Reverse catenary equation of the embedded installation line and application to the kinematic model for drag anchors

The penetration behavior and trajectory of the drag anchor in seabed soils are not only determined by properties of the anchor and soil, but also controlled by the installation line especially the segment embedded in the soil. Correctly understanding and describing reverse catenary properties of the embedded line are crucial for improving the drag embedment performance, precisely predicting the anchor trajectory, and solving the positioning problem in offshore applications. The investigation on reverse catenary problems demonstrates that, the reverse catenary shape of the embedded line has to be solved almost through numerical incremental methods. In the present study, based on the mechanical model for the embedded line, the relationship between the tension and geometry of the embedded line, and the interactional equation between the anchor and embedded line are derived. By introducing the concept of the initial embedment depth of the installation line, the reverse catenary equation and the expression for calculating the length of the embedded line are obtained for soils with a linear strength, and the position of the embedment point can be reasonably solved through the derived reverse catenary equation. The reverse catenary equation is then introduced into the kinematic model for drag anchors, which combines the drag anchor, the installation line and the movement of the anchor handling vessel being an interactional system. More information related to the drag embedment problem can be definitely gained through the present work, including not only the anchor behaviors such as the trajectory, penetration direction and ultimate embedment depth, but also the properties of the installation line for both the embedded and horizontal segments. By comparing with drum centrifuge tests and model flume experiments, the efficiency of the theoretical method for predicting the anchor trajectory is well verified.