# Seismic Behavior of Triple Tunnel Complex in Soft Soil Subjected to Transverse Shaking
## 1 Introduction  
Tunnels are one of the important means of underground transportation. They are useful in the build-up area where further surface construction in order to accommodate large traffic infrastructure is not possible. Second, they also provide fast, uninterrupted flow from one point to the other. Many densely populated cities in the world are now planning to provide metro lines through an underground tunnel system. Although it has many useful purposes, at the same time, it is vulnerable to excessive damage if present in an earthquake-prone area. The condition becomes more critical when multiple tunnels lie in closer proximity. Previously, it was believed that the underground structures are less prone to damage in comparison with the on-surface constructions, but major earthquakes in the recent past like Kobe (1995), Coyote (1979), Kocaeli (1999), Chi-Chi (1999), etc. have proved these to be equally vulnerable. The damage suffered by the tunnels depends upon the type of surrounding soil, embedment depth, the amplitude of the earthquake, and the groundwater table (GWT) conditions. The type of soil plays a very important role in the overall behavior of tunnels under seismic activity. Tunnels constructed in soft soil are far vulnerable to severe damage than in dense rock. Similarly, the more shallow tunnels suffer more distortions in comparison to the deeper ones [1]. Researchers now focus on the dynamic behavior of tunnels in different types of rocks and soils. [PERSON] [2], [PERSON] [3], and [PERSON] [4] developed closed-form solutions to estimate the seismically-induced moments and thrust in rectangular and circular tunnels causing racking and ovaling, respectively. [PERSON] and [PERSON] et al. [5] and [PERSON] and [PERSON] et al. [6] conducted an extensive review of the available methods used to determine seismic induced forces that aid in the seismic design of different tunnels. [PERSON] and [PERSON] [7] and [PERSON] and [PERSON] [8] studied the seismic behavior of shallow tunnels subjected to horizontal and vertical shaking in the liquefiable sands in order to assess the distortions occurring in the tunnel lining and its uplift due to excess pore pressure generation. [PERSON] [9] investigated the liquefaction possibilities of soil surrounding the tunnels using 3D finite element modeling (FEM) and studied the acceleration variations and the power spectra developed under the seismic vibrations for various tunnel embedment depths. [PERSON] and [PERSON] et al. [10] studied the behavior of circular tunnels, both using a centrifuge and analytical modeling in order to determine the hoop forces and the distortions produced in the tunnel lining and concluded that both techniques produce results in good agreement. [PERSON] and [PERSON] performed centrifuge tests to study the effect of embedment depth and behavior of circular and rectangular tunnels in dry sand subjected to different intensity seismic vibrations [11; 12; 13]. [PERSON] and [PERSON] et al. [14] conducted centrifuge testing to study the effect of ground movements and the interaction between twin tunnels in loess and concluded on the optimized spacing and the interval between the tunnels. [PERSON] and [PERSON] et al. [15] numerically studied the seismically-induced bending moments and soil dilatancy around tunnels in soft soils. [PERSON] and [PERSON] et al. [16] performed FEM on circular tunnels and studied the lining distortions, bending moments under variable ground vibrations, and different embedment depth and tunnel lining thickness to develop better understanding of tunnel behavior in soft soils. [PERSON] [17] conducted FEM to study response characteristics of rectangular tunnels under seismic shaking varying the tunnel-soil interface properties and input motion characteristics embedment depths and concluded in the development of racking-flexibility (RF) relations for rectangular tunnels in soft soils.