## 3 Earthquake Loading and Seismic Response of Silos
The study emphasized the influence of the aspect ratio on the seismic response and concluded that assuming a constant value of acceleration distribution along the height of squat silos (based on EN 1998-4) leads to conservative design pressures for a squat silo, while this assumption is not conservative for a slender silo. [PERSON] and [PERSON] [89] further investigated the effect of granular material-structure interaction under earthquakes for RC silos. This study takes into consideration of different sources of nonlinearity in silo walls and in granular material. As the main result, it was observed that shear cracks developed when the interaction is neglected in the model. [PERSON] et al. [21] evaluated, with an analytical approach, the exerted actions provided by grains on walls in circular flat-bottom silos during earthquake, leading to a new physically-based evaluation of the effective mass of grain. The study excluded thewavy wall silos. In particular, this study was devoted to the evaluation effective mass that acts on the silo walls during the earthquake. It turns out that this mass could be far less than the value proposed by EN 1998-4 [87] (80% of the total mass). Consequently, lower horizontal actions than the one provided by EN 1998-4 [87] can be adopted (especially for squat silos) and this result is also in accordance with the outcomes of the study presented by [PERSON] and [PERSON] [86]. For example, for a low height/diameter ratio (less than 1), the effective mass can be assumed in a range from 30 to 70% of the total mass of the silo, with a variation depending on the friction coefficient developed between silo wall and filling material [21]. Nevertheless, some theoretical limits were founded [90]. Refinements of the theoretical framework of [PERSON]'s approach [21] were introduced by [PERSON] et al. [90], which provided a new set of analytical formulas for estimating wall pressures, wall shear, and bending moment. A series of shaking table tests on scaled silos was performed by [PERSON] et al. [85], offering an experimental verification of EN 1998-4 [87] provisions and the analytical approach introduced in [21]. The experimental campaign (on a silo-sample made of polycarbonate sheets) revealed the strong effect of the wall-grain friction coefficient on the base overturning moment. This fact is consistent with the analytical approach in [21], whereas this effect is disregarded by EN 1998-4 [87]. Moreover, the results of this study stated that the base overturning moment is conservatively estimated by EN 1998-4 [87]. It also suggested that the horizontal acceleration is not linear in the vertical profile under earthquake input, although it is almost constant under low-frequency sinusoidal input. Later, based on these findings, [PERSON] et al. [91] presented an analytical formulation aiming to predict the natural periods of grain silos. A study presented by [PERSON] and [PERSON] [92] the effect of soil structure interaction (SSI) on the dynamic behavior of silo system containing bulk material under seismic activity. The study concluded that the SSI could be ignored in practice, especially for squat silos since there are no considerable effects. Recently, [PERSON] et al. [93] presented a study comparing applicable analysis approaches for seismic load calculations of grain-filled cylindrical steel silos. The results provided by static equivalent load approach and nonlinear time history analysis were compared. Both grain behavior nonlinearity and grain-wall interaction nonlinearity were considered for nonlinear time history analysis, as well as the SSI. Authors concluded that using a simplified linear acceleration profile along the height provides conservative results. Alternatively, it is suggested to use multimodal analysis on a simplified beam model to determine more realistic acceleration profile. In addition, the study affirmed that the approach of static equivalent loads does not accurately consider the fact that stresses vanish through the bulk material, especially in squat silos.