Mathematical Modeling of Wave-Induced Pore Pressure Dynamics in Silty Seabeds

This study investigates the dynamic response of seabed pore pressure under wave loading, focusing on silty and layered seabed conditions, with the aim of providing insights into seabed stability and coastal engineering design. A series of wave flume experiments were conducted to explore the spatial and temporal evolution of pore pressure under varying wave parameters, soil permeability conditions, and degrees of sediment stratification. The pore pressure signals were analyzed using Daubechies wavelets to distinguish between oscillatory and cumulative components in homogeneous silty seabeds. For layered seabeds, two distinct response patterns were observed. In shallow layers, pore pressure accumulation occurs gradually, enhancing stability by mitigating dynamic stresses. However, in deeper layers, pore pressure accumulation increased significantly, posing potential risks to structural stability. The experiments revealed that the permeability of the surface soil layer plays a critical role in modulating the amplitude and rate of pore pressure oscillations, as well as the accumulation patterns across depths. Based on the experimental findings, a mathematical model was developed to characterize the spatial–temporal evolution of excess pore pressure, incorporating key parameters related to wave properties, water depth, and soil characteristics. These parameters were fitted using nonlinear optimization techniques. Validation against established experimental and analytical data confirmed the model’s accuracy and capability in describing the complex interactions between wave loading and seabed dynamics. The outcomes of this study provide a theoretical foundation for understanding wave-induced pore pressure responses and offer practical guidance for the design and stability assessment of nearshore structures under dynamic wave conditions.