15].

The purpose of the current study is to develop a simplified method to quantify the elastic support reactions of bridges under vertical earthquake ground motion. It is noted that nonlinear effect is not generally considered for the vertical earthquake ground motion [4]. The developed method requires few calculations and can be readily used by design offices for the design of simple highway bridges and preliminary design of more complex bridges. The method has been found to be in excellent agreement with the analytical results.