The Dynamic Behavior of Silos with Grain-like Material during Earthquakes

Grain security is an important guarantee for sustainable development. However, the dynamic behavior of silos containing grain-like material is not well understood. The effective mass and dynamic effects are the key parameters for the assessment of the silo-bulk material system during earthquakes. Herein, on the basis of the Janssen continuum model, it is proposed that the seismic energy is entirely dissipated by the interactions between the materials and the silo and the materials themselves. The seismic inertia forces among storage materials were introduced, and dynamic equilibrium equations considering the vibrations of storage materials were established. Theoretical solutions for the horizontal forces exerted and the effective mass of the silo-bulk material system during earthquakes are proposed. It is worth noting that the additional stress on the side wall proposed in this work is related to the depth, silo radius, storage density, internal friction coefficient, lateral pressure coefficient, and seismic acceleration. In addition, the effective mass coefficient is negatively correlated with the external friction coefficient, the lateral pressure coefficient, and horizontal seismic acceleration under a storage vibration state. A narrower silo (i.e., with a larger height-diameter ratio) has a low effective mass coefficient. The results from our method are in good agreement with those attained using experimental data, which demonstrates the accuracy and universality of the proposed formulations.

Automated summary

The study proposes that seismic energy is entirely dissipated by the interactions between the materials and the silo and the materials themselves based on the Janssen continuum model. Seismic inertia forces among storage materials are introduced and dynamic equilibrium equations considering the vibrations of storage materials are established. Theoretical solutions for the horizontal forces exerted and the effective mass of the silo-bulk material system during earthquakes are proposed. The results from our method are in good agreement with experimental data, demonstrating the accuracy and universality of the proposed formulations.