# Vulnerability Analysis of Column-Supported Reinforced Concrete Silo Structures
## 1 Introduction  
Reinforced concrete silos are widely used and mainly designed to contain granular materials (e.g., cement, sand, and grain). For example, a column-supported reinforced concrete silo is often employed in logistics parks with a high degree of mechanization, merely for its large lower space. In practice, the lateral stiffness of the lower support columns of a silo is lower than that of ground-based silos, and it is also significantly lower than that of the upper part of the silo. Consequently, overturning and collapse accidents can easily occur under the action of earthquakes, leading to huge economic losses and even casualties [1, 2]. Several tests and analyses have been conducted on the seismic performance of reinforced concrete silos under the effect of earthquakes [3]. Wagner and Meskouris [4] conducted a numerical study through a model comprising a granular material, an interface element between the granular material and the silo wall, and the silo itself to study themechanical properties of bulk-filled silos under seismic excitation. The dynamic behavior of the granular material in the numerical study was described by four different material laws and compared with the experimental results. Steel silos are often used to study the effect of the granular material-structure interaction on the behavior of the silo (Holler and Meskouris [5]; Nateghi and Yakhchalian [6; 7]). Silvestri et al. [8] and Furinghetti et al. [9] performed a series of shaking table tests on a full-scale flat-bottom steel silo filled with soft wheat to study the relationship between the fundamental frequency and the input acceleration peak. They discussed the problems of dynamic amplification and dynamic overpressures. Subsequently, they set up seismic isolation devices at the base of the aforementioned silo system and assessed the main benefits of the proposed isolation system and its suitability for seismic protection purposes. At the same time, Mansour S and Silvestri S [10] provide a procedure to directly estimate an average global friction coefficient between the granular solid and a corrugated silo wall by a series of'miniature silo' tests. Chen J et al. [11] the granular-structure interaction (GSI) analysis method is proposed with considering the combined effect of the friction between the particles-particles and the particles-silo wall. Based on the above discussion, the granular material-structure interaction on the mechanical response of silos has been studied in detail. Meanwhile, the results of many studies based on the overall structure have been used to investigate the damage and seismic performance of silos. Yang et al. [12] conducted a cumulative damage analysis through shaking table tests and confirmed the influence of aftershocks on structural damage. Hussein A H [13] explored the effects of near-fault ground motions (NFGM) and far-field ground motions (FFGM) on the seismic response of reinforced concrete cylindrical silos. Through the ABAQUS software (2006), Guo et al. [14] developed a refined finite element model considering particle-structure interaction based on a sub-plastic constitutive relationship, and finally, the seismic vulnerability was evaluated using the incremental dynamic analysis (IDA), which is a computational method used in earthquake engineering to estimate the structural response distribution under seismic loads. The vulnerability study of the cylindrical ground-supported steel silo was also given attention [15]. Based on the IDA curve of the top displacement and base shear, Tuska [16] defined five damage states of a typical cylindrical reinforced concrete silo, providing a reference for the vulnerability analysis of silo structures. Kanyilmaz and Castiglioni [17] put forward a seismic strengthening scheme for a curved-surface single-pendulum seismic isolation device through a vulnerability analysis.