resulting in some failures。

To analyze a jack-up unit during jacking operations for safety evaluation of a proposed design under the specified conditions, the proposed control elements and gap elements are used for the connections between pin- ion and chord and the interactions between guide/wear plate and chord, respectively。 These two kinds of ele- ment are incorporated into finite element analysis with extra control techniques。

The behaviours of a jack-up system during jacking operations vary with the load and boundary conditions。 Wind load is one of the factors that affect the system seriously。 Sometimes, wind speed is extremely high on the site。 Apart from the wind load condition, another important factor is the fixity of the footings。 The seabed fixity has been measured, analyzed and discussed by Springett et al。 [7], Temperton et al。 [10] and Nelson et al。 [11] based on the instrumentation data measured on site。 Generally, the fixity of a jack-up leg would be some- where between pinned connection and fixed connection。 However, according to the research done by Hoyle et al。 [12], Langen [13] and SNAME report [14], legs may even be sliding if the penetrations of the spudcans to seabed are not desirable。 Therefore, the effects of wind load and leg fixity on the behaviours of a jack-up unit are inves- tigated。

2。Finite element (FE) model for a jack-up    unit

A full three-dimensional finite element model is built based on a practical design。 The model consists of three parts, i。e。, legs, hull and connections between the legs and the hull。 Pipe elements and beam elements are used for all members such as chords, horizontal braces and diagonal braces of the K-lattice legs。 Comparing to the stiffness of the jack-cases and the legs, the stiffness of the hull is very large。 Simplification is made for the hull, which is assumed to be always above the water level。 With consideration of both stiffness distribution and mass distribution according to the design, the hull is represented by beam elements。 The total mass of the hull

Fig。  1。 FE model of the jack-up   unit。

is about 14,000 Tonnes。 Initial distance measured from seabed to the hull is 47。4 m。 The elements proposed for the connections between legs and hull are sorted  into two types: control element and gap element。 Since the connections between pinions and chords and the inter- actions between guides/wear plates and chords are varying from time to time, a lot of these two types of element with control switch functions, which will be discussed later, are created in the  model。

To be conservative, all of the three legs are pinned for the basic simulation case。 The overall view of the FE model is displayed in Fig。 1。 Horizontal force induced by wind is assumed to act on the hull in the direction of port/starboard leg to forward leg as shown in Fig。 2。 Maximum value of the wind load is estimated up to 2200 kN according to the site   conditions。

3。Connection between pinion and  chord

There are four pinions on each chord。 Each pinion is driven by one motor。 The motor speed varies with the torsion on the pinion。 In the model, a motor is repre- sented by a transfer function of moving-up speed versus vertical reaction force of a pinion。 The vertical force and the moving-up speed are expressed as  follows:

Fig。  2。 Top view of the jack-up  unit。

In the FE model, there are four separated structural systems, i。e。, one hull and three legs。 The hull is con- nected with the legs through pinions。 Since the hull goes up along the legs during jacking, the pinions would contact different positions on the chords at  different time。 That means a pinion node should have relations with all the nodes on the corresponding chord within the jacking region。 However, at any time during jacking, one pinion node should be connected only with one node on the chord。 Unfortunately, normal FE elements cannot fulfill such requirement。 Therefore, a special type of ele- ment, namely control element, is developed to build up the relations between the pinions and their correspond- ing chords。 Although a lot of control elements will be generated between one pinion node and all the nodes on the corresponding chord within jacking region, only one element will be activated by elevation control at any specific time。