Static pile ended with cone apex angle is widely used in practical engineering. However, the corresponding penetration resistance is still impossible to be predicted accurately. To address this, the penetration process of static pile is simulated by using the coupled Eulerian-Lagrangian (CEL) method in this study. During the penetration process of static pile in clay, the effect of cone apex angle and soil rigidity index on pile-end resistance and the distribution of the plastic zone of the soil around the pile-end are analyzed. The corresponding results indicate that the pile-end resistance is positively correlated with the size of cone apex angle and soil rigidity index, and the pile-end resistance rises with the increase of penetration depth until reaching a certain depth. Besides, the expansion process of the plastic zone near the pile-end is characterized by the expansion of spherical cavity. Since the position of expansion cavity center is different from the traditional theory, the corresponding radius in the traditional theory of cavity expansion is modified according to the corresponding numerical results. Finally, a semi-empirical method, in which the effect of cone apex angle and the soil rigidity index are considered, is proposed to predict the ultimate pile-end resistance of static pile.

Numerical simulations are conducted to investigate the near-bed flow behaviors of submarine canyons with periodic ridge-valley topography on continental slopes. In the numerical simulation, two topographic parameters are defined: α represents the basal slope angle of the continental slope, and β denotes the side slope angle of the submarine canyon. The topographic modulation of these two parameters on near-bed flow velocity and pipeline on-bottom stability is explored. The results show that the ribbed slope exerts two distinct modulation mechanisms on near-bed flow fields, which are governed by the relative angle between incoming flow and ridge-valley structures. When the flow is perpendicular to the canyon axis (θ = 0°), local topographic contraction and expansion accelerate flow over ridge crests and reduce near-bed velocity in valleys as β increases. In contrast, when the flow is parallel to the canyon (θ = 90°), lateral confinement by bilateral ridges forms a topographic channel, leading to persistent flow acceleration throughout the entire valley area. Moreover, such directional velocity differences substantially alter the on-bottom stability of pipelines deployed within the canyon. Two pipe-soil interaction models are employed in the stability analysis: the Verley-Lund model for a flat clayey seabed and the Slope-Silt model for a sloping silty seabed. The sensitivity of their predictions to soil undrained shear strength is further evaluated.