# Seismic Damage Analysis of Box Metro Tunnels Accounting for Aspect Ratio and Shear Failure
## 1 Introduction  
Recent large earthquakes have revealed that underground structures can experience a severe damage when subjected to a strong ground motion [1; 2]. A number of studies investigated the damage pattern of tunnel structures in past earthquake events [1; 3; 4; 5; 6; 7; 8; 9; 10; 11]. Such observations highlight the need to better understand the seismic performance and structural damage pattern of underground structures.  
Seismic damage analyses of box tunnels can be performed by using experimental or/and numerical methods. [PERSON] et al. [12] conducted a series of numerical simulations and a verified shaking table test to investigate the seismic response and damage of a multi-story subway station. Then, they defined four damage states based on the damage parameter, which depends on the ductility of structural members. [PERSON] et al. [13] studied the effect of pulse-like ground motions on seismic responses of a multi-story subway station using shaking table test. Based on experimental results, they pointed out that the center columns were sensitive structural members, which can be suffered a significant vulnerability under earthquake excitations. [PERSON] et al. [14] investigated the effects of axial compression ratio of interior columns on failure modes and damage patterns of a multi-story underground structure using a series of numerical pushover analyses. Recently, some studies employed numerical approach to analyze the seismic failure and collapse mechanism of Daikai subway station [15; 16; 17; 18; 19; 20]. They both gave a mutual conclusion that the structure was completely collapsed due to an extreme failure and loosing load capacity of the center column. Furthermore, an extensive summary of previous studies on the seismicanalysis of tunnels are presented by [PERSON] et al. [1] and [PERSON] et al. [21]. The previous studies dealt with a specific tunnel and soil stiffness. A wide range of tunnel shapes and soil conditions is therefore needed to consider in seismic damage analyses. A set of damage states and corresponding damage indices of the box tunnels should also be defined and updated accordingly.  
The dynamic analysis is recognized to provide the most realistic estimate of the seismic response of tunnels. However, it was reported that the difference between the dynamic and pseudo-static analyses is insignificant [22; 23]. Therefore, the numerical pseudo-static method is widely used in practice and also in research [1; 12; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37].  
[PERSON] et al. [21] performed a pushover analyses for three representative cut-and-cover metro tunnels in South Korea with an aspect ratio of unity, where the aspect ratio is defined as the width to height ratio (B/H) of a single unit. Damage state was defined as the number of plastic hinge formation and damage index (DI) was defined as the ratio of the elastic moment (M) to the yield moment (M\({}_{y}\)). The damage states and corresponding DIs of single, double, and triple box tunnels were presented. Three damage states were defined, which are minor, moderate, and extensive. The collapse state was not defined because only flexural failure mode was simulated and a structural failure was not observed. It was reported that the effect of the geometry and dimension of the box tunnels, and the possibility of a shear failure should be investigated in a follow-up study.  
We expand the study of [PERSON] et al. [21] to investigate the effect of aspect ratio. A more advanced numerical model that can simulate the shear failure in the structural member that is used. We extensively collect design sections of metro tunnels built in Korea to investigate the variation of the aspect ratios and to develop representative sections. We perform a series of inelastic push-over analyses to identify the failure mechanisms of representative single, double, and triple box tunnels subjected to seismic loading. Finally, recommendations for an update of the damage states and DIs of box tunnels are presented.