# Seismic Vulnerability Assessment of a Shallow Two-Story Underground RC Box Structure
## 1 Introduction  
In previous design specifications for underground structures in Japan, the seismic design is not usually considered in the transverse direction because there has been a strong belief that underground structures are stable following the deformation of the surrounding soil during an earthquake. Consequently, the Daikai subway system as well as tunnels and metro stations wherethe design did not consider the earthquake load [1] were hit by the Hyogoken-Nanbu earthquake of magnitude 7.2 based on Japan Meteorological Agency scale (roughly equivalent to a moment magnitude M\({}_{\text{w}}\) of 6.9) in 1995 [2]. The general damage pattern showed the lack of load carrying capacity against shear at the center columns that led to the collapse of the tunnel ceiling slabs [1, 3]. Moreover, many of infrastructures worldwide have also experienced significant damages in recent earthquakes such as in the M\({}_{\text{w}}\) 7.7 Chi-Chi Taiwan in 1999 [4], M\({}_{\text{w}}\) 6.3 Baladeh in 2004 [5], and M\({}_{\text{w}}\) 7.0 Haiti in 2010 [6]. Several design hypotheses for the analysis applying seismic loadings are suggested. However, the real seismic behavior during shaking remains unaddressed [7]. There are many methods used to perform the soil-structure interaction (SSI). Whereas the sophisticated model using full dynamic numerical analysis is expected to provide accurate results at high computational cost, other methods such as pseudo-static or equivalent static solutions are also acceptable for practical purposes despite a low accuracy in calculation. The static seismic analysis method, so-called the ground response acceleration method for buried structures (GRAMBS) has proven its effectiveness in modeling the dynamic response behavior considering the SSI [8, 9]. The method was first proposed by [PERSON] in 1990 [8], where the calculated accelerations were converted into static force and applied to the finite element method (FEM) model which assigning horizontal rollers at both sides and a fixed base condition. The analytical method had been verified to be effective by comparing its results with those of the dynamic analysis using FLUSH-VB [8]. From the experiment in [PERSON]'s research, the required computing time for GRAMBS was only one-tenth of that for the analysis using FLUSH-VB, with relatively identical results. In addition, other recent quasi-static methods also show satisfactory results similar to GRAMBS. Particularly, [PERSON] proposed a new method called the ground response method (GRM) in 2005 [9] by studying a seismic load for the seismic deformation method based on the dynamic substructure method. Then, those seismic stresses and seismic deformation of the ground were verified to be applied to underground structure. The GRM uses the inertia forces calculated from response accelerations of a free field as the main seismic load similar to GRAMBS, and the difference is that the outer boundary conditions are replaced with equivalent nodal forces that reproduce seismic strains of a free field to a near field. The GRM results had proven the accuracy of [PERSON]'s method. Out of the GRAMBS's benefits such as time efficiency and its simplicity, its main shortcoming is not applicable to an inclined input of a shear wave and a longitudinal wave because of the constraints of displacements at the boundaries [9]. Even though GRAMBS has been developed for a long time, it is still the most effective and reliable static seismic analysis method because it was verified with various dynamic finite element analyses [10, 11, 12], especially the validity of GRAMBS was confirmed from the result of a small-scale model of tunnel embedded in a shear soil column on shaking table conducted by [PERSON] et al. [13]. Therefore, GRAMBS is trusted to be a tool for structural analysis in this study. Most of the structures in the form of tunnels or parking lots have at least two levels, which allow functional arrangements for ticket machines, platforms, ATM, passenger access, ventilation, equipment, and staff rooms.