Wave-Driven Sliding, Ratcheting, and Overturning of Coral Transplant Units: An Idealized Nonsmooth Contact Model

Sandy Hardian Susanto Herho , Iwan Pramesti Anwar, Faruq Khadami, Karina Aprilia Sujatmiko, Alfita Puspa Handayani, Dasapta Erwin Irawan

Coral transplantation attaches fragments to a structure placed on the seabed, and that structure must stay put long enough for the fragments to fuse to it. We examine that requirement with an idealized model in which a transplant unit is a planar rigid body on a rigid bed under two unilateral frictional contacts, loaded through a Morison description of near-bed wave kinematics and integrated by a nonsmooth contact time-stepping scheme. No measurement enters the model and no coefficient is calibrated. Three closed-form results follow from the balance of forces at rest. Whether a unit slides or tips is decided by comparing the base half-width divided by the height at which the flow pushes hardest against the friction coefficient of the bed; lift cancels exactly, and no material or wave property enters. Material affects the thresholds only through the submerged weight, so changing it rescales every threshold by one factor and reorders nothing. A wave riding on a current drives a net drift per cycle rising as the square of the overshoot above threshold. Five reference structures carrying growing colonies are compared at four idealized Indonesian site classes. Every unit loses margin as its corals grow, so success in the biological sense erodes the margin that permitted it, and an internal solitary wave (ISW) at transplant depth triggers a sliding step rather than an overturning. Across samples varying every uncalibrated coefficient together, the ranking of the structures proves far firmer than the thresholds. The solver is verified against closed-form impact, sliding, and rocking results.