The maximum design significant wave heights and peak periods specified by the rig

owner for operating and survival conditions are listed in Table 3.1.

Table 3.1. User Specified Wave Heights and Periods.

Load Condition Description of Waves Hs (m) Tp (s)

Survival 100-Year Hurricane 18 15

Normal Operating 10-Year storm 6.9 14.6

Hydrodynamic load calculation

Hydrodynamic loads are generated by water moving past the platform leg. Loads are made up of drag and inertial components (relative velocity and acceleration of the water) and they act over the exposed height of the platform leg.

Regular wave analysis

Wave theories yield the information on wave motion like water particles kinematics and wave speed, using the input information of wave height, its period and depth of water at the site.

Currently there are a number of wave theories that are applied in the analysis of jack-up platforms. In most cases the deterministic computations are performed using Stokes fifth order or Dean Stream function theories. In this analysis, the Stokes fifth order wave theory is applied.

Current

The current profile may be expressed as a series of velocities at certain stations from seabed to water surface. A site specific study will normally be required to define the current velocity components. When there is no site specific data available, assumptions should be made.

Figure 3.1 - Suggested current profile

The Morison’s equation

A structural member is considered to be of ‘small diameter’ when its diameter is less that about 0.15 times the wave length; for example, members of Jacket structures and piled jetties.

Figure 3-2: Wave impact

In general, wave forces on offshore structures are calculated in three different ways based on the type and size of the structure:

Diffraction theory: inertia force predominates, on large structures

Froude-Krylov theory: inertia force predominates, on small structures

Morison equation: drag force is significant, on small structures

When member diameter is small incident waves do not get much scattered by the obstruction and in that case the equation given by Morison et al.(1950) becomes applicable.

Morison et al. (1950)’s equation:

It states that the total force, in-line with the wave direction can be obtained by addition of the drag force and the inertia force, i. e.,

where,

ρ =mass density of fluid

u = flow velocity is coefficient of drag. Its value depends on body shape, roughness, flow

viscosity and several other parameters.

CD =Coefficient of Inertia. It depends on shape of the body, its surface roughness and other parameters. = in-line (horizontal) force per meter length at member axis at given time at given location.

Note that . Hence velocity and acceleration are out of phase by 90 and are not maximum at the same time.

Leg Hydrodynamic Model

General

The hydrodynamic modeling of the leg of a jack-up may be carried out by utilizing either 'detailed' or 'equivalent' techniques. In both cases the geometric orientation of the elements are accounted for. The hydrodynamic properties are then found as described below:

'Equivalent Model'

The hydrodynamic model of a bay is comprised of ‘equivalent' number of one meter diameter columns located at the geometric center of the actual leg.

Calculations have shown for smaller diameter tubular in higher waves, the wave force mainly consists of the drag contribution. In other words, the inertia force for these tubular is much smaller than the drag force.

Morison’s equation shows that the drag term is linear with respect to the diameter of a tubular. Thus it is a fair approximation to state that the wave forces on a tubular are proportional to the exposed area of the tubular.

To take into consideration of the direction of the members when calculating the total effective area of the leg, a factor is applied, whereφis the angle between the member’s axis and the wave and current direction. Hence, for a member parallel with the wave and current, the angle is 0 degree, and for a member perpendicular to the wave and current, the angle is 90 degree.

The term can be explained as follows:

(a) The normal wave particle velocity is sinφ times the actual wave particle velocity.(b) The drag force is proportional to the square of the normal wave particle velocity.(c) The resultant horizontal force is the projection of the total drag force which means

another factor sinφ.

Similarly, the inertia term should include a term to allow for oblique angles of attack. In line with the earlier force estimation, this inertia term is further disregarded.

The leg area is to be compared with the area of the standard 1.0 m diameter column and the ratio between the two is to be used as the multiplication factor.

Hydrodynamic Coefficients for Leg Members

Recommended values for hydrodynamic coefficients for tubular (<1.5m diameter) are

given in Table 4.3.

Table 4.3: Base hydrodynamic coefficients for tubulars

Note: The smooth values will normally apply above MWL + 2m and the rough values below MWL + 2m. If the jack-up has operated in deeper water and the fouled legs are not cleaned the surface should be taken as rough for wave loads above MWL + 2m.

Marine Growth

When applicable, marine growth is to be included in the hydrodynamic model by adding the appropriate marine growth thickness, to, on the boundary of each individual member below MWL + 2m. for a tubular Di= Doriginal+ 2tm. Site specific data for marine growth is preferred. If such data are not available all members below MWL + 2m shall be considered to have a marine growth thickness tm= 12.5 mm(i.e. total of 25 mm across the diameter of a tubular member). Marine growth on the teeth of elevating racks and protruding guided surfaces of chords may normally be ignored.

