# Three-Dimensional Finite Element Analysis for Pressure on Flexible Wall Silos
## 3 Three-Dimensional Analysis of Square Silo
### Flat vs. Deep Flexible Silo  
To study the effect of silo cross section dimensions on lateral wall pressure, additional square models with dimensions \"a\" ranging from (0.5-12.5 m width), as shown in the example, and at a constant height of (2.5 m) were created with the flat-bottomed condition and filled with Leighton Buzzard sand. All other factors were kept unchanged, and the silos' lateral wall pressures were compared. In section (1-1), in the center of the silo side, lateral wall pressures were measured and compared in Table 3. Table 4 shows the classification of silos according to EN1991-4 [28]. According to Table 4, when H/a ratios are less than 1.0, the silos are considered squat (as specified in EN 1991-4). These silos are covered by the majority of silo codes. Silos that are shallow and/or long will normally be classified as bunkers [13], and pressure projections on the longer wall may be valid using plane strain calculations. This establishes a definite upper limit for stress levels. Figure 12 illustrates the lateral wall pressure for different flexible silo dimensions (a = 0.5-12.5 m, h = 2.5 m). Lateral pressure on the wall increases as the slenderness ratio decreases. This indicates that lateral wall pressure in a squat silo is greater than that in a slender wall silo. However, with flexible walled silos, the wall pressure is lower at the mid-point of each wall, which is deemed as a structurally flexible zone, and greater at the silo corners, which are considered stiff areas. \begin{table}
\begin{tabular}{c c} \hline \hline
**Silo Classification** & **hc/dc** \\ \hline Slender & hc/dc \(\geq\) 2 \\ Intermediate & 1 \(<\)hc/dc \(<\) 2 \\ Squat & 0.4 \(<\)hc/dc \(\leq\) 1 \\ Retaining silos & hc/dc \(\leq\) 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Silo classifications according to EN1991-4 (d\({}_{\text{c}}\) = a, for square silo). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Square Silo Side “a”, Meters** & **Height “H”, Meters** & **H/a** \\ \hline
1 & 0.5 & 2.5 & 5 \\
2 & 1 & 2.5 & 2.5 \\
3 & 1.25 & 2.5 & 2 \\
4 & 1.67 & 2.5 & 1.5 \\
5 & 2.5 & 2.5 & 1 \\
6 & 6.25 & 2.5 & 0.4 \\
7 & 12.5 & 2.5 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Silos with different planform dimensions. Consequently, an arching mechanism begins to develop within the granular materials throughout the diagonals of the silo, distributing vertical loads from the mid-side of the flexible wall to the structurally rigid corners. As a result, the mid-side of the wall is subjected to substantially lower pressures [11]. To clarify the loading process inside the flexible walled silo, the vertical load distribution exerted by bulk materials on the walls and silo base was studied. Several square cross section models [a = 0.5, 1.0, 1.25, 1.67, 2.5, 6.25, 12.5 m] with a constant height [2.5 m] were examined to estimate load distribution percentages. These models have the same flat bottom end condition and are filled with the same granular material to investigate the effect of the slenderness ratio on lateral wall pressure, as shown in Table 5.  
Figure 13 indicates that the percentage of vertical distributed load on walls increases as the slenderness ratio increases. The percentage of distributed vertical loads on flexible walls, on the other hand, is around 1% to 17% lower than on rigid walls compared to Figure 14. This decrease occurred as a consequence of wall deformation away from the bulk solids, which affected the contact between the silo wall and the bulk solids. Consequently, the vertical loads supported by the traction force on the walls have been decreased. Figure 15 shows two curves representing the ratio of vertical load carried by the walls and the base concerning the total weight of bulk solids. It can be seen that when silo slenderness ratios increase, the percentage of load distribution on the base decreases. With a slenderness ratio of 2.2, the vertical loads on the walls and base are equal and reach an equilibrium point.