# Responses of Laterally Loaded Single Piles Subjected to Various Loading Rates in a Poroelastic Soil
## 3 Results
### Pore-Water Pressure Distribution  
To see the effect of loading rates on the pore-water pressure of the porous media, the pile was laterally loaded under a fast transient loading rate of 2 kN/s, a slow transient loading rate of 2 kN/h, and an almost stationary loading rate of 2 kN/day over a total period of 100 s, 100 h, and 100 days, respectively. In all cases, the final lateral load acting on the pile cap at the end of the incremental loading stage was thus the same at 200 kN. The analyses were allowed to continue under this constant load and were only terminated at the end of 10,000 s, 500 h, and 500 days, respectively, to allow for the study of the response of the pile during the dissipation of the pore-water pressure. It was expected that during the loading process, in particular during the transient stage, excess pore-water pressure would be generated, and hence they were monitored at both the passive and active sides of the pile, i.e., 0.3 m from the left- and right-hand perimeters of the pile (Sec. A-A and Sec. B-B in Figure 1a). The observed excess pore-water pressure, which is the difference between the total pore-water pressure generated and the hydrostatic pressure, are plotted in Figure 2. In all cases, positive excess pore-water pressures were mainly observed in the passive zone (right-hand side, RHS) of the pile while negative excess pore-water pressures (suction) were mainly observed in the active zone (left-hand side, LHS) of the pile.  
In the fast and slow transient loading cases, the maximum positive and negative excess pore-water pressures were both observed at the end of the loading, at \(t\) = 100 s (Figure 2a) and at \(t\) = 100 h (Figure 2b), respectively. The maximum positive excess pore-water pressure computed at \(t\) = 100 s was 53.4 kPa, and then it decreased to 37.3 kPa and 26.8 kPa at \(t\) = 1000 s and 10,000 s, respectively. The suction at \(t\) = 100 s was (\(-\))84.5 kPa, the suction decreased to (\(-\))57.0 and (\(-\))33.3 kPa at \(t\) = 1000 s and 10,000 s, respectively.  
Comparing the positive and negative excess pore-water pressure profiles under the slow loading rate (Figure 2b) to those under the fast loading rate (Figure 2a), the excess pore-water pressure profiles were rather symmetrical. The active side in the case of fast loading rate resulted in the generation of a higher excess pore-water pressure than the passive side, but as the loading rate decreased to the slow loading rate, the magnitude at both sides of the pile was almost equivalent. The absolute maximum excess pore-water pressure at the end of the incremental loading application at \(t\) = 100 h was about \(|\)8\(|\) kPa(Figure 2b). One hundred hours after the end of this load application, the excess pore-water pressure dissipated some 90% of its maximum value generated at \(t=100\) h. In other words, the excess pore-water pressure gradually increased over a transitory period of 100 h, peaked at 100 h, and then dropped back to the hydrostatic pressure through the subsequent 100 h of consolidation. It was also observed that under the loading rate of 2 kN/h (Figure 2b), the excess pore-water pressure profiles were smoother than those under the loading rate of 2 kN/s.  
For the case of almost-stationary loading rate, there was no discernible excess pore-water pressure generated throughout the loading stage. At this loading rate, full drainage was provided and, hence, its excess pore-water pressure remained at zero. Thus, it can be deduced that the current loading rate of 2 kN/s represents an undrained loading, the case of 2 kN/h represents a partially drained loading, and that of the 2 kN/day case represents a drained loading.  
It was also observed in the current analysis that most of the production of the excess pore-water pressure was seen to occur in the top 6 m of the pile. The depth at which the maximum excess pore-water pressure was encountered was about 1.0 m immediately below the ground surface in the case of undrained loading, while that in the partially drained case the depth was about 2.5 m.