A Simplified 1D Seafloor Liquefaction Model Applied to Nonlinear Waves

Previous studies report a significant decrease of seabed destabilization under nonlinear waves compared to linear waves. To investigate this effect, we simplify the equations governing the sediment stability to a single vertical diffusion equation, which encapsulates the properties of the media (water and sediment) in a single effective diffusivity parameter. The simplified model provides an effective means for deriving a maximum liquefaction depth under linear waves and for a comprehensive investigation of the liquefaction effects under nonlinear waves expressed by third order wave statistics, skewness, and asymmetry. Fourier liquefaction modes are shown to lag bottom pressure components by $3\pi /4$. Under nonlinear shallow water waves lagged liquefaction harmonics can combine to modify significantly the intensity and duration of bed decompression rate. Under positively skewed waves with negative asymmetry, this results in a weaker sediment destabilization. For practical applications, popular linear wave estimates such as the random phase approximation can significantly overestimate liquefaction effects and burial depths under nonlinear waves.