Elsevier

Engineering Structures

Volume 30, Issue 1, January 2008, Pages 141-153
Engineering Structures

Significance of SSI and nonuniform near-fault ground motions in bridge response I: Effect on response with conventional expansion joint

https://doi.org/10.1016/j.engstruct.2007.03.002Get rights and content

Abstract

This paper studies the influence of spatially varying near-source ground motions and soil–structure interaction (SSI) on the relative response of two bridge frames. The spatial ground motions are simulated according to a near-fault ground motion model with different wave apparent velocity and a coherency loss function. Numerical calculations of bridge structure responses including pounding and SSI effect to a number of simulated spatially varying ground motions are carried out. The study reveals that the assumption of uniform ground excitation and fixed base in the analysis and design might not provide a realistic estimation of the pounding responses of bridge frames. The consequence of adjusting bridge fundamental frequency ratio towards unity to minimize relative response and consequently girder pounding potential as recommended by current design regulations is also evaluated.

Introduction

Damages of adjacent bridge structures due to relative responses such as poundings and unseating have been observed in many earthquakes in the past, e.g. during the 1994 Northridge earthquake [1], the 1995 Kobe earthquake [2], and the 1999 Chi–Chi earthquake [3]. In fact, after the Mexico earthquake in 1985 structural poundings became a subject of many researchers. In the case of bridge structures, pounding between the girders might cause collapse of bridge decks. Even if the collision does not unseat the bridge decks the damage at the deck ends can significantly affect the function of the bridge. In the case of traditional bridge designs with girder expansion joint of a few centimetres, poundings during strong earthquakes are unlikely avoidable. Investigations of pounding response of bridge structures are therefore important. To avoid pounding and unseating of bridge decks, nowadays, more and more bridges are designed to allow large closing and opening deck movement at the joints, e.g. using modular expansion joint systems. The required gap size for ensuring the effectiveness of such systems will be discussed in the second part of this work [4].

Many previous works investigated the cause that leads to collisions, how poundings can be avoided and how their effect can be reduced. DesRoches and Muthukumar [5], for example, investigated not only the pounding effect on the behaviour of the bridge; they also evaluated the current recommendations by CALTRANS for mitigating the pounding effect. Hao [6] investigated the required seating length of bridge decks. Jankowski et al. [7], Ruangrassamee and Kawashima [8] studied possible measures to reduce the effect of poundings. Malhotra [9] proposed a procedure for determining the restitution coefficient obtained from the investigations of two impacting rods and applied the procedure in the analysis of pounding effect on two adjacent bridge segments using two single-degree-of-freedom systems.

The relative displacement between the adjacent bridge girders determines the effect of poundings. These relative girder responses depend on the characteristics of the bridge structure, ground excitation, and the support conditions of the bridge piers. In the case of a bridge on a soft soil site, the assumption of a fixed base or neglecting the soil–structure interaction (SSI) effect in the analysis may not lead to accurate prediction of bridge responses. Investigations on the influence of SSI on the pounding response of bridge girders are very limited. Kim et al. [10] and Zhu et al. [11], for example, included the SSI effect in their studies, but they used frequency-independent soil stiffness owing to the intrinsic difficulty in using the frequency-dependent soil stiffness in modelling pounding response.

In building response analysis an assumption of uniform ground excitation can be justified. In the case of bridges this assumption may not be applicable, especially when the supporting piers are far apart. The spatial variation of the ground motions is not only determined by the characteristics of the propagating seismic waves but also by the properties of the transmitting medium. Hao et al. [12], [13] and Zanardo et al. [14] investigated the effect of spatially varying ground motions on the pounding behaviour of neighbouring structures.

This study focuses on two primary factors: the influence of the spatially varying near-source ground excitations and SSI effect on the pounding response of two adjacent bridge frames. In a previous work [15] the authors focused on the fundamental effect of SSI and nonuniform ground excitation on the maximum closing relative girder displacement and pounding responses. 3 sets of ground motions based on the Japanese design spectrum were simulated and used in the latter study. Only the prototype bridge model with the fundamental frequency ratio of 0.42 of the two adjacent bridge structures was considered. This paper is a continuation of the latter study. The primary differences between the present work and [15] include: (1) The ground motion time histories are generated according to a near-source ground motion model [16], instead of the Japanese design spectrum; (2) To obtained a less biased estimation, in total, 120 sets of spatially varying ground motions are used, and assembled-mean responses are obtained and presented, as compared to only three sets in the previous study; (3) Besides the girder relative displacements responses as in [15], activated contact forces between the girders, and bending moment at both pier supports are also calculated, presented and discussed; (4) A detailed description and discussion of a new method to model pounding between adjacent structures are presented, and a validation of this new method by comparing the results with those obtained using the more traditional impact spring–dashpot model and analytically derived model is given; (5) As a parametric investigation, a wide range of fundamental frequency ratios of the adjacent bridge structures is considered and an important conclusion is derived in this paper, i.e. when the frequency ratio is close to 1.0, as suggested by most design codes, the ground motion spatial variation and SSI effects are most significant.

Unlike previous works [10], [11] frequency-dependent soil stiffness is modelled in this study. In order to limit the number of influence factors the effect of multiple-sided poundings and nonlinear structural and soil behaviour are not considered in this study. In many design regulations, e.g. the CALTRANS Seismic Design Criteria [17], it is suggested that the fundamental frequency of the flexible bridge frame should be at least 0.7 times the frequency of the stiff neighbouring bridge frame. This requirement is used to prevent highly out-of-phase vibrations of the adjacent structures. DesRoches and Muthukumar [5] studied the effectiveness of this code requirement. In their study they assumed uniform ground excitation and neglected SSI effect. In this study the CALTRANS recommendation is also examined with the consideration of SSI and spatial ground motion effect.

Section snippets

Bridge model

In this study two adjacent bridge frames are considered. The left and right bridge frames have two and three piers, respectively. The bridge model is adopted from the work performed in [5]. While in the latter study each of the bridge frames is simplified to a single-degree-of-freedom (sdof) system with an assumed fixed base, in this study they are modeled as single-pier frames as shown in Fig. 1. The properties of the structural members are given in Table 1. The structural member is indicated

Bridge–subsoil system

In the analysis a substructure technique is used. The bridge frames with the foundations and the subsoil are described in the Laplace domain by finite elements and boundary elements, respectively. Utilizing a finite element method in the Laplace domain enables an application of exact axial and transverse deformations of a vibrating beam element as a shape function. The obtained model is called continuous-mass model. Because the exact deformation is used, a beam does not have to be broken down

Numerical results

This section presents numerical results of pounding responses of adjacent bridge structures to spatially varying ground motions. Discussions on the effects of ground motion spatial variations and SSI on bridge responses are made.

Conclusions

This paper studied SSI and ground motion spatial variation effect on bridge pounding responses. It is found that:

The recommendation of current design regulations by adjusting the ratio of fundamental frequencies of the adjacent structures towards unity to eliminate the relative displacement between the adjacent girders, and consequently the pounding potential is valid only if SSI effect and ground motion spatial variation are negligible. Otherwise this recommendation is not sufficient to

Acknowledgement

The first author wishes to thank the University of Western Australia for the Gledden Fellowship.

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