# Experimental Study of Wave-Induced Response of Piles in Seabed with Various Permeability
## 3 Testing Results
### Pore Pressure around Piles  
Figure 5 shows the response of pore pressure recorded in T2(f-\(H8\)-\(D3\)p) in Sample 1 seabed around a pile. A similar response of pore pressure with different amplitudes could be seen, showing a non-negligible effect of the pile on surrounding soil. Based on the  
Figure 4: Pore pressure in pure Sample 2 seabed: (**a**) \(z=5\) cm; (**b**) \(z=15\) cm; (**c**) \(z=25\) cm. Figure 3: Pore pressure in pure Sample 1 seabed: (**a**) \(z=5\) cm; (**b**) \(z=15\) cm; (**c**) \(z=25\) cm. measurements, Figure 6 illustrates the vertical distribution of the average amplitude of the pore pressure in Sample 1 seabed, where \(p_{\text{m}}\) is the average amplitude of the pore pressure in the seabed and \(p_{0}\) is the amplitude of the dynamic water pressure on the seabed surface. Comparing with the result of T1(f-\(H8\)), \(p_{\text{m}}\) around the pile increased by 15.7%, 16.5% and 25.9% at depths of 5 cm, 15 cm and 25 cm, respectively (see Figure 6), indicating that the effects of drained-path extension and surrounding-soil compression could be obvious in fine sandy seabed with a pile. Moreover, no evidence of residual pore pressure was observed because wave-induced pore pressure dissipated over time. Similar to the responses of pure Sample 2 seabed (see T7(s-\(H8\)) in Figure 4), the pore pressure in the vicinity of the pile accumulated in T8(s-\(H8\)-\(D3\)p) in Sample 2 seabed, as shown in Figure 7. Further examination indicated that pore pressure increased more rapidly in T8(s-\(H8\)-\(D3\)p) than in T7(s-\(H8\)), which is associated with the early-liquefaction phenomenon. For example, the liquefaction that occurred at a depth of 15 cm (Figure 7b) occurred about 200 s earlier than that observed in T7(s-\(H8\)) (see Figure 4b). In the resting time between these two wave-action stages in T8(s-\(H8\)-\(D3\)p), pore pressure drained slowly and its decreased values were closely related to depth. Figure 7a,b also shows a sharp decrease after liquefaction at \(z=5\) cm and a remarkable increase during the first loading stage at \(z=15\) cm. An expected explanation was a seepage path forming in the liquefied seabed close to the pile, which released pore pressure and brought higher wave pressure to the deep seabed. Figure 5: Pore pressure around a pile in Sample 1 seabed: (**a**) \(z=5\) cm; (**b**) \(z=15\) cm; (**c**) \(z=25\) cm. Figure 6: Measured values and analytical solutions in Sample 1 seabed. Solid line represents data taken form reference [19]. As mentioned in Figure 6, the mean value of the amplitudes of the pore pressure in Sample 1 seabed, \(p_{\rm m}\), was much higher in shallow seabed because of shorter seepage paths, e.g., \(p_{\rm m}\) at \(z=5\) cm (\(z/h=0.09\)) was 5.6 times that at \(z=25\) cm (\(z/h=0.43\)). With respect to pore pressure varying with depth, [PERSON] and [PERSON] [19] suggested an analytical solution for wave-induced pore-pressure response, applicable to sandy seabed of finite thickness. The governing equations were deduced from [PERSON]'s consolidation theory [20] and the amplitudes of pore pressure (\(\mid\Delta_{\rm u}\mid\)) normalized with those of dynamic-wave pressure at the seabed surface (\(p_{0}\)), expressed as  
\[\frac{\Delta{\rm u}}{p_{0}}=\frac{(1-\lambda-2\
u)(C_{2}e^{kz}-C_{4}e^{-kz})+ (1-\
u)(\delta^{2}-k^{2})(C_{5}e^{\delta z}+C_{6}e^{-\delta z})}{1-2\
u} \tag{4}\]  
where \(\
u\) is [PERSON]'s ratio for the seabed.