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SUMMARYAs a special shell structure, silos are used in storing a wide range of multitudinous granular materials. However, seldom have researchers assessed seismic vulnerability of the reinforced concrete (RC) silo. This paper aims at studying the seismic vulnerability assessment of a silo, which is located in Zhoushan, China. Prior to assessing the seismic vulnerability of the selected RC silo, the validation of the hypoplastic constitutive model, which is used to simulate granular materials, is studied. After discussing the validation of the hypoplastic theory, the numerical model considering granular material-structure interaction is developed by means of the ABAQUS software. And the numerical simulation results are compared with the experimental data obtained from a shaking table test discussed in order to confirm the validation of the numerical model, which is used to study the seismic vulnerability of the RC silo. Then the seismic fragility assessment of the selected RC silo is performed using the incremental dynamic analysis. The analytical results showed that the hypoplastic theory can be used to simulate the stored materials in the silo considering the collapse property before entering plastic state of granular materials. For the design basic acceleration, the fragility curves of the selected RC silo showed that the probability of exceeding the no or light damage state was about 2.12%. For the maximum considered earthquake, the exceeding probability of no or slight and the moderate damage states was 17.63% and 1.31%, respectively. With respect of the severe and total damage state, the exceeding probabilities were almost zero. Therefore, the selected RC silo structure has enough safety stock to withstand strong earthquakes in the future. Finally, a general design procedure considering seismic fragility assessment was presented in order to provide references for other structure design.

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Rewriting the formulation of the Bloch waves, this paper presents a new perspective for analyzing the complex band structures of the in-plane waves in 2D phononic crystals. Using the proposed formulation, a new finite element based method is developed for analyzing 2D periodic systems. The results of the validation example prove that the proposed method can provide exact solutions for both the real and complex band structures of 2D periodic systems. Furthermore, using the proposed method, the complex band structures of a 2D periodic structure are calculated. The physical meanings of the obtained complex band structures are discussed by performing the wave mode analysis.