Date Published: October 17, 2018
Publisher: Public Library of Science
Author(s): Lei Zhang, Yong Liu, Eva O. L. Lantsoght.
Observations from past earthquakes have shown that subway tunnels can suffer severe damage or excessive deformation due to seismic shaking. This study presents the results of finite element analyses on subway tunnels installed in normally consolidated clay deposits subjected to far-field ground motions. The clay strata were modelled by a hyperbolic-hysteretic constitutive model. The influences of three factors on the seismic response of the clay-tunnel systems were examined, namely ground motion intensity, tunnel wall thickness and clay stiffness. Furthermore, the computed racking deformations of the tunnel were compared with several analytical estimations from the literature, and the relationship between racking ratio and flexibility ratio for rectangular tunnels installed in normally consolidated clay deposits was proposed. The findings may provide a useful reference for practical seismic design of tunnels.
To ensure sustainable development, much attention has been paid to constructing more tunnels and other underground structures in view of the relatively limited land resources and the increasing number of immigrants encountered in most of metropolitan cities. The performance of these tunnels and underground structures against natural hazards (e.g. earthquakes) deserves to be examined fully. Many previous publications have reported that tunnels and underground structures can suffer severe damage or excessive deformation due to seismic shaking [1–4]. To date, the guidelines for seismic design of tunnels predominantly rely on simplified methods [3,5–13]. At the absence of the dynamic soil-structure interaction mechanism, those methods may result in a considerable overestimation or underestimation of the seismic response of a tunnel [14–15].
As Fig 1 shows, three types of base motions were adopted in this study. The base motion with a peak acceleration of 0.06g shown in Fig 1(a) represents a type of far-field shaking event that may be felt in Singapore. It is a synthesized signal with reference to the past seismic-induced motions measured in Singapore, which was also used by Zhang  and Zhang et al.  for both the centrifuge tests and FE analyses. In addition, the ground motions shown in Fig 1(b) and 1(c) were compiled based on two horizontal earthquake records (east-west direction) measured at Stations El Monte-Fairview Av and TTN005 during the 1992 Landers and 1999 Chi-Chi earthquakes, respectively. These two earthquake records were selected from the Ground Motion Database provided by the Pacific Earthquake Engineering Research (PEER) Centre. They have site-to-source distances of approximately 136 km and 83 km, respectively, which fall within the scope of far-field ground motion according to Dadashi and Nasserasadi  and Bhandari et al. . For simplicity, these ground motions are termed Type-1, Type-2 and Type-3 base motions. The response spectra corresponding to a peak acceleration of 0.06g are plotted in Fig 1(d). The displacement plots of the input base motions are also provided in Fig 2. As can be seen, due to the differences in time duration and frequency content, the peak displacements are generally different even though the peak accelerations are same. In addition, to investigate the influence of ground motion intensity, each of these base motions was scaled into four ground motions with peak values of 0.03g, 0.06g, 0.12g and 0.24g.
The present numerical analysis consists of two phases, namely gravity loading and earthquake loading phases. Initial stress condition is assigned to the soil domain to account for the gravitational stress field of the clay-tunnel system in the gravity loading phase; subsequently, far-field ground motions are excited at the model base in the earthquake loading phase. Some other information on the numerical modelling procedure is given below.
Three influencing factors on the seismic response of clay-tunnel systems were considered in the present study; that is, tunnel wall thickness, ground motion intensity and clay stiffness. The instantaneous profiles of the maximum bending moment and shear force of the tunnel wall correspond to the instant when the tunnel wall attained its respective maximum values. Unless otherwise stated, the parameter A is set as 2060.
A series of 2D FE parametric studies incorporated with a hyperbolic-hysteretic soil constitutive model were performed to investigate the seismic response of rectangular tunnels installed in clay strata subjected to three types of far-field ground motions, in which three crucial factors, namely tunnel wall thickness, peak base acceleration and clay stiffness, were considered. All the three factors have significant influence on both the responses of ground acceleration and tunnel structure. Some specific conclusions are summarized below.