## 4 Result and Discussion  
### Silo Wall Pressure  
Pressure on the silo wall caused by material discharge is a subject studied intensively using the first algebraic equation proposed by [PERSON] (1992). [PERSON] proposed an equation to determine the wall pressure by dividing the cylindrical silo into several elements and by analyzing the equilibrium conditions of each element. The characteristic of this equation is that the frictional resistance of the wall increases with the depth of the silo, and thus, the wall pressure is \"saturated\" at a certain depth. [PERSON] (1992) improved this equation to determine the pressure applied to the hopper by applying it to a conical hopper, and [PERSON] (1993) considered the hopper shape factor for the rapid stress change between the silo vertical wall section and the hopper section. [PERSON] (1993) reviewed the equation for obtaining this hopper stress and calculated the pressure distribution in the silo.  
Figure 11(a) shows the silo internal stress pattern (horizontal component \(\sigma_{\rm xx}\)) obtained via the silo material discharge simulation. The shape of the internal stress distribution varied depending on this section. In the vertical wall section, the frictional force generated on the wall could be balanced with gravity, and therefore, the internal stress of the silo increased with the depth of the material. In the hopper section, because the frictional force generated on the inclined wall balanced gravity with a certain level, the internal stress was gradually released toward the discharge port.  
The maximum stress value occurred in the transition region from the vertical wall section to the hopper section. In the theoretical equation, the transition zone is simply regarded as a plane, which is not as realistic as the \"arch\" in FE modeling, which caused a pressure difference at a silo depth of 9-17 m, as shown in Figure 11(b).  
The pressure acting on the silo wall can be observed as the horizontal component of the stress (\(\sigma_{\rm xx}\)) in the vertical wall section (variable SVAVG11 of Abaqus output). In the hopper section, it must be obtained through the transformation of \(\sigma_{\rm xx}\), \(\sigma_{\rm yy}\) (SVAVG22), and \(\sigma_{\rm xy}\) (SVAVG12) because of the slope of the hopper wall. Figure 11(b) is a graph plotting the pressure acting on the silo wall obtained from the FEM simulation when a flow field was formed inside the silo. As shown in Figure 11(b),  
Figure 11: Silo internal stress distribution (stress unit is Pa) (a), comparison of silo pressure between the experiment [PERSON] (1993) and FEM result (b).  
the results of the theoretical equation and the results of the FEM simulation are almost identical; however, some differences were observed in some sections.  
There is another difference between the theoretical and FEM simulation results. Unlike in the theoretical approach, the FEM results shown in Figure 12 considered the nonuniformity of the frictional force depending on the wall position. The wall pressure graph shows the vibration phenomenon, as in Figure 12b. In addition, the FEM simulation can be used to check the silo internal velocity and stress results in more detail. The silo wall pressure is affected by internal particle flow patterns and velocities [15; 33; 34]. In theory, it is difficult to fully address this phenomenon; however, it can be explained more easily with the FEM simulation.