# Experimental Study of Wave-Induced Response of Piles in Seabed with Various Permeability
## 2 Testing Arrangements and Programs
### Soil and Model Piles  
Two soil samples made from commercial silicon materials were adopted for testing. Sample 1 was fine sand mixed with particle sizes of 0.15 mm and 0.06 mm in a mass ratio of 3:1. Sample 2 was uniform silt with a particle size of 0.06 mm. No other particle sizes were adopted in the tests. The test soil beds were prepared by pluviation to achieve a targeted relative density (Dr) of 0.73 for Sample 1 seabed and 0.82 for Sample 2 seabed. The submerged unit weights of the two samples were \(\gamma^{\prime}=7.3\) kN/m\({}^{3}\) and 11.5 kN/m\({}^{3}\)  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & **Pile** & **Wave** & **Loading** \\
**Test No. ** & **Related Model** & **Soil Type** & **Pile** & **Diame-** & **Height** & **Time** \\  & & & & & **H** & **f (s)** \\ \hline T1(_H_-_H_S) & Seabed & Sample 1, fine sand & - & - & 8 & 640 \\ T2(_H_-_H  
respectively. The permeability coefficient of the two samples was determined by a constant-head-permeability test, which showed \(k=1.88\times 10^{-3}\) cm/s and \(4.32\times 10^{-5}\) cm/s for Sample 1 and Sample 2 seabed, respectively. Table 2 summarizes the properties of the soil samples. Four closed-end model piles were fabricated as shown in Table 1 and as follows: (1) an upright pile made from a plexiglass tube (a frequently-used material in flume experiments [27]) with a thickness of 2 mm, an outer diameter of 30 mm and a length of 1 m; (2) a similar plexiglass pile with a 50 mm outer diameter; (3) a 30 mm outer-diameter plexiglass pile to which two fins were attached (0.2 cm in thickness, 3 cm in width and 6 cm in height), as shown in Figure 1; (4) an aluminum pile with a 30 mm diameter and a 2 mm thickness. The Young's modulus of plexiglass and aluminum was found to be 4.4 GPa and 70.8 GPa, giving a bending rigidity \(EI=76.25\) N\(\bullet\)m\({}^{2}\) and 1.23 kN\(\bullet\)m\({}^{2}\). As shown in Figure 1, the piles were hoisted in the center of the pit during pluviation and their tip was kept at least 5.6 \(D\) (\(D=50\) mm) above the pit bottom to exclude the boundary effects on a laterally loaded pile [6]. The lateral distance from the piles to the pit side-wall was larger than 10 \(D\) to eliminate side effects [28; 29]. Three non-dimensional numbers relative to flow characteristics in the wave-pile interaction problem [30] are (1) the Froude number, \(\text{Fr}=U_{\text{m}}/(gD)^{1/2}\), which is the ratio of inertia force to gravitational force and represents the dynamic similarity; (2) the Keulegan-Carpenter number, \(\text{KC}=U_{\text{m}}T/D\), which controls the generation and development of a vortex around a pile and is related to the hydrodynamic force acting on the pile under wave motion; and (3) the Reynolds number, \(\text{Re}=U_{\text{m}}D/v\), which is the ratio of inertia force to viscous force. Note that \(U_{\text{m}}\) is the flow velocity, \(D\) is the pile diameter, \(T\) is the wave period and \(v\) is the kinematic viscosity of water. Given all tests were conducted under normal gravity (1 g) conditions, the similarity of the Froude number was satisfied, so \(\lambda_{\text{Fr}}=\lambda_{\text{Um}}\)\(/(\lambda_{\text{g}}\lambda_{\text{D}})^{1/2}=1\), where \(\lambda\) represents the ratio of the parameters of the model to those of the prototype. Considering \(\lambda_{\text{g}}=1\), the following relationship should be maintained:  
\[\lambda_{\text{Um}}=\lambda_{\text{D}}{}^{1/2}, \tag{1}\]  
Using the dimensional analysis method to consider the similarity of period \(T\), it could be further rendered to  
\[\lambda_{\text{T}}=\lambda_{\text{D}}\ /\ \lambda_{\text{Um}}=\lambda_{\text{D}}{}^{ 1/2} \tag{2}\]  
Therefore,  
\[\lambda_{\text{KC}}=\lambda_{\text{Um}}\ \lambda_{\text{T}}\ /\ \lambda_{\text{D}}= 1 \tag{3}\]  
The above analysis indicates that the KC number follows [PERSON]'s law; this could also be satisfied during the flume experiments, meaning that the hydrodynamic force on the pile followed the principle.