Hydrodynamic Coefficients for Split Tube Chords

For non-tubular geometries (e.g. leg chords) the appropriate hydrodynamic coefficients may, in lieu of more detailed information, be taken in accordance with Figures 4.4 and corresponding formulas, as appropriate.

Figure 4.4: Split tube chord and typical values for CDi

The drag coefficients for 0°are dominated by the tubular part and no particular effect of the rack on the drag coefficient is seen from the tests. That is, for typical dimensions of the tubular diameter and rack plate thickness t, D i/t >> 1.0, tests show values of about CD ≈0.65. This indicates that the drag coefficients chosen for the tubular are also valid for the split tube chord for the 0° direction. In order to be consistent with the roughness dependence of the drag coefficient for tubular, the drag coefficient in the marine growth region is increased due to roughness to CDrough= 1.0 for θ= 0°.

For the 90°direction the drag coefficient should be similar to that of a flat plate for large W/Di ratios, CDplate= 2.0. However, test results seem to indicate that the CD values for this direction referring to the mean rack width W, are, on average, about 1.8. The suggested drag coefficient is therefore set to be 1.8 for small W/Di ratios, increasing to 2.0 for large W/Di ratios. The interpolation between these two numbers is based on engineering judgment.

For the interpolation between the directions 0°and 90° a number of formulations are available, but since there were a number of test results available, a best fit of a new formulation was decided.

For a split tube chord as shown in Figure 4.4, the drag coefficient CDi related to the reference dimension Di= D+2tm, the diameter of the tubular including marine growth, may be taken as:

where;

θ = Angle in degree

CD0 = is the drag coefficient for the chord at θ= 0°and is to be taken as that of a tubular with appropriate roughness, i.e. CD0= 0.65 above MWL + 2.0m and CD0= 1.0, below MWL+2.0m. Possible dependence on KC and Re numbers as for a tubular.

CD1 = The drag coefficient for flow normal to the rack (θ= 90°), related to

the projected diameter (the rack width W). CD1 is given by

The inertia coefficient CMi= 2.0, related to the equivalent volume, may be applied for all heading angles and any roughness.

Calculation

The following parameters and assumptions are adopted for the calculation of total horizontal force and overturning moment on the leg.

Wave

Wave theory: Stokes fifth order wave theory

Wave height: H=18 m;

Wave period: T=15 s;

Water Depth: d=121.9 m;

Current

1.0 m/s, assuming uniformly distributed from MWL to 5 meter below MWL0 m/s, 5 meter below MWL to the seabed

Wave and current direction

1. Assuming in line with each other to be conservative.2. 0 degree and 45 degree of environmental heading relative to the leg was assumed

respectively.

Marine growth

Assuming 12.5 mm covering the entire leg length

Chords

Mean rack width: W=0.8934m;

Characteristic length: D=0.8124m;

Hydrodynamic coefficients for bracing members

The smooth values apply above MWL + 2m and the rough values below MWL + 2m.

Hydrodynamic coefficients for chords in leg

At 0 degree environmental heading, all 4 racks will be at rack angle 45 degrees; at 45 degree environmental heading, 2 racks will be at rack angle 0 degree and the other 2 will be at 90 degrees. The drag coefficients and inertia coefficients for chords at different rack angles are calculated and tabulated below.

Multiplication factors

Based on all the member sizes and directions, multiplication factors are calculated for bracing members and chords members for two environmental heading respectively. For chords members, the hydrodynamic force also depends on rack angles, hence multiplication factors for different set of chords with different rack angles are calculated separately. The results are illustrated in the table below.

Hydrodynamic force on unit diameter columns

Based on the assumptions made above, hydrodynamic forces under different hydrodynamic coefficient assumptions for unit diameter columns are summarized in the table below.

The total base shear and overturning moment for 1 meter diameter columns for the 4 cases above are obtained by SACS software and illustrated in the table below

Hydrodynamic force on entire leg

In combination of multiplication factors and forces on unit diameter columns, total force on the entire leg for 0 degree and 45 degree environmental headings are obtained.

Total base shear with 0 degree environmental heading: 76 kN

Total overturning moment with 0 degree environmental heading: 461912.85 kN.mTotal base shear with 45 degree environmental heading: 5108.45 kNTotal overturning moment with 45 degree environmental heading: 391343.83 kN.m