In this study, an analytical model for the three-dimensional (3D) dynamic stability analysis of vegetation-rooted slopes is first developed under steady-state unsaturated flow conditions. Root reinforcement, defined as the increase in the soil shear strength produced by the mechanical and hydrological effects of vegetation roots, is included in the proposed analytical model. By combining the modified pseudo-dynamic approach (MPDA) and the kinematic theory of limit analysis to the 3D discretized failure model, the most critical failure surface and the corresponding factor of safety (FS) are derived to examine the stability of vegetation-rooted slopes with the aid of the optimization algorithm of particle swarm. The proposed approach is verified by comparing with published analytical solutions and numerical results. A series of parametric analysis are then conducted to examine the influence of seismic-related parameters, vegetation properties, possible surcharge and slope geometry parameters on the slope stability. Finally, a comparison between the slope stability under different root architectures is provided and discussed. The results show that, for these selected cases, the stability of vegetation-rooted slopes is significantly improved by approximately 45% compared to bare soil slopes, and the divergences of reinforcement effects between different root architectures can be negligible.

The water jet trenching technique is widely used in the burial of submarine pipelines. However, its application in cohesive soils often leads to complexity in trench morphology and challenges in predicting trench dimensions due to unclear soil erosion mechanisms. These issues significantly impact pipeline burials. To investigate the soil erosion mechanism of water jet trenching in cohesive soils, two-dimensional physical simulation experiments of submerged vertical water jet erosion were conducted. The influence of jet pressure, impingement height, and nozzle diameter on the shape of the scour hole was analyzed. The erosion damage patterns of water jets on cohesive soils were studied, and a theoretical model for the development of scour holes was established. The study revealed that when the jet velocity reaches 1000 m/s and the nozzle diameter reaches 1 mm, a contracted neck forms at the upper part of the scour hole. The appearance of the contracted neck is due to excessive jet impact energy causing impact shear failure in the soil. The effective height and width of the contracted neck increase with jet pressure and nozzle diameter and decrease with impingement height. Based on Prandtl's bearing capacity model, a model for predicting impact shear failure in cohesive soils was established, and a predictive formula for the effective height and diameter of the neck was proposed. Experimental validation confirmed the accuracy of the predictive formula. These findings provide theoretical support for the application of water jet trenching techniques in cohesive seabed soils.