For a heavy object falling on a free-span pipeline, this study assesses three-dimensional (3-0) pipe-span responses with the torsional (Ix-) coupling of a pipeline through the biaxial (y) bending responses. The static pipe-span equilibrium is achieved with its self-weight and buoyancy and the external torsional moment induced by the cross-flow (y-directional) current on the sagged pipe span. Load steps taken for 2 different sequences of applying static loads induce different pipe deformations, and the pipe twists in entirely different pattern. The two types of impact loads are applied in the vertical (z-) direction to excite the pipe span in its static equilibrium:
triangular impulse loading and
ramp loading.
Boundary condition of the span supports is "fIXed-fixed" at both ends in both displacement and rotation. 3-D coupled axial (x-), bending (y- and z-) and torsional (/lx-) responses, both static and dynamic, to the z-directional impact loadings, are modeled and analyzed by a nonlinear FEM method for a 16-in pipeline. The 3-D responses are compared with 2-D responses. The comparison shows significant torsional vibrations caused by the cross-flow current, especially for longer spans. For very large impact loads, the response frequencies differ from the fundamental frequencies of the span, exhibiting beatings and strong bending-to-axial and to-twist couplings. Also, the eigenvalues for the linear system are not necessarily the resonance frequencies for these nonlinear coupled responses.
A free span of a pipeline on the seafloor, can experience excessive stresses due to hydrodynamic forces in the x-, y-, and z-directions and impact loads in the z-direction in addition to its wet weight (self-weight and buoyancy) in the zdirection and the steady drag by the cross-flow current in the y-direction. Free span can occur when a pipeline is laid on an uneven bottom and during the laying operations.
