RESEARCH PAPER International Journal of Recent Trends in Engineering, Vol. 1, No. 6, May 2009 30 Numerical and Analytical Solutions for Ovaling Deformation in Circular Tunnels Under Seismic Loading Ahmad Fahimifar 1 , Arash Vakilzadeh 2 1 Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran Email: fahim@aut.ac.ir 2 Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran Email: vakilzadeh.arash@gmail.com Abstract: Ovaling deformations develop when waves propagate perpendicular to the tunnel axis. Two analytical solutions are used for estimating the ovaling deformations and forces in circular tunnels due to soil–structure interaction under seismic loading. In this paper, these two closed form solutions will be described briefly, and then a comparison between these methods will be made by changing the ground parameters. Differences between the results of these two methods in calculating the magnitudes of thrust on tunnel lining are significant. For verifying the results of these two closed form solutions, numerical analyses were performed using finite element code (ABAQUS program). These analyses show that the two closed form solutions provide the same results only for full- slip condition. Key words: Seismic analyses, ovaling deformation, circular tunnel, soil-structure I. INTRODUCTION Ovaling deformation is the most significant influence on the tunnel lining under seismic loading, except for the case of the tunnel being directly sheared by a fault (Penzien, 2000). Ovaling deformations develop when waves propagate perpendicular to the tunnel axis and are therefore, designed for in the transverse direction (typically under two-dimensional, plane-strain conditions). Studies have suggested that, while ovaling may be caused by waves propagating horizontally or obliquely, vertically propagating shear waves are the predominant form of earthquake loading that causes these types of deformations [1]. II- A Review on the Ovaling Deformations of Circular Tunnels A. Ovaling Deformations of Circular Tunnels Without Soil-Structure Interaction The simplest form of estimating ovaling deformation is to assume the deformations in a circular tunnel to be identical to ‘‘free-field’’, thereby ignoring the tunnel– ground interaction. This assumption is appropriate when the ovaling stiffness of the lined tunnel is equal to that of the surrounding ground. Ground shear distortions can be defined in two ways, as shown in Fig. 1. In the non-perforated ground, the maximum diametric strain is a function of maximum free-field shear strain only deformations [2]. 2 max γ ± = ∆ d d (1) The diametric strain in a perforated ground is further related to the Poisson’s ratio of the medium [2]. ) 1 ( 2 max m d d ϑ γ − ± = ∆ (2) Where max γ is the maximum free-field shear strain of soil or rock medium, m ϑ is the Poisson’s ratio of the medium and d is the diameter of tunnel lining. Both of these equations assume the absence of the lining, therefore ignoring tunnel-ground interaction. In the free-field, the perforated ground would yield a much greater distortion than the non-perforated, sometimes by a factor of two or three. This provides a reasonable distortion criterion for a lining with little stiffness relative to the surrounding soil, while the non-perforated deformation equation will be appropriate when the lining stiffness is equal to that of the medium. A lining with large relative stiffness should experience distortions even less than those given by (1), [1]. Fig. 1. Free-field shear distortion of perforated and non-perforated ground, circular shape(after Wang, 1993) © 2009 ACADEMY PUBLISHER