# Responses of Laterally Loaded Single Piles Subjected to Various Loading Rates in a Poroelastic Soil
## 3 Results
### Pile Response during and after the Application of Lateral Load  
The response of the pile during and after the application of the incremental lateral load in undrained (loading rate at 2 kN/s), partially drained (loading rate at 2 kN/h), and drained (2 kN/day) conditions is studied here. At the end of the incremental loading, i.e., after \(t=100\) s, \(t=100\) h, and \(t=100\) days, the cumulative load attained was all the same, i.e., 200 kN; at which point, the displacements were 12.40 mm, 17.70 mm, and 21.37 mm, respectively (Table 2). The displacement results in Figure 3a-c and Table 2 revealed that the lateral displacement of the pile is affected by the consolidation process, i.e., the dissipation of the excess pore-water pressure. In Figure 3a, the lateral displacement of the pile cap was about 12.40 mm at \(t=100\) s; as the excess pore-water pressure continued to dissipate, the lateral displacement increased to about 21.46 mm at \(t=10\) h; subsequent consolidation, even for a further period of 100 h, saw only a minute (0.96 mm) or basically insignificant increase in the pile cap displacement. Figure 2: Generation and dissipation of excess pore water pressure at Sec. A-A and Sec. B-B (see Figure 1a) during the loading of the pile: (**a**) fast loading rate: 2 kN/s (undrained); and (**b**) slow loading rate: 2 kN/h (partially drained). In the case of partially drained loading, the maximum lateral displacement at the end of the incremental loading at \(t=100\) h was 17.70 mm; after letting it consolidate for 100 h (\(t=200\) h), at which time the excess pore-water pressure was about 34.5% of its maximum value at \(t=100\) h, it can be seen that almost all the lateral displacement was mobilized to a value of 21.43 mm (97.8% of the value at \(t=1000\) h). The effect of consolidation or dissipation of excess pore-water pressure on the lateral displacement of the pile is clearly demonstrated in the case of drained loading (Figure 3c) where the lateral displacement of the pile cap is identical at the end of 100, 200, and 500 days. \begin{table}
\begin{tabular}{l l c c c c c c} \hline \hline
**Loading Rates** & **Pile Responses (Maximum)** & \multicolumn{5}{c}{**Elapsed Time**} \\ \hline  & & 10 s & 50 s & 100 s & 1 h & 10 h & 100 h \\ \cline{2-8}
2 kN/s (Undrained) & Lateral displacement (mm) & 1.10 & 5.68 & 12.40 & 15.69 & 21.46 & 22.42 \\  & Bending moment (MNm) & 5.86 & 31.90 & 67.82 & 80.74 & 87.04 & 87.67 \\ \hline  & & 10 h & 50 h & 100 h & 200 h & 500 h & 1000 h \\ \cline{2-8}
2 kN/h (Partially-drained) & Lateral displacement (mm) & 1.37 & 7.89 & 17.70 & 21.43 & 21.84 & 21.90 \\  & Bending moment (MNm) & 6.71 & 36.73 & 77.59 & 86.13 & 86.23 & 86.28 \\ \hline  & & 10 days & 50 days & 100 days & 200 days & 500 days & — \\ \cline{2-8}
2 kN/day (Drained) & Lateral displacement (mm) & 1.64 & 8.73 & 21.37 & 21.77 & 21.77 & — \\  & Bending moment (MNm) & 6.77 & 36.83 & 85.22 & 85.87 & 85.87 & — \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum pile responses under various loading rates and different elapsed times. Figure 3: Responses of pile under various loading rates: lateral displacement under the rate of (**a**) 2 kN/s (undrained); (**b**) 2 kN/h (partially drained); (**c**) 2 kN/day (drained); bending moment under the rate of (**d**) 2 kN/s (undrained); (**e**) 2 kN/h (partially drained); and (**f**) 2 kN/day (drained). The distribution of bending moment \(BM\), on the other hand, may be obtained from [21], as  
\[BM=\frac{EI\Delta\varepsilon}{D} \tag{5}\]  
where \(EI\) is the bending stiffness of the pile section, \(\Delta\varepsilon\) is the increment of the pile strain between two depths, and \(D\) is the diameter of the pile.