Since the hull is moving-up, friction also exists when a gap force occurs。 The friction force is calculated   by

Ffriction  ¼ lFGAP ð6Þin which, l is the friction coefficient。

(a)Schematic configuration of gap element

Chord(b)Applying friction

Fig。 5。 Gap element used for guides, wear plates and horizontal effect of pinions。

and the force on the guide/wear plate node   is

Fdown  ¼ —Ffriction ð8Þ

Along each chord, gap elements are created between the nodes for the corresponding guides/wear plates and the nodes on the chord within the jacking region。 To con- sider the horizontal effect of pinions, gap elements are also created for the pinions。 The only difference is that the friction force in the vertical direction will not be applied for pinions anymore。 Different from control ele- ments, all gap elements are set inactive with a large gap distance before simulation at each time step。 Afterwards, the active gap elements are determined by comparing the jacked up distances and the elevation level of neigh- bouring nodes on the chord and then activated by set- ting real gap distances。 Real gap distances of 0, 5, 13 and 38 mm are used for pinions, upper guides, lower guides and wear plates, respectively。

5。Numerical investigation  on jacking  procedure

5。1。Simulation method

According to the practical jacking operations, simu- lation procedures are proposed and described as follows。 Firstly, the whole model is pre-stressed by self-weight of the structure and external forces, i。e。, wind loads, if ex- isting。 Thereafter, the hull is jacked up step by step until the end of the time。 The time step is determined auto- matically。 For each step, vertical reaction forces Fv are taken out to calculate the moving-up speeds of the corresponding pinions based on the force–speed curve。 The displacements of the pinion nodes are then ob- tained。 Afterwards, the pinions are jacked up by dis- placement control on the dummy control nodes。 Active control elements are determined automatically with switch-on parameters。 By comparing the current eleva- tion level of nodes on the chords with the jacked up distance, a set of corresponding gap elements are acti- vated。 The structure is then analyzed。 In order to per- form the analysis smoothly, a control program  is built for this jacking operation   procedure。

5。2。Basic  case study

To verify the proposed method, a basic case simula- tion is carried out。 Three legs are all pinned at the ends。 Total horizontal wind load being applied is 1100 kN, which is equal to the value in the practical design to

estimate the maximum RPD value using empirical method。 To jack the hull up from water level to its de- signed elevation, duration of the jacking operations is about 1800 s。 Positions of the hull being lifted up along the legs for five selected time steps are shown in Fig。 6。 Due to the horizontal loads, large vertical forces and bending moments could be generated in the legs。 The bending moment is resisted by the hull either through couples of horizontal forces going through the leg guides/wear plates or through couples of vertical forces going through the pinions。 The systems under the above mentioned two conditions are normally called as floating

jacking system and fix jacking system, respectively。

Various behaviours of the jack-up unit can be mon- itored during the whole jacking process。 From the sim- ulation results, the whole jacking process can be pided into four stages。 As shown in Fig。 7, the maximum  RPD

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