Theoretical Model For Determining Rotational Behaviour Of Spud Cans
Authors: Van Langen Harry , Van Hospers Bareld 
Published: October 2008

ABSTRACT
The integrity of jack-up foundations is usually assessed on the basis of maximum preload applied or ultimate bearing capacity assuming pinned footing conditions. However, disregarding spudcan foundation rotational stiffness in a jack-up structural analysis is conservative if this stiffness can be demonstrated to exist. The beneficial effect of rotational foundation stiffness on the global jack-up response may lead to the conclusion that jack-up rigs are acceptable from a structural point of view, whereas disregarding it would result in rejection of the unit.
The paper discusses non-linear jack-up foundation behaviour and describes a theoretical model for the determination of a rotational spring stiffness, based on hardening plasticity. Initial results of validation work are presented. The method is applied to a jack-up with shallow spud can penetration subjected to purely static loads to illustrate the effect of foundation stiffness on some aspects of global jack-up response. The need for further validation of the proposed model is discussed.

INTRODUCTION
The last few years significant effort has been put into the development of procedures, methods and criteria for the site specific assessment of jack-ups. Usually the assessment requires the ability of the jack-up unit to survive safely the 50 year return period storm conditions and comprises a check on the structural integrity of the jack-up unit and an evaluation of foundation stability. In the draft Industry's Recommended Practice for the site specific assessment of mobile jack-up units (Ref.1), three levels of foundation assessment are distinguished with increasing order of complexity and model refinement, i.e:step 1preload checkstep 2bearing capacity checkassuming pinned foundationsincluding rotational, vertical and horizontal foundation stiffness.step 3displacement check
Levels 1 and 2a assume pinned conditions at the foundations in a structural analysis, disregarding the actual foundation behaviour. A drawback of this approach is that the beneficial effects of rotational stiffness on structural response and load redistribution between the spudcans are not taken into account. Measurements (Ref.2) and computations (Ref.3) show that inclusion of rotational foundation stiffness results in a redistribution of the leg bending moment at the leg hull connection to the bottom of the leg and reduces the natural period of the jack-up unit.
Step 2b allows the use of a model with non-linear rotational and linear translational foundation stiffnesses. The translational spring stiffnesses should be included since they tend to decrease the sway stiffness of the unit and hence increase the natural period and second order effects, Step 3 includes the effect of displacements and allows the determination of foundation system reserve capacity after first spudcan failure (sliding/ penetration). It involves full non-linear foundation response, i.e. coupled penetration, sliding and rotation of the spudcans. The foundation characteristics and the checks required at each step are schematically illustrated in Figure 1.