Three-dimensional (3-D), nonlinear, coupled axial, bending and torsional responses of a 4, OOO-rt pipe system are studied with a new nonlinear FEM code. A possible mining system is proposed for the recovery of cobalt-rich crusts in the Pacific Ocean. The pipe top is pinned to a ship undergoing motion in waves, while the bottom end of the pipe is connected to equipment on the seafloor. The pipe system is subject to a vertically-varying current, in establishing the static (initial) equilibrium configuration. For dynamic analysis, the pipe system is excited by horizontal and vertical ship (or pipe-top) motions, the bottom equipment motion, the internal slurry now, and the external, axial and normal, hydrodynamic forces. A consistent mass-matrix formulation is used for torsional coupling. Random phase takes care of the interactions between the motions of pipe top and the seafloor equipment. The now-induced torsional moment on an asymmetric pipe arrangement induces biaxial bending moments and displacements, static as well as dynamic, in response to a unidirectional ocean current and causes appreciable pipe twist. Dynamic axial and horizontal motions reduce the mean pipe deflections from the static equilibrium. Resonance frequencies for the present nonlinear coupled motion responses are different from those of the linear vibrations. Axial forces and bending moments change the natural frequencies of vibrations of a pipe column. Excitation frequency dominates the system vibrations, except for the pipe twist at the torsional resonance. The internal upward slurry flow reduces the axial stress and increases the horizontal displacements. Stability of the solutions is sensitive to the specific sequence of load steps, large flow-induced torsional moment, excitation frequencies, and excessive axial oscillation amplitudes.
Previously, the importance of the axial stress for design was first pointed out by Chung (1981), for which only uncoupled axial stress was investigated for an 18,000-ft vertical pipe.