# Experimental Study of Wave-Induced Response of Piles in Seabed with Various Permeability
## 4 Discussion of Wave-Induced Pile-Seabed Response  
### Pile-Diameter Effect  
Figure 10 shows the average pore-pressure amplitudes, \(p_{\text{m}}\), varying with depth in the experiments with Sample 1 seabed. The value of \(p_{\text{m}}\) for the piles with a 3 cm diameter in T2(f-\(H8\)-\(D3\)p) was close to the value for 5 cm diameter piles in T5(f-\(H8\)-\(D5\)p), especially as depth increased. This result indicates that the effect of diameter on pore-water dissipation was negligible, probably because of the high permeability of Sample 1, although previous studies have found that piles with larger diameters could be disadvantaged because of drainage boundary conditions. The pore pressure measured in pure Sample 2 seabed (see T7(s-\(H8\)) in Figure 4) comprises two temporal components, i.e., residual pore pressure \(p_{\text{r}}\) and oscillating pore  
Figure 8: Pile-head displacement in Sample 1 seabed. Figure 10: Averages of pore-pressure amplitudes in Sample 1 seabed. Figure 9: Pile-head displacement in Sample 2 seabed. pressure \(p_{\rm o}\). Residual pore pressure can be derived by applying the linear-moving-average (LMAV) scheme, as suggested by [PERSON] and [PERSON] [32]. Oscillating pore pressure is obtained by subtracting the residual component from the total pore pressure. Figure 11 presents the development of residual pore pressure close to the piles in Sample 2 seabed against wave-loading time. As the pile diameter increased from 3 cm (T8(s-_H8_-_D3p_)) to 5 cm (T11(s-_H8_-_D5p_)), the maximum \(p_{\rm r}\) decreased by 57.0%, 35.2% and 37.4%, with depth increasing from 5 cm to 25 cm. By inference from these results, it can be concluded that the contribution of pile displacement response to pore-pressure accumulation in Sample 2 seabed was greater than that of pile diameter. This deduction is further demonstrated in the following discussion. Figures 12 and 13 show the permanent components and cyclic components deduced from the pile-head-displacement values using the LMAV. Increases in pile diameter led to smaller permanent and cyclic components under 640 s of regular wave action in both Sample 1 and Sample 2 seabed, with curves shown in Figure 12 (T2(f-_H8_-_D3p_), T5(f-_H8_-_D5p_)) and Figure 13 (T8(s-_H8_-_D3p_), T11(s-_H8_-_D5p_)). From the results of the present experiments, a more stable state is expected for large-diameter piles under wave loading in Sample 2 seabed. Figure 11: Residual pore pressure in Sample 2 seabed: (**a**) \(z=5\) cm; (**b**) \(z=15\) cm; (**c**) \(z=25\) cm. Figure 12: Displacement components in Sample 1 seabed experiments: (**a**) permanent component; (**b**) cyclic component. Although larger-diameter piles are subjected to enormous wave loads, an extra area of pile-seabed interaction also provides more lateral resistance, which limits pile displacement. Further work was conducted to explore the effect of pile diameter on pile displacement response. Wave length \(L\) in the tests was 1.55 m according to the linear wave theory, meaning that the maximum value of \(D/L\) was only 0.03. Hence, the wave load on the piles (\(F_{w}\)) could be calculated through the Morison equation (\(D/L\leq 0.15\)) [33] as follows:  
\[F_{\text{W}}=\frac{1}{2}C_{\text{D}}\rho D(u+\dot{x})\big{|}u+\dot{x}\big{|}+ \frac{\pi}{4}C_{\text{M}}\rho D^{2}\dot{u} \tag{8}\]  
where \(C_{\text{M}}\) and \(C_{\text{D}}\) are the inertia and drag coefficient, respectively; \(\dot{\rho}\) is the water density; \(u\) is the horizontal component of water-particle velocity; \(\dot{u}\) is the horizontal component of water-particle acceleration; and \(\dot{x}\) is the horizontal velocity of the pile. For simplification, the velocity of the piles was considered as zero, since the analysis here was mainly focused on small pile responses. It is worth noting that the horizontal acceleration of piles should be considered when pile displacement is large in actuality. \(C_{\text{M}}\) and \(C_{\text{D}}\) were given as 2 and 1.2, respectively.