1715
Fast frequency-domain analysis method for longitudinal seismic response
of super-long immersed tunnels
Méthode d'analyse rapide dans le domaine fréquentiel pour la réponse sismique longitudinale
d'un tunnel immergé à super longueur
Huang M., Liu H.
Department of Geotechnical Engineering, Tongji University, Shanghai, China
ABSTRACT: This research is prompted by the need of a practical project, which is a sea-crossing immersed tunnel between Hong
Kong, Zhuhai and Macao (HZM) in China. Longitudinal seismic response of the immersed tunnel is the main focus of this paper.
Based on the Fast Fourier Transformation and the theory of dynamic elastic Winkler foundation beam, a modified response
displacement method in the frequency domain is proposed in this paper. Inertia of the tunnel and the dependance of dynamic stiffness
coefficients on external loading frequency are considered and seismic response of the HZM tunnel is analyzed using the proposed
method. Finally, some useful suggestions for aseismic design and analysis are presented.
RÉSUMÉ : Cette recherche est motivée par la nécessité d'un projet concret, qui est un tunnel immergé traversée maritime entre Hong
Kong, Zhuhai et Macao (HZM) en Chine. Réponse sismique longitudinale du tunnel immergé est l'objet principal de cet article. Basé
sur la transformation de Fourier rapide et la théorie de l'élasticité dynamique Winkler poutre de fondation, une méthode de
déplacement modifié de la réponse dans le domaine fréquentiel est proposé. Inertie du tunnel et de la dépendance des coefficients de
rigidité dynamique à la fréquence de chargement externe sont considérées comme, et réponse sismique du tunnel HZM est analysée
en utilisant la méthode proposée. Enfin, quelques suggestions utiles pour la conception sismique et de l'analyse sont présentés.
1 INTRODUCTION
Recently, the Chinese government is building a large sea-
crossing bridge connecting Hong Kong, Zhuhai and
Macao(HZM), which is about 35.578 km long and will be the
most long sea-crossing bridge after being constructed. The
super-long submarine immersed tunnel(Fig. 1) over 6 km,
which will be the first long immersed tunnel in the world after
being built, is a very important component part of the HZM
bridge. Analysis of the seismic safety of the tunnel is essential
for engineering design since the HZM immersed tunnel is
located at the Circum-Pacific earthquake zone. Moreover, the
introduction of a simplified analysis method is also important
and urgent because there is no specific code to date in China for
the seismic design of immersed tunnels. Considering that the
safety of the tunnel under longitudinal vibration is more
important than that under lateral and vertical vibrations, this
paper focuses mainly on computational methods for the seismic
response of immersed tunnels under longitudinal seismic
loading.
Figure 1. Location of Hong Kong-Zhuhai-Macao immersed tunnel
A number of analysis methods have been presented in the
literature for computing the longitudinal seismic response of
immersed tunnels. Originally, the standard for longitudinal
seismic design of immersed tunnels was established during the
process of constructing the Bay Area Rapid Transit (BART)
system in San Francisco (Kuesel, 1969). Axial deformation due
to longitudinal vibration was estimated using a simple analytical
expression. BART approach was adopted in the seismic design
of Kinuura Port tunnel (Aoki & Maruyama, 1972). Later, in
1988, the Japanese Society of Civil Engineers released an
earthquake resistant design code for immersed tunnels, with two
principal approaches of ground deformation method and
dynamic response method presented (Kiyomiya, 1995). In the
authors
’
opinion, the two methods could be all categorized as
the response displacement method because the principle of them
is almost identical, namely the seismic response of tunnels is
estimated by applying the seismic displacement of strata around
tunnels to immersed tunnel structures. However, there is still
one difference between them - that is, the external loading
applied to the tunnel structure corresponds the maximum
response displacement of soil for the first one, whereas that is
the dynamic response displacement of soil for another one. The
dynamic response method is used to design the immersed tunnel
across the Pearl River in China (Han & Zhou, 1999). In addition,
there is another simple analytical model in which an immersed
tunnel structure is discretized into a series of particles and
combined with soil springs. The seismic response of tunnels is
investigated by applying the ground seismic acceleration to soil
springs at the base of tunnels. The model had been utilized to
analyze the seismic response of several practical projects in
different countries (e.g. Hamada, 1984; Kiyomiya & Tanabe,
1994; Anastasopoulos et al., 2007). With the development of
computer technology, 3D dynamic finite element method has
become a major way of computing seismic response of 3D
tunnels. A number of studies have been reported in related
literature (e.g. Stamos & Beskos, 1995 and 1996; Hatzigeorgiou
& Beskos, 2010). Despite the more accuracy of 3D dynamic
finite method, the cost of this method is too expensive to be
used in the actual engineering design.
Immersed Tunnel
Hong Kong
Macao
Zhuhai
