Modified Shields Number Considering the Vertical Seepage on Underwater Three-Dimensional Slopes

Scour has been a topic of significant concern among coastal geotechnical engineers in recent years. The Shields number serves as a crucial parameter for erosion calculations, reflecting the balance between sediment particle conditions and hydrodynamic forces, derived from the mechanics of sediment particle equilibrium. Seepage flow, a common phenomenon driven by pressure in soil, further influences the movement of sediment particles. Building upon the classical three-dimensional two-slope angle erosion model, this study incorporates the vertical seepage force. It comprehensively considers slope angles, sediment response angles, incident current angles, and vertical seepage intensities to adjust the Shields number for sediment particles on slopes. The calculation encompasses both transverse and longitudinal slope configurations. Based on the derived formula and parametric analysis, the study draws the following conclusions: 1. The modified Shields number (θcr/θcr0) decreases non-linearly with the increase of slope angle; 2. θcr/θcr0 is central and has axial symmetry about 180° incident current angles for transverse and longitudinal slopes, respectively; 3. θcr/θcr0 increases non-linearly with the increase of soil angle of response; 4. θcr/θcr0 decreases linearly with the increase of seepage intensity; 5. There exists an approximately zero θcr/θcr0 area when the response angle approaches the slope angle, and the area increases non-linearly as the seepage intensity becomes greater.