Foundation

Soil shear strength (su) at mudline Rate of increase of su with depth Soil rigidity index  (G/su)

Spudcan diameter

50 kPa

2 kPa/m

100

20 m

Footing penetration under preload 5。2 m

Loading

Direction

Loaded along axis of symmetry, single leg to   windward

Mean water depth 90 m

Wave height and  period Variable — see main text for   details

Current velocity 1 m/s

Wind velocity 42 m/s

Total wind load 3。23 MN

Analysis

Timestep for dynamic  analysis

0。002 s ( = 0。1 × lowest period of linear   system)

as the sum of five harmonics, each comprising a sinus- oidal term for the velocity at the mean water level together with a hyperbolic term describing how the velo- city decays with depth。 The extended Morison equation is then used to convert the kinematics to hydrodynamic forces。 This is one of the standard deterministic approaches used for analysing wave loading on a frame with slender members。 It is suitable for modelling a sub- stantial range of wave heights in intermediate or deep waters, but breaks down in shallow water [7]。 The dis- tributed hydrodynamic forces are integrated over each finite element within the leg using 7-point Gaussian inte- gration to obtain an equivalent set of nodal    loads。

Work is in progress on extending the analysis to incor- porate random sea states using  the  New  Wave approach [8]。

2。5。Dynamic analysis

The non-linear equations of motion are solved by step- wise integration in the time domain, using the Newmark

þ = 1/4 method, in which accelerations are assumed to be constant over a timestep。 This is an implicit, uncon- ditionally stable, method that gives accurate results pro- vided a sufficiently short timestep is   used。

3。Example structure

The program described above has been used to per- form a series of structural analyses of a simplified jack- up rig。 Fig。 2 shows the model used and Table 1 sum- marises the main analysis parameters。 The number of elements in the model has deliberately been kept small, since the analyses are not intended to provide detailed design data, but to highlight some important trends in jack-up behaviour。 Sensitivity studies showed that greater discretisation would result in some quantitative changes but would not alter the qualitative meaning of the results。

The dimensions of the model were chosen after con- sideration of ‘typical’ rigs analysed by NDA [9],  Jensen

Fig。 2。    Plane finite element model of a representative   jack-up。

et al。 [10], SNAME [11], Martin [4] and Nielsen et al。 [12]。 The leg spacing in side elevation of 51。96 m rep- resents three legs positioned at the corners of an equi- lateral triangle of side 60 m in plan。 Each K-lattice leg is represented by a beam-column  passing  through the leg centroid, with equivalent stiffness and hydrodynamic properties。 In this plane model the hull is also rep- resented by a beam element, and the leg/hull connection is assumed rigid。 Non-linearities in the jack housings are not at present modelled, though it is recognised  that these can be significant。