1。Introduction  A jack-up rig is a mobile offshore drilling unit。 The essential features of a jack-up are shown in Fig。 1; a hull is supported by (usually) three K-lattice legs, each resting on a large inverted conical footing known as a spudcan。 During installation, the rig is positioned with the footings resting on the seabed and the hull is   raised a few metres above the water surface。 The unit is then preloaded by pumping seawater into the hull, forcing the spudcans into the seabed。 Once the desired penetration has been achieved, the preload is removed and the  hull is raised to its operating  height。82310

Jack-up units are widely used in offshore oil and gas exploration。 While originally designed for use in shallow waters, there is growing demand for their use in deeper waters and harsher environments。 In particular, the suit- ability of jack-ups for some deep water sites may   have a significant influence  on  the  viability  of marginal field developments。

In order to extend the working range of jack-ups, it is essential to have accurate, reliable analysis and design

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methods, eliminating excessive conservatism。 An accur- ate structural analysis must include realistic models of the wave loading, the geometrically non-linear behaviour of the slender legs, and the complex non-linear response of the spudcan footings to combined loads。 Because jack-up rigs are flexible, dynamic effects are significant。 A dynamic analysis is therefore required and, because of the numerous non-linearities present, this must be car- ried out by direct integration of the equations of motion in the time  domain。

This paper presents results from a non-linear dynamic finite element program that has been developed to meet the above requirements。 First, the essential features of the program are introduced。 The representative jack-up model used for the parametric study is then briefly described。 Results are presented from a series of analy- ses, first using the program’s quasi-static analysis option, then using dynamic analysis。 The effects of varying wave height and period are studied   independently。

2。Non-linear analysis program

Analyses are performed using a specially developed two-dimensional, non-linear finite element  program。 This is described in detail by Thompson [1] and    Willi-

0141-0296/99/$—see front matter 1998 Elsevier Science Ltd。 All rights reserved。 PII: S 0141- 02 96 (97)00 22 2 - 8

Fig。 1。    A typical jack-up unit。

ams et al。 [2], therefore only a brief summary is given here。 The essential elements of the program are the struc- tural modelling of the rig legs, the foundation model, the representation of environmental loads and the dynamic analysis algorithms used。

Since the model is two-dimensional, certain effects cannot be taken into account。 The wave forces are assumed to be aligned with the axes of symmetry of the rig, but in any case this is usually a worst-case assump- tion。 More significantly the effect of wave direction (spread seas) is not taken into account。 Torsional dis- placement modes of the rig cannot be modelled in a 2- D analysis, but approximate analysis shows that these are expected to be much less significant than the modes of displacement studied  here。

2。1。Structural model

The structural behaviour of a jack-up is dominated by the deformations of the slender lattice legs, since the hull is comparatively rigid。 The legs act as beam-columns, due to the presence of significant axial loads。 In addition, P-A effects and shear deflections are significant。 The behaviour is therefore highly non-linear, and cannot be adequately represented by linear bending theory。 Note, however, that all the non-linearities considered here arise