Jackup Leg Hydrodynamica Interaction Schematization
Authors: Massie W.W. , Liu Ping , Zeelenberg B.L. 
Published: October 2008

ABSTRACT
Time histories of hydrodynamic interaction of a truss-type jack-up platform leg bay have been computed using a complete model in which each bar is individually represented. Other time histories computed using a more efficient schematization have been compared with the results from this complete model. All computations are based on the Morison Equation using relative, perpendicular flow components.
Study of the force time history from the complete model shows that the resulting horizontal force can act in a direction which deviates from the wave direction. An explanation is given for why the resulting force on the bay can appear very sinusoidal while the forces on the individual members are drag dominated and quadratic.
The desire to use the resulting schematization in non-linear time domain analyses, requires that the drag and inertia force components be examined and modeled separately since the drag contributes to both the excitation and the damping of a non-rigid structure.
Schematization of drag proved to be the most difficult. Shorter waves -so important for fatigue calculations - gave additional difficulty.
Schematization of a leg as a single cylinder cannot be used universally. An acceptable alternative places one vertical element at the location of each leg chord.
The schematizations have been checked in regular and irregular waves, with currents and with relative motion. Various wave directions have been tried as well. In all cases, fits without correction factors - to within a 5% error have been attained for a triangular leg. The fit with a square leg was less precise.

INTRODUCTION
The computation of the hydrodynamic interaction of (moving) truss-type structures - such jack-up - legs is a cumbersome process if each truss bar is included separately; some degree of schematization is very desirable. The purpose of this study has been to investigate the validity of various schematizations for truss-type jack-up legs in order to streamline the computation of hydrodynamic influences in dynamic response computations for elevated jack-up rigs.
The motivation for this study comes from the need to efficiently include all facets of hydrodynamic interaction in the computer modeling of the non-linear, dynamic response of elevated jack-up rigs.
This requires as precise a schematization as possible; small inaccuracies in a nonlinear dynamic representation can be the cause of large, but spurious responses.
The Morison Equation with the use of perpendicular, relative (water - structure) velocities and accelerations forms the basis for the current study. The model is to be used in the time domain. With relative velocities present, the drag force is both an excitation and a damping; it must be precisely modeled and segregated from the inertia component in order to prevent unwanted effects.
The schematization sought is to be quite universal. The same schematization should be useful for both local (single leg) and overall (total structure) hydrodynamic influences; it should be equally acceptable for survival (large waves) conditions and fatigue (smaller, shorter wave) conditions.