RPD Analysis of Jack-Up Rigs Using 3D Models
Authors: Chakrabarti Partha , Chawan Abhijeet 
Published: September 2014

Rack Phase Difference or RPD may occur during jacking up at a location when the jack-up spudcan is eccentrically supported on the bottom or has lateral offset and the resulting moment and shear is carried essentially by the horizontal guide reactions. The RPD is the difference in vertical positions of rack teeth of different chords of one leg. This is a result of vertical shear deformation of the adjacent chords of one leg of a trussed jack-up. Among the causes of RPD the following are common: uneven or sloping seabed, preexisting spudcan holes, leg offset, rapid penetration, uneven jacking force on different chords of a leg, scour etc. While jacking up at a location, operating procedures normally dictate that the RPD be measured. When there is significant RPD, it means the leg chords are not centrally placed within the legwell area but one side could be touching the upper guide while the opposite side is in contact with the lower guides. There is a safe limit of the RPD that is normally specified for a given jack-up that has to be kept in mind while jacking up at a location.
For a jack-up fitted with rack chocks, once at the elevated condition, the jack-up is designed to take up the moment produced at the legs due to the environmental loads by the vertical couple at the chocks and pinions rather than the horizontal couple at the guides. As a result, the brace size requirement is normally lower than units that do not have the chocks. For these units RPD becomes all the more important as it could be built-in unless suitable mitigating measures were taken before the chocks are engaged. The built-in RPD could affect the strength for design environmental loads.
Unfortunately, the most commonly used guidelines for jack-up design such as SNAME T&R 5-5A, ISO 19905-1 or DNV OS-C104 do not have any detailed discussion on the topic. HSE Research Report 289 prepared by MSL Engineering has a good technical description of this phenomenon and some general qualitative guidelines. There are some studies published in the public domain that have details of RPD analysis. However, most of these papers deal with very simplified modeling of only one leg of the jack-up and idealized behavior.
The present paper discusses complete and more realistic analysis of a 3D model of the jack-up that uses non-linear analysis methods for including large deformations and rotations. The nonlinearities come about due to physical reasons, such as pinion-rack contact is compression only and guide contact is also compression only with a gap. In addition, one may like to include nonlinearities due to geometric stiffness for large deformations and plasticity effects. Geometric stiffness allows it to include so-called P-delta effects and simulate buckling behavior of beam elements.
The results of such 3D non-linear analysis for various levels of assumptions are compared with a more traditional single leg analysis. The paper brings out the important differences in behavior of these two types of models and discusses the importance of those in the analysis results. The authors think that the meaning of RPD has to be understood properly in relationship with moment or shear carrying capacity at the spudcan for a given jack-up. The behavior of a trussed leg jack-up depends heavily on the bracing pattern, chord and bay spacing as well as the size of the braces. The paper discusses these aspects also. Finally, although the analysis is for one particular jack-up, it recommends the most appropriate modeling for RPD analysis for similar jack-up rigs that could be beneficial to other rigs.