# Study on Stability of Elastic Compression Bending Bar in Viscoelastic Medium
## 3 Results and Discussion
### Time Dependence of the Effect of Bar Length on the Lateral Deflection of the Bar Top  
By maintaining the lateral pile load strength of the bar at a constant value of 50 kPa and using axial force values of \(P=2500\) kN, 5000 kN, 7500 kN, and 10,000 kN, the transverse deflection \(w(L)\) of the bar top over time was calculated for bar lengths ranging from 50 m to 140 m. Figure 11 illustrated the results obtained over a calculation period of 100 years. Analysis of the data reveals that when the axial force assumes smaller values (e.g., 2500 kN and 5000 kN), the correlation between bar length and the time course of bar displacement is minimal within the calculation period. Conversely, when the axial force assumes larger values (e.g., 7500 kN and 10,000 kN), an increase in bar length results in an  
Figure 10: Relationship between axial force \(P\) and critical instability time \(t_{cr}\). initial slight decrease in the time course of bar instability, followed by an increase within the calculation period. By maintaining the loading intensity of the bar-side pile at 50 kPa and considering axial forces, denoted as P, of 2500 kN, 5000 kN, 7500 kN, and 10,000 kN for computing the temporal evolution of the lateral deflection, denoted as \(w(L)\), at the top of the bar for bar lengths ranging from 50 m to 140 m over a period of 100 years. Based on the obtained  
Figure 11: Relationship between axial force \(P\) and \(t_{cr}\) corresponding to different length of bar \(L\). (**a**) Different axial force (\(P\)) series under variable length of bar (\(L\)); (**b**) Single axial force (\(P\)) series under variable length of bar (\(L\)). results, when \(w(L)\) reaches 10 cm, the relationship between bar length and the critical instability time, denoted as \(t_{c}\) as shown in Figure 12.  
As illustrated in Figure 12, the \(t_{cr}\)-\(L\) curve remains relatively horizontal within the small bar length interval when the axial force is 2500 kN, 5000 kN, and 7500 kN. With an increase in \(L\), \(t_{cr}\) experiences a slight decrease before beginning to increase. For larger axial forces such as 10,000 kN and 12,500 kN, \(t_{cr}\) remains relatively constant before continuously increasing with \(L\). Given that pile foundation lengths between 50 m and 80 m are prevalent in deep soft foundation areas, it can be inferred that within this range of bar lengths, the instability time of bars is minimally impacted by bar length under equal pile loading intensity. However, for bar lengths exceeding 80 m, the relationship between bar length \(L\) and bar instability time \(t_{cr}\) under varying axial load levels should be carefully considered. Figure 13 depicts the relationship between axial force \(P\) and critical instability time \(t_{cr}\) for different values of bar length \(L\). It is evident that as axial force \(P\) increases, the critical instability time \(t_{cr}\) decreases more rapidly for smaller bar lengths \(L\). Additionally, for bar lengths \(L\) less than 80 m, there is a high degree of overlap in the \(t_{cr}\)-\(L\) curve. This observation aligns with the conclusion that for bars with a length less than 80 m, bar length has minimal impact on its instability time. Figure 12: Relationship between \(L\) and \(t_{cr}\) under different axial forces. Figure 13: Relationship between \(P\) and \(t_{cr}\) corresponding to different \(L\). Time Dependence of the Effect of Bar-Side Pile Loading Intensity on the Lateral Deflection of the Bar Top  
For a bar length \(L\) of 50 m, the change in lateral deflection \(w(L)\) of the bar top over time was calculated for axial forces of 2500 kN, 5000 kN, 7500 kN, and 10,000 kN respectively and pile loading intensities on the side of the bar of 10 kPa, 20 kPa, 30 kPa, 40 kPa, and 50 kPa. The calculation period spanned 100 years.