# Cnoidal Wave-Induced Residual Liquefaction in Loosely Deposited Seabed under Coastal Shallow Water
## 4 Result Analysis
### Effective Stress and Pore Pressure  
The time histories of the effective stresses at three typical buried depths on the symmetrical line \(x=100\) m are demonstrated in Figure 4. It is observed that the pore pressure at the three typical buried depths all builds up under the cnoidal wave loading. In the upper seabed floor, the residual component of pore pressure can reach a stable status (meaning that the residual pore pressure cannot accumulate anymore) within a relatively short period. In the medium depth of the seabed floor, it is about 300 s for the residual pore pressure to reach its stable status. In the lower seabed floor, it is found that the residual pore pressure does not reach its stable status until the end of the computation (\(t=500\) s). It is indicated that the time for the residual pore pressure to reach its stable status is positively related to the buried depth. Another phenomenon observed is that the magnitude of the accumulated residual pore pressure in the medium depth of the seabed floor is much greater than that in the upper and lower seabed floor. It can be attributed to the fact that (1) the drainage path is relatively short and the initial effective stresses are relatively small in the upper seabed floor, and (2) the cnoidal wave-induced cyclic shear stress is not significant in the lower seabed floor. Finally, we find that the amplitude of the oscillatory component of the pore pressure is also positively related to the buried depth. In Figure 4, it can also be observed that the mean effective stress \(I_{1}/3\) in the upper seabed floor gradually reduces, accompanying the accumulation of pore pressure. When \(|I_{1}/3|\) is less than a small critical value, the seabed soil will become partially liquefied first, and then sequentially become fully liquefied at the moment when \(|I_{1}/3|=0\). In the reduction process of the effective stress, the amplitude of the cnoidal wave-induced shear stress gradually becomes less and less. Finally, it becomes zero when the seabed soil becomes fully liquefied. It means that the fully liquefied seabed soil behaves like a kind of heavy fluid with great viscosity. It cannot bear any external shear loading due to the complete loss of the stiffness of the soil skeleton. The successful capture of this physical phenomenon indicates that the integrated model FSSI-CAS 2D is powerful to handle the problem of seabed dynamics. Currently, a lot of commercial software/packages do not have this capability. In the medium part of the seabed floor, although the residual pore pressure has built up to more than 100 kPa, the mean effective stress has never reached zero. The full liquefaction cannot occur. Partial liquefaction is possible depending on the judgment criterion chosen. In the lower seabed floor, the pore pressure is only slightly accumulated under the wave loading. However, the magnitude of \(|I_{1}/3|\) is around 190 kPa, far away from the status of partial liquefaction. Most importantly, it is found that the magnitude of effective stress is not always reduced in the accumulation process of pore pressure. It can also be increased, accompanying the pore pressure buildup. It is indicated by this phenomenon that the cnoidal wave-induced dynamics of a loose seabed floor is apparently complicated. We cannot understand these dynamics mechanisms, adopting a linear way of thinking. The distributions of the cnoidal wave-induced dynamic pore pressure and \(I_{1}/3\) at two typical moments are illustrated in Figure 5. It is clearly observed that the accumulation of the residual pore pressure in the range of \(z=15\) to 23 m is significantly greater than that in the other parts. The reason is presented above. Correspondingly, the reduction of \(|I_{1}/3|\)  
Figure 4: Time histories of the pore pressure, mean effective stress \(I_{1}/3\), and shear stress at three typical buried depths (note: compression is taken as negative). in the range of \(z=15\) to \(23\) m is also most obvious.