# Three-Dimensional Finite Element Analysis for Pressure on Flexible Wall Silos
## 2 Numerical Approach
### Numerical Result and Validation
#### 2.5.1 Comparison with Experimental Data (Flexible Wall)  
The bulk material is in contact with the wall through the Coulomb friction model. The results of the finite element analysis are then compared to [PERSON]'s experimental data [25].  
Due to the extensive readings of wall pressure cells along the silo height in [PERSON]'s experiment, a huge amount of data was obtained. Three vertical sections were generated and used to evaluate the finite element model in this validation to address the change in lateral wall pressure distribution along the silo wall. These three sections are illustrated in Figure 7.  
Figure 6: Boundary conditions assignment for one-quarter silo.  
Figure 8 shows a comparison between the finite element results and the experimental measurements for the lateral pressure distribution along the silo height. The bottom of the silo, where the silo wall meets the hopper, is represented by the zero value on the vertical axis of the silo height.  
For the vertical sections 2-2 and 3-3, the numerical results relatively match with data from the experimental work, as shown in Figure 8b,c, with some discrepancies around the  
Figure 8: Comparison between lateral filling pressure of the finite element and experimental work along the silo height in the case of the flexible walled silo. (**a**) section 1-1: at mid-side of the wall; (**b**) section 2-2: at 0.35 m from silo center; (**c**) section 3-3: at 0.55 m from silo center.  
Figure 7: Sections of the silo.  
top of the silo height and near the bottom. These changes become more pronounced as a consequence of the silo corner's vicinity, which is thought to be a rigid section.  
As seen in Figure 8a, the finite element results closely match those of the experimental work. Both trends are in good agreement across the whole silo height with a discrepancy above the base, where the experimental results suddenly decreased to 5.1 kPa, while the finite element model is homogenous with the smooth value of 8.2 kPa. This change might be the consequence of a minor variation of pressure acting on the load cell due to its vicinity to the base.  
Based on the results shown in Figure 8, the influence of wall flexibility can be observed clearly in these curves. The lateral wall pressures increase gradually toward the corner section, where the peak value is shown in Figure 8c. These findings demonstrate that the horizontal pressure distribution is not uniform at any depth during the filling phase.  
In conclusion, there are qualitative and quantitative agreements between the finite element results and the outcomes of [PERSON]'s work in predicting the lateral pressure distribution for two reasons:  
* The trend of the finite element distribution matches the average of the experimental work over the entire silo height.
* The finite element lateral wall pressure values are close to those of [PERSON]'s experimental work for all vertical sections, with the coefficient of determination, R\({}^{2}\), equaling 0.81, 0.83, and 0.84 for sections 1-1, 2-2, and 3-3, respectively.