## 3 Earthquake Loading and Seismic Response of Silos  
Accounting for seismic excitations, as one of the main hazardous actions on structures and infrastructures, the response of silos has long been the subject of intensive research studies [4]. A considerable research work has been undertaken through the last century, addressing fluids-filled tanks to quantify the wall loads induced by seismic excitation where the sloshing action is a governing factor [81]. However, what distinguishes silos from tanks is that the filling material is of solid nature. Consequently, only a specific portion of the seismic inertia load is transmitted to the walls thanks to the shear strength and the stiffens of stored bulk. Thus, the stored material properties have a significant effect on the silo seismic response. For instance, the wall-solids interaction and its effect on seismic response is a critical point to be mentioned [82]. In general, the imposed loads by seismic excitation on a circular cylindrical silo walls are significant and could cause unsymmetrical pressures distributions on the silo walls. The main parameters governing the seismic response of the system are: (i) the height-to-radius ratio [83]; (ii) the physical properties of the contained material [82]; (iii) the characteristics of the ground motions [20]; (iv) the effects of the wall flexibility [5]. Several studies in the scientific literature were introduced to increase the knowledge about the response of cylindrical silos storing granular material to earthquakes [84]. In this context, shaking-table/vibration tests [85; 86] were carried out in many cases, aiming to characterize the response of the system and observe the relevant parameters, such as the dynamic wall pressure, base shear, base moment in the wall, and the stresses exerted on the silo's foundation. Going into detail, [PERSON] and [PERSON] [20] analytically examined a vertical, rigid, and circular cylindrical tank storing homogeneous and linear viscoelastic solid under a harmonic earthquake-induced ground motion. The purpose of the study is to introduce a simple and reliable method of analysis for this kind of system. An analytical formulation was developed to describe the seismic response of the filled silo, which was adopted by the European standards EN 1998-4 [87]. In particular, the seismic response of the system can be analyzed by quantifying the contributing mass to the base shear, which was demonstrated to be governed by the slenderness ratio [20] and by the wall flexibility (relative to that of the stored material) [5]. Based on a FE model, [PERSON] and [PERSON] [4] derived design criteria for steel squat ground-supported silos, accounting for earthquake response under quasi-static horizontal body force (uniform horizontal acceleration). In this study, the stored material was characterized by its elastic modulus as an isotropic and homogeneous material. The results obtained in this study were implemented in EN 1998-4 [87]. In this regard, aiming to verify load assumptions recommended by EN 1998-4 [87], [PERSON] and [PERSON] [86] characterized the behavior of seismically excited granular material steel silos. The study considered the variation of some key parameters, such as aspect ratios, the influence of the nonlinearity of the granular material, the wall--solids interaction effect, and the soil--structure-interaction influence. The results of this study suggested to reduce the effective mass considered in the analysis to achieve more economic and realistic design than the ones provided by EN 1998-4 [87]. Specifically, the proposed loads are conservative in the case of squat silos, while they are adequate for slender silos. Similarly, [PERSON] and [PERSON] [88] presented further numerical investigation addressing the seismic behavior of flat bottom ground-supported steel silos.